Control of perfusion flow bioprocess

Abstract

A method for controlling a perfusion biological process is described, the method comprising: controlling a value of one or more controlled variables using one or more control loops, the value of the one or more controlled variables is selected from the group consisting of the number or density of living cells in the bioreactor, the volume of culture in the bioreactor, and the concentration of one or more metabolites in the bioreactor, each control loop for controlling a non-overlapping subset of the controlled variables by setting the value of the one or more manipulated variables, the one or more manipulated variables are selected from the group consisting of a feed flow rate, a discharge flow rate, and a permeate flow rate, where at least one of the control loops uses a controller, the controller uses predictions of values of a subset of controlled variables from a dynamic model of the biological process describing a rate of change of the values of the one or more controlled variables to identify values of one or more manipulated variables that optimize the control target. A system implementing such a method, a computer readable medium, and a method for providing a tool for implementing such a method are also provided.

Description

Technical Field

[0001] The present disclosure relates to computer-implemented methods, computer programs, and systems for controlling a perfusion flow bioprocess. Certain methods, programs, and systems of the present disclosure use a state-space model within a controller to determine adjustments to manipulated variables that maintain process stability. Background Art

[0002] Bioprocesses use biological systems to produce specific biological materials, such as biomolecules with therapeutic effects. The process generally involves placing cells and / or microorganisms in a bioreactor with a culture medium containing nutrients under controlled atmospheric conditions. The culture medium is consumed by the cells and used for growth and other metabolic functions, including the production of specific biological materials and byproducts.

[0003] Perfusion operation mode, in which fresh media is continuously added to the bioreactor and spent media is continuously removed to maintain a constant working volume while retaining cells in the bioreactor, is becoming increasingly popular for upstream processes and in the production phase. Indeed, such an operation mode enables the maintenance of high viable cell concentrations for long periods of time. However, stable and reliable process performance in terms of cell growth and productivity of a bioprocess critically depends on precise and robust control of the process throughout its duration, including at least ensuring an adequate supply of nutrients.

[0004] A simple method commonly used to control such processes is to control the feed flow rate to maintain a predetermined ratio of the feed flow rate to the viable cell density (VCD) (also known as the viable cell concentration (VCC)). This is generally referred to as "cell specific perfusion rate" (CSPR) control. This control strategy can be implemented as an off-line approach, in which the feed flow rate is updated based on an off-line VCD measurement or based on a predicted VCD of the current growth rate derived from an off-line measurement. This control strategy can also be implemented as an on-line approach, in which an online biomass sensor allows the VCD to be permanently measured during the process. This value can then be used to adjust the feed flow rate accordingly, thereby ensuring true online cell-specific perfusion rate (CSPR) control. The main disadvantage of these methods is that CSPR control requires empirical knowledge of the relationship between the cell culture medium used and the cultured organism / cell line, i.e., the identification of key CSPRs. Therefore, the implementation of these methods is time-consuming and laborious, and, for example, when perfusion culture is performed with different cell lines, organisms, and culture media, it is usually not directly transferable to other production platforms. Furthermore, because the feed to biomass ratio is kept constant throughout the process, this approach cannot capture potential physiological and metabolic changes in long-term cultures, for example due to genetic drift.

[0005]

[0006] Therefore, there is a need for systems and methods for improved control of perfusion flow bioreactors without all of the disadvantages of the prior art. Summary of the invention

[0006] According to a first aspect of the present disclosure, there is provided a method for controlling a bioprocess comprising cell culture in a bioreactor, the method comprising the following steps: using one or more control loops to control the value of one or more controlled variables, the one or more controlled variables being selected from the number or density of viable cells in the bioreactor, the volume of the culture in the bioreactor, and the concentration of one or more metabolites in the bioreactor, the values ​​of the one or more controlled variables being used to control a non-overlapping subset of the controlled variables by setting the value of one or more manipulated variables, the one or more manipulated variables being selected from the feed flow rate, the bleed flow rate, and the permeate flow rate, wherein at least one of the control loops uses a controller, the controller using a prediction of the value of the set of controlled variables to identify the value of the one or more manipulated variables that optimizes the control objective, the prediction of the value of the subset of controlled variables being derived from a dynamic model of the bioprocess describing the rate of change of the one or more controlled variables. The method according to this aspect comprises receiving a measurement of the value of the one or more controlled variables or a measurement from which the value of the one or more controlled variables can be derived, and before predicting a state trajectory of the bioprocess, using the measurement or an estimate of the value derived from the measurement to automatically update the value of one or more terms of the dynamic model of the bioprocess.

[0007] The method of the first aspect may have any one or any combination of the following optional features.

[0008] The dynamic model of the biological process can be referred to as a "state space model". Such a controller can be referred to as a "model predictive controller" (MPC). One or more metabolites can be substrates. Unless otherwise specified, the concentration (of metabolites or cells) refers to the concentration in the bulk fluid. The method can be repeated each time a new measurement is received. A state observer can be used to obtain an estimate of (multiple) values. The method can include updating the values ​​of one or more terms of the dynamic model of the biological process selected from cell growth rate and substrate uptake rate. The state observer can also include a dynamic model of the biological process that describes the rate of change of one or more controlled variables. The dynamic model of the biological process used by the state observer can be the same model used by the controller.

[0009] The dynamic model may include one or more equations describing changes in the number and / or density of live cells (kinetic growth model) and / or changes in the concentration of one or more metabolites (e.g., substrates) in the bioreactor and / or changes in the volume of the culture in the bioreactor. The values ​​of one or more terms of the updated dynamic model of the biological process may include the effective growth rate of the cells (also referred to as "growth rate" or "cell growth rate" - strictly speaking, this can be the effective growth rate (e.g., in equation (11)), or the growth rate that combines growth and death (e.g., in equation (26))) and / or the substrate uptake rate (this can be the cell-specific substrate uptake rate (substrate uptake rate) (e.g., in equations (25), (25a), (25b)), or the coefficient that combines the live cell density and the cell-specific substrate uptake rate (e.g., in equation (9) or (9a))). The coefficients may be updated by estimating the values ​​of the coefficients as state variables of the state-space model (e.g., by integrating the state-space model in a pseudo-steady state). Thus, the method may include estimating, by the state observer, values ​​of one or more terms of the state-space model, and predicting, by the controller, a trajectory of the biological process using the estimates of the one or more coefficients using the dynamic model.

[0010] In an embodiment, a state observer may use a model that describes changes in substrate concentration and may receive measurements of substrate concentration. The state observer may use these measurements and models to provide estimates of current values ​​of one or more state variables (including substrate concentration) and one or more coefficients of the model (e.g., substrate uptake rate), which the controller uses to predict values ​​of VCD and substrate concentration using a dynamic model of the biological process and one or more candidate values ​​of manipulated variables (e.g., values ​​of feed flow), where the manipulated variables may represent inputs to the state-space model. The predictions may be evaluated using control objectives to identify an optimal control strategy.

[0011] In an embodiment, a state observer may use a model describing changes in cell density and substrate concentration, and may receive measurements of viable cell density and substrate concentration. The state observer may use these measurements and models to provide estimates of current values ​​of one or more state variables (including VCD and substrate concentration) and one or more coefficients of the model (e.g., growth rate and / or substrate uptake rate), and the controller may use these estimates to predict the values ​​of VCD and substrate concentration using a dynamic model of the bioprocess and one or more candidate values ​​of the manipulated variables (e.g., values ​​of feed flow, effluent flow, and permeate flow), wherein the manipulated variables may represent inputs to the state space model. The predictions may be evaluated using control objectives to identify an optimal control strategy.

[0012] In an embodiment, a state observer may use a model that describes changes in cell density and volume, and may receive measurements of viable cell density and volume. The state observer may use these measurements and models to provide current values ​​of one or more state variables (including VCD and volume) and estimates of one or more coefficients of the model (e.g., growth rate), and the controller may use these estimates to predict the values ​​of VCD and volume using a dynamic model of the bioprocess and one or more candidate values ​​of manipulated variables (e.g., values ​​of feed flow, effluent flow, and permeate flow), where the manipulated variables may represent inputs to the state-space model. The predictions may be evaluated using a control objective to identify an optimal control strategy.

[0013] In an embodiment, a state observer may use a model describing changes in cell density, substrate concentration, and volume, and may receive measurements of viable cell density, substrate concentration, and volume. The state observer may use these measurements and models to provide estimates of current values ​​of one or more state variables (including VCD, substrate concentration, and volume) and one or more coefficients of the model (e.g., growth rate and substrate uptake rate), which are used by the controller to predict the values ​​of VCD, substrate concentration, and volume using a dynamic model of the bioprocess and one or more candidate values ​​of the manipulated variables (e.g., values ​​of feed stream, effluent stream, and permeate stream), wherein the manipulated variables may represent inputs to the state-space model. The predictions may be evaluated using control objectives to identify optimal control strategies.

[0014] The state observer and / or the models used in the MPC can be automatically updated using measurements from the biological process.

[0015] Automatically updating the values ​​of one or more items of the dynamic model can include comparing the measurement or estimate of the state variables of the model derived from the measurement with the corresponding prediction of the dynamic model, and adjusting the values ​​of one or more parameters of the model to reduce (or minimize) the difference between the measurement or estimate of the state variables of the model derived from the measurement and the corresponding prediction of the dynamic model. In the context of control of perfusion bioprocesses, the use of an automatically updated dynamic model is very advantageous because it improves the stability of the controlled bioprocess by more accurately reflecting the evolving behavior of the bioprocess. This is particularly relevant in perfusion bioprocesses because these processes can be carried out for extended periods of time during which any physiological characteristics of the cells and / or physical parameters of the bioprocess can change. The automatic updating of the model enables the model to remain simple while taking into account such changes, without the need to use more complex models to explicitly simulate phenomena associated with such changes. As a specific example, when the infection process affects the growth rate, a bioprocess involving infection of cells with a virus can be effectively operated at a varying growth rate. Enabling a kinetic growth model (used as a dynamic model of a biological process) to automatically update to changing effective growth rates during process operation is a simple way to account for this, thereby ensuring that the model accurately predicts the internal state of the system throughout the biological process and is therefore able to determine appropriate control actions. Failure to do so may lead to undesirable cycles in control actions as the controller may overestimate the control action to be taken. This is simpler than using a kinetic growth model that explicitly accounts for the effects of viral infection on cell growth kinetics. The advantages in simplicity translate directly into increased robustness, increased ease of use (because fewer parameters need to be calibrated), and increased transferability of the control approach (because the model is applicable to a variety of situations).

[0016] The value of controlling one or more controlled variables can include controlling the value of the following: the number or density of viable cells in the bioreactor, the volume of the culture in the bioreactor, and the concentration of one or more metabolites in the bioreactor. The value of controlling one or more controlled variables can include setting the value of the following: feed flow rate, discharge flow rate, and permeate flow rate. One or more metabolites can be substrates, such as glucose. This can be used as a control target alone or in combination with a medium exchange rate. Therefore, the control target can include a penalty (penalise) for the deviation from the target of one or more substrates and / or the target of the medium exchange rate. This can improve the stability of the bioprocess by ensuring that a sufficient amount of nutrients are provided to cells during the entire operation of the bioprocess, while reducing the potential waste of nutrients caused by the excessively high medium exchange rate.

[0017] The control objective can be an expression that penalizes the difference between the prediction of the value of a subset of the controlled variables and the corresponding predetermined target value, and the change in the value of one or more manipulated variables. The control objective can be an expression that includes any one or more terms of equations (1), (6), (7), or (8) (or equations derived from the above equations, such as equations (1a) to (1f), (6a) to (6e), (7a) to (7e), (8a) to (8e)). For example, when the control loop controls the concentration of a metabolite by manipulating a feed flow, the control objective can include only terms related to the metabolite concentration and the feed flow in equation (1). Using a control objective that penalizes changes in the value of one or more manipulated variables improves the stability or controlled process compared to methods using conventional controllers. In other words, one of the goals of the model predictive controller is to maximize stability (minimize changes in the value of the manipulated variables). This is in contrast to conventional methods of controlling perfusion flow bioprocesses, in which the process is controlled by making active adjustments to keep the VCD and / or medium exchange ratio as close to predetermined targets as possible to meet those goals.

[0018] The control objective can be used to more strongly penalize the change of the value of one or more manipulated variables than the difference between the prediction of the value of a subset of controlled variables and the corresponding predetermined target value. The control objective can be used to give priority to the stability of the manipulated variable rather than approaching the predetermined target value. The control objective can at least equally (or approximately equally) weight the term of the change of the value of one or more manipulated variables and the term of the difference between the prediction of the value of a subset of controlled variables and the corresponding predetermined target value. In other words, the control objective can be used to make the controller select smooth control actions / make slow gradual adjustments to gradually drift the bioprocess to one or more target values ​​of the controlled variables. Therefore, the control objective can be calibrated to give the controller freedom to deviate from the set point so as to make a slow adjustment that gradually drifts to the set point. This is in contrast to conventional models, in which some variables, such as the liquid volume in the bioreactor, are actively controlled. Because cells usually perform better in a stable environment (in terms of, for example, growth, productivity, etc.), smooth / progressive input actions may be beneficial to cell culture.

[0019] The control objective may include at least one term that penalizes a predicted value of a controlled variable that is below a predetermined first threshold. If the predicted value is below the predetermined first threshold, the term that penalizes the predicted value of the controlled variable that is below the predetermined first threshold may penalize the difference between the predicted value of the controlled variable and the predetermined first threshold. The control objective may include at least one term that penalizes a predicted value of a controlled variable that is above a predetermined second threshold. If the predicted value is above the predetermined second threshold, the term that penalizes the predicted value of the controlled variable that is above the predetermined second threshold may penalize the difference between the predicted value of the controlled variable and the predetermined second threshold. Thus, the objective function may be used to include constraints applied to thresholds (i.e., values ​​that the controlled variable is preferably not above / below), such as where a stronger control action can be taken, and constraints applied to targets (i.e., values ​​that the controlled variable is ideally close to). The control objective may weight terms that penalize predicted values ​​of the controlled variable that are below / above the corresponding threshold, rather than weighting terms that penalize the difference between the predicted value of the controlled variable and the corresponding predetermined target. This may result in hard and soft constraints, where the controller may choose a larger control action to avoid the first type of penalty rather than avoiding the second type of penalty. This may be useful, for example, where physical constraints are such that some values ​​of the controlled variable will be detrimental to the biological process. For example, when using volume as the controlled variable, it may be advantageous to allow fine adjustments to the volume around the target, and to select more drastic control actions to control the volume (e.g., to avoid overflow) if the maximum volume is predicted to be exceeded. The control target may be an expression that includes any one or more of equation (7). For example, when the control loop controls the concentration of a metabolite by manipulating a feed stream, the control target may include only the terms in equation (7) that are related to the concentrations of the metabolite and the feed stream.

[0020] One or more controlled variables may include viable cell density, and the control target may use the corresponding total number of cells instead of viable cell density as the control variable. Instead of penalizing the difference between the predicted value of the viable cell density in the biological process and the corresponding predetermined target value or in addition to penalizing the difference between the predicted value of the viable cell density in the biological process and the corresponding predetermined target value, the control target may include a term that penalizes the difference between the predicted value of the total number of cells in the biological process and the corresponding predetermined target value. The control target may be an expression including any one or more terms of equation (6). The control target may include a term that penalizes the predicted value of the total number of cells below a predetermined first threshold, and / or a term that penalizes the predicted value of the total number of cells above a predetermined second threshold. The first and / or second thresholds and / or predetermined target values ​​may be determined from a threshold / target value of viable cell density using a measurement, set value, estimate or predicted value for culture volume when predicting.

[0021] The method may include using a state observer to provide an estimate of the value of the one or more state variables of the biological process using one or more measurements of the state variables of the biological process and a dynamic model of the biological process that describes the rate of change of the state variables, the one or more state variables of the biological process including one or more controlled variables. The state observer may provide the estimate of the value of the one or more state variables of the biological process using multiple measurements of at least one of the state variables of the process, wherein the multiple measurements include a first measurement and a second measurement, wherein the first measurement is obtained more frequently than the second measurement. The state observer may provide the estimate of the value of the one or more state variables of the biological process using measurements obtained with a time delay, and wherein the state observer provides the estimate of the value of the one or more state variables of the biological process that accounts for the time delay. The one or more state variables may include at least one variable selected from the following: the consumption rate of the substrate, the production rate of the product, the specific transport rate of the metabolite (wherein the metabolite can be a substrate or a product), the bulk fluid concentration of the metabolite (wherein the metabolite can be a substrate or a product), the bulk fluid concentration of the biological material that accumulates in the culture as a result of cell growth and inhibits cell growth, the live cell density, the dead cell density, the total cell density, the cell viability, the effective growth rate of the cells, the death rate of the cells, and the lysed cell density. The one or more state variables may include any variable of the dynamic model of the biological process that describes the evolution of one or more of the controlled variables. For example, the one or more state variables may include any one or more of the variables of equations (9) to (10) and (25) and their equivalents. In addition to the one or more state variables as controlled variables, the dynamic model may also include one or more other state variables. For example, a dynamic model including an equation describing the rate of change of the concentration of the substrate in the bulk fluid may have a state variable as the concentration of the substrate in the bulk fluid and a state variable as the consumption rate of the substrate. The consumption rate of the substrate may represent the consumption of cells in the biological process and any losses through the harvest and / or discharge streams. The dynamic model used in the controller and the state observer may be the same model. The state observer may use multiple measurements of at least one of the state variables of the process, wherein the multiple measurements include a first measurement and a second measurement, wherein the first measurement is obtained more frequently than the second measurement. For example, the state observer may use the latest value of the first measurement and the second measurement, wherein the latest value of the second measurement may be the same value for multiple iterations, and the latest value of the first measurement may be different in each iteration of the control method. For example, the first measurement may be obtained using an online sensor, and the second measurement may be obtained using an offline sensor.

[0022] The method may include identifying one or more values ​​of one or more manipulated variables that minimize a control objective over a period of time, and controlling a biological process to use one of the one or more values ​​for each of the one or more manipulated variables. A controller that identifies the values ​​of one or more manipulated variables that optimize the control objective may control two or more controlled variables using a prediction of the values ​​of a subset of controlled variables from a dynamic model of a biological process that describes the rate of change of two or more controlled variables together, and a measurement of the values ​​of two or more controlled variables or an estimate of the values ​​of the variables obtained from the measurement. An MPC that uses a joint prediction of two controlled variables and a measurement-based regulation process of these two variables may be superior to independent control of controlled variables because this control method is more robust to failures of the measurement system used to measure any one of the two variables. This may be particularly advantageous when one of the measurements is difficult to obtain or available using a sensor system that is prone to failure. For example, the measurement of substrates / metabolites may be more difficult to obtain than the measurement of viable cell density. Therefore, as described herein, combining the regulation of substrates / metabolites with the regulation of VCD may improve the robustness of the substrate / metabolite regulation process.

[0023] Identifying the value of one or more manipulated variables that optimize the control target can include using a dynamic model of the bioprocess to predict the state trajectory of the bioprocess using one or more candidate values ​​of one or more manipulated variables. This can be performed by finding the value of one or more state space variables representing the solution of the dynamic model at one or more future time points. Identifying the value of one or more manipulated variables that optimize the control target can include using the prediction of the value of a subset of the controlled variables in the state trajectory as the variable of the control target. The method can include selecting and comparing candidate values ​​using an optimization algorithm. The state observer can be a Kalman filter, a Luenberg observer, or a moving horizon estimation. Controlled variables can include viable cell density, the volume and concentration of one or more metabolites. Manipulated variables can include feed flow rate, permeate flow rate, and discharge flow rate. The one or more control loops may include: a control loop using a controller that uses predictions of values ​​of a subset of controlled variables from a dynamic model of the biological process that describes the rate of change of the one or more controlled variables to identify values ​​of one or more manipulated variables that optimize a control objective; and one or more other control loops, optionally wherein the one or more other control loops do not use the dynamic model of the biological process, and / or wherein the one or more other control loops use a controller selected from a proportional controller, a proportional-integral controller, and a proportional-integral-derivative controller.

[0024] The manipulated variable may include a permeate flow rate, and the control objective may include a term that penalizes a difference between a candidate permeate flow rate and a corresponding predetermined target value, a term that penalizes a candidate value of a permeate flow rate that is below a predetermined first threshold, and / or a term that penalizes a candidate value of a permeate flow rate that is above a predetermined second threshold. The control objective may include a term that penalizes a difference between a candidate medium exchange rate and a corresponding predetermined target value, a term that penalizes a candidate value of a medium exchange rate that is below a predetermined first threshold, and / or a term that penalizes a candidate value of a medium exchange rate that is above a predetermined second threshold. The control objective may be an expression that includes any one or more of equation (8).

[0025] The controller uses predictions of values ​​of a subset of controlled variables from a dynamic model of the bioprocess describing the rate of change of one or more controlled variables, the subset of controlled variables controlled by the control loop using the controller includes: (i) concentration of one or more substrates, and / or (ii) volume and viable cell density, optionally wherein the values ​​of the one or more manipulated variables include permeate flow rate, bleed flow rate, and feed flow rate. When the subset of controlled variables includes the concentration of one or more substrates, the one or more manipulated variables may include feed flow rate. The one or more control loops may also include a control loop that uses permeate flow rate as a manipulated variable to control volume as a controlled variable, and a control loop that uses bleed flow rate as a manipulated variable to control viable cell density as a controlled variable, the control loop optionally using a control loop of a P, PI, or PID controller, control loop.

[0026] The method may also include obtaining measurements of one or more controlled variables or variables from which one or more controlled variables can be derived. The method may also include repeating the control method at one or more time points during the operation of the bioprocess to determine the corresponding values ​​of one or more manipulated variables. The method may also include repeating the control method at regular intervals during the operation of the bioprocess to determine the corresponding values ​​of one or more manipulated variables. The method may also include receiving a set of measurements of one or more controlled variables or variables from which one or more controlled variables can be derived, and using one or more controller loops and measurements to determine the value of the manipulated variable, optionally, wherein the determination step is repeated each time a new set of measurements is received. The method may also include providing a set of values ​​of the manipulated variables determined by one or more control loops to a user, a user interface, a computer, or an actuator. The method may also include providing a signal to a control unit, the signal being used to control one or more effectors to set the value of one or more manipulated variables according to the value determined by the one or more control loops. The method may further include receiving, optionally via a user interface, values ​​of one or more parameters of the controller from a computer device, a data store, or a user, optionally wherein the parameters include parameters selected from the group consisting of: one or more predetermined targets for one or more controlled variables (e.g., set points for one or more controlled variables; one or more of the predetermined targets may be variable during the course of the bioprocess, i.e., a different set point may be provided for each of a plurality of time points in the bioprocess), one or more parameters of the bioprocess (e.g., parameters related to a physical configuration of the bioprocess, a physical constraint of the bioprocess, a property of the cell culture, temperature, etc.), one or more parameters of a dynamic model of the bioprocess (e.g., coefficients, initial values, etc.), ), one or more predetermined thresholds for one or more controlled variables (e.g., a low threshold / high threshold with a penalty included in the objective function when below the low threshold / above the high threshold), selection of one or more controlled variables, selection of one or more manipulated variables, values ​​of one or more parameters of the control objective (e.g., values ​​of weights applied to any term of the control objective), and selection of a state observer model (e.g., a Kalman filter, a moving range estimator, a specific cost function of the moving range estimator, a dynamic model of the biological process to be used by the state observer, one or more parameters of the state observer, such as a gain of the Kalman filter, etc.), a time period for integration of the dynamic model of the biological process, and an iteration frequency of the control method. The method may also include providing, via a user interface, to a computing device, a data store, or a user, a prediction of the value of one or more states of the biological process determined by integrating the dynamic model of the biological process. In other words, the control method may be iterative.

[0027] The method may also include selecting the value of one or more parameters selected from the following: parameters of a dynamic model used by a controller and / or a state observer, parameters of a state observer, and parameters of a control target, using a simulation of the state trajectory of a biological process to model the response of the biological process to a control action selected by a controller. The method for simulating the state trajectory of a biological process may be as described in WO2021 / 165495. The value of the selected parameter may include comparing the state trajectory of the biological process and the control action selected by the controlled person using a first set of parameters and a second set of parameters (optionally using different sets of initial conditions), and optionally selecting a parameter set that performs best in terms of the stability of the model and the compliance with the control target under multiple initial conditions (i.e., a parameter set that produces a robust model). The inventors have found that the control method described herein is generally very robust and does not require recalibration of the model and the controller at each use, especially when the model is automatically updated as described above. In particular, the weight of the control target (a parameter that weights the relative importance of different items of the control target) can be set to ensure stability in a tested or simulated biological process, and for any other biological process without modification. In particular, all weights of the control target can be set to 1. Alternatively, the control objective may weight the term that penalizes the change in the value of one or more manipulated variables at least two, five, ten, or one hundred times more than the term that penalizes the difference between the prediction of the value of a subset of the controlled variables and the corresponding predetermined target value. For example, the term that penalizes the change in the value of one or more manipulated variables may be set to a weight of 2, 5, 10, or 100, and the term that penalizes the difference between the prediction of the value of a subset of the controlled variables and the corresponding predetermined target value may be set to a weight of 1. The control objective may include quadratic terms. All terms of the control objective may be quadratic. The dynamic model of the bioprocess may include one or more material balance equations. Material balance equations may be used to describe the rate of change of volume and / or the rate of change of concentration of one or more metabolites in a bioreactor. For example, for each of the one or more metabolites, the dynamic model may include an equation of the form given by Equation (25) or Equation (9).

[0028] The dynamic model may include one or more equations of a kinetic growth model. The kinetic growth model may include a viable cell density x representing the cell culture. v , dead cell density x d , total cell density x t and lysed cell density x lOne or more equations for the change of one or more of as a function of time. The kinetic growth model may include a Monod kinetic model or a saturation kinetic model. The kinetic growth model can be used to estimate the growth of microbial cells as a function of time. For example, any one or all of equations (11) to (14) or equations derived therefrom can be used. For example, these derived equations can be derived in the following manner: replacing one or more terms in equations (11) to (13) with corresponding terms derived from equation (14), removing one or more terms in any of equations (11) to (14) based on corresponding assumptions (e.g., assuming that a particular flow does not exist), or adding one or more terms in any of equations (11) to (14) based on corresponding assumptions (e.g., assuming that an additional flow exists). In equations (11) to (13), the term μ eff and / or μ d Any of equations (15) to (24) may be used for modeling. The material balance model may include one or more equations representing the changes in volumetric concentration of one or more metabolites in the bioreactor.

[0029] The bulk fluid concentration of metabolites can be obtained using a material balance equation (e.g., equation (25) or its equivalent). The viable cell density can be obtained using equation (11) or its equivalent. Cell viability can be obtained using equations (11) to (14) or their equivalents (ratio of viable cell density to total cell density). Dead cell density can be obtained using equation (12) or its equivalent. Lysed cell density can be obtained using equation (13) or its equivalent. The bulk fluid concentration of biological materials that accumulate in the culture and inhibit cell growth as a result of cell growth can be obtained using equation (16) or its equivalent. The bulk fluid concentration of products can be obtained using a material balance equation (e.g., equation (25) or its equivalent). The effective growth rate can be obtained using equation (22) or its equivalent. The death rate can be obtained using equation (15) or its equivalent. Equivalents of the provided equations can refer to equations that obtain the same process but differ due to one or more underlying model assumptions.

[0030] Obtaining the values ​​of one or more state variables of a dynamic model (also referred to as a "state-space model") of a biological process at one or more time points may include predicting the state trajectory of the biological process using the state-space model. Predicting the state trajectory of a biological process using the state-space model may include finding the values ​​of one or more state-space variables representing the solution of the state-space model at one or more maturity levels. In other words, obtaining the values ​​of one or more state variables of the state-space model or variables derived therefrom at one or more time points may include solving the state-space model at one or more time points, such as by integrating together to form one or more equations of the model, or using any other suitable method depending on the model, such as stochastic simulation. The state of a process may include the values ​​of any variable in such a model, such as the values ​​of one or more cell culture state variables (e.g., live cell density, dead cell density, lysed cell density, or total cell density), the volume of the culture, and / or metabolite concentration. The state trajectory of a process may include the values ​​of state variables at multiple time points. Therefore, the concentration of metabolite i (or any other controlled variable that can be measured to provide feedback to a controller) may be considered as the output of the biological process (where the input is a manipulated variable) and the state variable of the state-space model. Predicting the state trajectory of a biological process using a state-space model may include determining the values ​​of one or more state-space variables at a single time point or multiple time points. In other words, the trajectory may include the values ​​of a set of state variables at a single point in time. According to a second aspect, there is provided a method for controlling a bioprocess comprising cell culture in a bioreactor, wherein the bioprocess is operated as a perfusion bioprocess, the method comprising: controlling the values ​​of a plurality of controlled variables using one or more control loops, the plurality of controlled variables being selected from the group consisting of the number or density of viable cells in the bioreactor, the volume of the culture in the bioreactor, and the concentration of one or more metabolites in the bioreactor, the control loops each being used to control a non-overlapping subset of the controlled variables by setting the value of one or more manipulated variables selected from the group consisting of a feed flow rate, a bleed flow rate, and a permeate flow rate, wherein at least one of the control loops uses a controller that jointly controls the plurality of controlled variables (which may be referred to as a "predictive controller"), wherein the controller is used to identify the values ​​of the plurality of manipulated variables that optimize the control objective using predictions of the values ​​of the subset of controlled variables from a dynamic model of the bioprocess describing the rate of change of the one or more controlled variables. In other words, the subset of controlled variables controlled by the predictive controller may include two or more of the following: the number or density of viable cells in the bioreactor, the volume of the culture in the bioreactor, and the concentration of one or more metabolites in the bioreactor. The method according to this aspect may have any features disclosed in combination with the first aspect. The method according to this aspect may also have any one or any combination of the following optional features.

[0031] The multiple controlled variables controlled by the predictive controller may include: the number or density of viable cells in the bioreactor, and the volume of the culture in the bioreactor. The manipulated variables used by the predictive controller may include the feed flow, the bleed flow, and the harvest / permeate flow. The multiple controlled variables controlled by the above-mentioned predictive controller may include: the number or density of viable cells in the bioreactor, and the concentration of at least one metabolite (preferably a substrate, such as glucose) in the bioreactor. The manipulated variables used by the predictive controller may include the feed flow, the bleed flow, and the harvest / permeate flow. The multiple controlled variables controlled by the predictive controller may include: the number or density of viable cells in the bioreactor, the volume of the culture in the bioreactor, and the concentration of at least one metabolite (preferably a substrate, such as glucose) in the bioreactor. The manipulated variables used by the predictive controller may include the feed flow, the bleed flow, and the harvest / permeate flow.

[0032] Unless the context indicates otherwise, all steps of the methods described herein are computer-implemented. In particular, any step of the method may be implemented by a computing device, optionally a computing device in operative communication with one or more sensors, other computing devices, and / or a user interface.

[0033] According to a third aspect, a system for controlling a biological process is provided, the system comprising: at least one processor; at least one non-transitory computer-readable medium containing instructions, when executed by the at least one processor, the instructions cause the at least one processor to perform operations, the operations comprising: steps of any method of any of the aforementioned aspects. Specifically, the at least one non-transitory computer-readable medium may contain instructions, when executed by the at least one processor, the instructions cause the at least one processor to perform operations including any operations described with respect to the first aspect and the second aspect.

[0034] According to another aspect, there is provided a non-transitory computer readable medium comprising instructions which, when executed by at least one processor, cause the at least one processor to perform a method of any embodiment of any aspect described herein.

[0035] According to another aspect, there is provided a computer program comprising codes which, when executed on a computer, cause the computer to perform the method of any embodiment of any aspect described herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Embodiments of the present disclosure will now be described by way of example with reference to the accompanying drawings, in which:

[0037] Figure 1 A simplified process diagram showing a general biological process according to an embodiment of the present disclosure;

[0038] Figure 2The logical flow of an embodiment of the control method according to the present disclosure is schematically shown;

[0039] FIG3 illustrates the effects of selected parameters on variables of a kinetic growth model according to an embodiment of the present disclosure; Figure 3A is a graph showing the value of the correction factor (y-axis) for the parameter θ i,n = θ , which captures the effect of a growth inhibitory variable on growth rate as a function of the value of the growth inhibitory variable (x-axis, e.g., the concentration of a cytostatic metabolite). In this example, the parameter θ i,n Represents the variable z n An approximate value of , above which the variable begins to inhibit growth; Figure 3B is a graph showing the value of the correction factor (y-axis), for the parameter θ s,n = θ , which captures the effect of a substrate-limiting variable on growth rate as a function of the value of the substrate-limiting variable (x-axis, e.g., concentration of a metabolite such as a nutrient). In this example, the parameter θ s,n Represents the variable z n The approximate value of , below which the growth starts to be restricted;

[0040] FIG4 illustrates the effects of selected parameters on variables of a kinetic growth model according to an embodiment of the present disclosure; Figure 4A and Figure 4B is a graph showing the value of the correction factor (y-axis) for μ q,n The fixed value (D) of the parameter θ q,n Three exemplary values ​​of and θ q,n The fixed value (C) of the parameter μ q,n = θ , which captures the effect of a variable with a quadratic effect on growth as a function of the value of the quadratic effect variable (x-axis, e.g., temperature, pH), where, in these examples, the parameter θ q,n represents the spread of the effect, parameter μ q,n represents the value at which maximum growth occurs;

[0041] Figure 5 A system according to an embodiment of the present disclosure is schematically shown;

[0042] Figure 6 Schematically illustrates an example of a control system and algorithm (advance predictive control (viable cell concentration, APC)) for controlling glucose and viable cell concentration (VCC) in a perfusion flow bioprocess according to the present disclosure;

[0043] Figure 7 shows the use of Figure 6Results of a system controlling a perfusion flow bioreactor with constant glucose and two different VCC set points. Fig. 7A , offline VCC and online VCC, discharge set point and viability profile. Figure 7B , offline and online values ​​of glucose concentration, Kalman filter (KF) estimation and glucose target. Figure 7C , Glucose uptake rate derived from the APC algorithm during the experiment. Fig.7D , the perfusion rate, i.e., the feed flow rate, is controlled by an advanced predictive control algorithm during the culture process.

[0044] Figure 8 shows the use of Figure 6 Results of a system controlling a perfusion flow bioreactor where two different glucose set points were applied to one VCC set point. Fig. 8A , offline VCC and online VCC, discharge set point and activity profile. Figure 8B , offline and online values ​​of glucose concentration, Kalman filter (KF) estimation, and glucose target. Figure 8C , Glucose uptake rate derived from the APC algorithm during the experiment. Fig.8D , the perfusion rate, i.e., the feed flow rate, is controlled by the APC algorithm during the culture process.

[0045] 9 shows the results of controlling a perfusion flow bioreactor with two different VCD set points using the control methods and systems as described herein, using the APC algorithm to jointly control volume and VCD. Fig. 9A , volume profiles, and set point targets. Fig. 9B , viable cell density profiles, and set-point targets. Fig. 9C , the feed flow rate, harvest flow rate, and drain flow rate determined by the APC algorithm. Fig.9D , the estimated combined growth / death rate μ calculated using the Luenberg observer tot .

[0046] While the drawings arranged herein illustrate various embodiments of the invention, these drawings should not be interpreted as limiting the scope of the invention. Where appropriate, the same reference numerals will be used in different drawings to refer to the same structural features of the illustrated embodiments. DETAILED DESCRIPTION

[0047] Specific embodiments of the present invention will be described below with reference to the accompanying drawings.

[0048] As used herein, the term "computer system" includes hardware, software, and data storage devices for implementing the system or execution method according to the above-described embodiments. For example, a computer system may include one or more processing units, such as a central processing unit (CPU) and / or a graphics processing unit (GPU), an input device, an output device, and a data storage device, which components may be embodied as one or more connected computing devices. Preferably, the computer system has a display or includes a computing device having a display to provide a visual output display (e.g., in the design of a business process). Data storage may include RAM, a disk drive, or other computer-readable media. A computer system may include multiple computing devices connected via a network and capable of communicating with each other via the network. For example, a computer system may be implemented as a cloud computer.

[0049] The methods described herein may be provided as a computer program or as a computer program product or computer-readable medium carrying a computer program, which when run on a computer is arranged to perform the methods described herein. The term "computer-readable medium" includes, but is not limited to, any non-transitory medium or medium that can be directly read and accessed by a computer or computer system. The medium may include, but is not limited to, magnetic storage media, such as floppy disks, hard disk storage media, and magnetic tapes; optical storage media, such as optical disks or CD-ROMs; electrical storage media, such as memory, including RAM, ROM, and flash memory; and hybrids and combinations of the above, such as magnetic / optical storage media. Bioprocess

[0050] As used herein, the term "bioprocess" (also referred to herein as "biomanufacturing process") refers to a process in which a biological component (e.g., a cell), a part thereof (e.g., an organelle), or a multicellular structure (e.g., an organoid or a sphere) is maintained in a liquid medium in an artificial environment (e.g., a bioreactor). In the context of the present disclosure, a bioprocess generally refers to a cell culture. A bioprocess generally produces a product, which may include biomass and / or one or more compounds produced as a result of the activity of the biological component. For example, in an upstream process, the goal is generally to obtain biomass. This can then be used in a fermentation phase (cell culture) to produce one or more desired products by living cells in culture. One or more desired products can be extracted from cells or culture medium in a downstream process. The downstream process may include one or more cells, such as separation and / or purification steps. A bioreactor may be a single-use container or a multiple-use container, in which a liquid medium suitable for carrying out a bioprocess may be contained. Exemplary bioreactor systems suitable for bioprocesses are described in US2016 / 0152936 and WO2014 / 020327. For example, the bioreactor may be selected from: an improved microbial reactor (e.g., from AutomationPartnership Ltd. or Bioreactors), single-use bioreactors (e.g., bag-based bioreactors, such as the STR bioreactors, available in capacities from 50 to 2000 L), stainless steel bioreactors (e.g. stainless steel D-DCU bioreactors with capacities from 10 to 200 L or Cplus with capacities from 5 to 30 L, both from Sartorius Stedim Systems GmbH), benchtop bioreactors (e.g. B and B-DCU, which support 2L single-use rigid wall containers or 1, 2, 5 and 10L glass containers), etc. The present invention is applicable to any type of bioreactor, in particular to any supplier and any scale of bioreactor from benchtop systems to manufacturing scale systems.

[0051] Cell culture refers to the biological process of maintaining living cells in an artificial environment such as a bioreactor. The methods, instruments and systems described herein are applicable to the biological process of using any type of cells that can be maintained in culture, whether eukaryotic cells or prokaryotic cells. The present invention is particularly useful for monitoring and / or controlling biological processes using cell types, cell types include but are not limited to mammalian cells (e.g., Chinese hamster ovary (Chinese hamster ovary, CHO) cells, human embryonic kidney (human embryonic kidney, HEK) cells, Vero cells, etc.)), non-mammalian cells (e.g., chicken embryo fibroblasts (chicken embryo fibroblast, CEF) cells), insect cells (e.g., Drosophila melanogaster cells, Bacillus mulberry cells, etc.), animal cells (e.g., induced pluripotent stem cells (induced pluripotent stem cells, iPSC), stem cells such as mesenchymal stem cells, immune cells such as T cells and natural killer cells) of any cell type, bacterial cells (e.g., Escherichia coli cells), fungi (e.g., yeast) cells (e.g., Saccharomyces cerevisiae cells) and plant cells (e.g., Arabidopsis cells). Biological processes typically result in the production of products, which can be cells themselves (e.g., cell populations used in other biological processes, cell populations used in cell therapy, cell populations used as products such as probiotics, raw materials, etc.), macromolecules or macromolecular structures, such as proteins, peptides, nucleic acids or viral particles (e.g., monoclonal antibodies, immunogenic proteins or peptides, viral or non-viral vectors for gene therapy, enzymes, e.g., for the food industry, for environmental applications such as water purification, decontamination, etc.), or small molecules (e.g., alcohols, sugars, amino acids, etc.).

[0052] Figure 1 A simplified flow diagram of a general bioprocess is shown. The bioprocess is carried out in a reactor 2, which in the embodiment shown is equipped with a stirring device 22. Four streams (also referred to herein as "streams") are depicted, but any or all of these streams may not be present, depending on the specific circumstances. The first stream 24 is a feed stream F containing any material added to the culture in the bioreactor. F (also referred to herein as the "perfusion stream") (typically this comprises fresh culture medium, in which case the bioprocess may be referred to as a "fed-batch" process, a "perfusion" process, or a "continuous" process), and the second stream 26 is a bleed stream F having the same composition as the culture in the bioreactor B , the third stream 28A is the permeate F HAuxiliary harvest stream 28C is obtained by processing auxiliary harvest stream 28C using cell retention device 28 (CRD, which may be any cell separation device suitable for separating cells from culture medium) to produce a third (harvest) stream and a fourth stream 28B, which is a recirculation stream F comprising cells and any culture medium that has not been completely separated in cell retention device 28. R (also called "retentate"). In embodiments, the recycle flow F may be neglected. R , because only the permeate flow F is considered H Sufficient to capture the flow that is effectively output from the bioreactor by the harvest and cell separation process. Thus, reference to the presence or absence of permeate can refer to the auxiliary harvest flow 28C (and the derived permeate and retentate - F H and F R ) is present or absent. It can be assumed that the penetration F H Contains medium having the same composition as the medium in the reactor, but without cells or with very few cells. The feed stream, bleed stream, and permeate stream (F F 、F B 、F H and F R ) may not exist at all, in which case the bioprocess is referred to as an "unfed batch process" or simply a "batch process". F and permeate flow F H When the feed flow and the permeate flow are present, the process can be referred to as "N-1 perfusion", in the absence of a bleed flow, keeping the volume of the culture constant. When the feed flow as well as the permeate flow and the bleed flow are provided so that the bioprocess operates in a (pseudo) steady state (from the point of view of the process conditions, i.e., in particular, keeping the volume of the culture constant), the process can be referred to as "dynamic perfusion". In both cases, the bioprocess can be referred to as a "continuous" culture. When the feed flow as well as the permeate flow and the bleed flow are provided so that the bioprocess operates in a (pseudo) steady state (from the point of view of the process conditions, i.e., in particular, keeping the volume of the culture constant), the process can be referred to as "dynamic perfusion". B and penetration F H ) provides a feed flow F FWhen the bioprocess is fed-batch, it can be referred to as a "fed-batch" process. The present disclosure is particularly related to the operation of perfusion flow bioprocesses. The terms "feed", "feed stream" or "feed rate" can be used interchangeably to refer to the flow rate of the culture medium in the feed stream in the bioreactor, usually in units of volume per unit of time (e.g., liters per hour). The terms "harvest", "harvest stream", "permeate", "permeate rate", "permeate stream" or "harvest rate" can be used interchangeably to refer to the flow rate of the culture medium in the permeate, usually in units of volume per unit time (e.g., liters per hour). The terms "drain", "drain stream" or "drain rate" can be used interchangeably to refer to the flow rate of the culture medium in the drain stream, usually in units of volume per unit time (e.g., liters per hour). The feed stream and the permeate stream are usually cell-free culture medium (or substantially cell-free, depending on the performance of the cell retention device in the case of permeation). The drain stream usually includes culture medium and cells. The feed stream can be characterized by one or more parameters, including the concentration of one or more substrates therein. The harvest stream and the effluent stream can be characterized by one or more variables, including the stream itself (typically expressed in volume units / time, such as liters / hour) and / or the concentration of one or more substrates and / or one or more products therein, typically in units of mass units / volume (e.g., g / l). The effluent stream can also be characterized by viable cell density (also called "viable cell concentration", typically expressed in terms of the number of cells per unit volume - where it is assumed that the viable cell density in the effluent stream is the same as the viable cell density in the container). It can be assumed that the concentration of VCD and one or more substrates or products is the same in the effluent stream and the bioreactor. Viable cell density (a term used interchangeably with viable cell concentration in this disclosure) is typically expressed in units of E06 / ml, i.e., 10 6 Depending on the specifics of the bioprocess, additional parameters for each stream may be known and / or additional variables may be measured or otherwise determined.

[0053] The product of a biological process (also referred to herein as "biological material" or "target biologic") may include metabolites, cells, desired proteins, antibodies, immunoglobulins, toxins, one or more byproducts, target molecules, or any other type of molecule manufactured using a biological process. There may be more than one biological material of interest. The product of a biological process may have one or more critical quality attributes (CQA). As used herein, "critical quality attributes" are any attributes of a product that can be defined and measured to characterize the quality of the product (specifically including any chemical, physical, biological and microbiological attributes). The quality characteristics of a product (in terms of the value of one or more CQA) can be defined to ensure that the safety and efficacy of the product remain within predetermined boundaries. The term "metabolite" refers to any molecule consumed or produced by a cell in a biological process. Metabolites specifically include nutrients such as glucose, amino acids, etc., byproducts such as lactate and ammonia, desired products such as recombinant proteins or peptides, complex molecules involved in biomass production, such as lipids and nucleic acids, and any other molecules consumed or produced by cells, such as oxygen (O2). Depending on the circumstances, the same molecule may be considered a nutrient, a byproduct, or a desired product, and this may even change as the biological process is operated. However, all molecules that participate in cellular metabolism (whether as input or output of a reaction performed by the cellular machinery) are referred to herein as "metabolites." In particular, metabolites may include any suitable analyte, including, but not limited to, amino acids (e.g., alanine, arginine, aspartic acid, asparagine, cysteine, cysteine, glutamic acid, glutamine, glycine, histidine, hydroxyproline, isoleucine, leucine, lysine, methionine, phenylalanine, proline, serine, threonine, tryptophan, tyrosine, valine, etc.), sugars (e.g., fucose, galactose, glucose, glucose-1-phosphate, lactose, mannose, raffinose, sucrose, xylose, etc.), organic acids (e.g., acetic acid, butyric acid and 2-hydroxybutyric acid, 3-hydroxybutyric acid, citric acid, formic acid, fumaric acid, isovaleric acid, lactic acid, maleic acid, propionic acid, pyruvic acid, succinic acid, etc.), other organic compounds (e.g., acetone, ethanol, pyroglutamic acid, etc.). Reference to one or more "metabolite concentrations" may include the concentration of one or more metabolites in a culture medium compartment. Unless the context indicates otherwise, metabolite concentrations generally refer to metabolite concentrations in the culture medium. Metabolites provided in the culture medium (feed) and consumed by cell metabolism can be referred to as "substrates". Substrates can include carbon sources, such as glucose. Depending on the specific biological process, any other molecule or molecules can be used as substrates. Improved Control of Perfusion Flow Bioprocesses

[0054] The present disclosure relates to an improved control strategy for cell culture processes, particularly for perfusion operation modes. As described above, perfusion refers to the use of culture medium exchange, wherein fresh culture medium is continuously added while continuously removing spent culture medium to maintain a constant working volume. Cells are retained in cell culture by separation devices such as alternating tangential flow (ATF) or tangential flow filtration (TFF), wherein cell-free spent culture medium is removed by harvesting flow (osmosis), and cells are retained and returned to the bioreactor by a membrane filter. In addition to feed stream and permeate flow, a discharge stream is generally included to maintain a desired viable cell density (VCD) (or viable cell concentration (VCC)). The discharge stream contains the same material content as the material content in the bioreactor working volume. These three flow streams (flow stream) (feed, permeate and discharge) can be controlled to maintain a desired culture medium exchange rate, a supply of sufficient nutrients, cell density, and working volume. The culture medium exchange rate can be defined as the total volume of culture medium flowing into or out of the bioreactor per unit time. The total volume of culture medium flowing into the bioreactor per unit time is generally equal to the total volume of culture medium flowing out of the bioreactor per unit time.

[0055] In a simple embodiment, three independent single-loop controllers (e.g., proportional integral derivative (PID) controllers) can be used to control each of the feed stream, harvest stream, and discharge stream. Control of the feed stream can be used to maintain the medium exchange rate (constant target or ratio of VCD), or to control the concentration of the substrate. Control of the harvest can be used to control the working volume. Control of the discharge stream can be used to control the VCD. In some cases, the harvest target and the feed target can be reversed, wherein the harvest is used to maintain the medium exchange rate and the feed to control the volume. The inventors have recognized that in this type of configuration, the three control loops interact with each other, resulting in oscillatory type behavior, thereby making the process unstable. This oscillatory behavior may be exacerbated by the pulse-type action unique to the ATF separation device.

[0056] In contrast, according to the present disclosure, a state-space model is used within a model predictive control (MPC) structure to predict the future trajectory of at least one of the parameters to be controlled (referred to as control variables or CVs, such as medium exchange or target substrate concentration, VCD, and volume) to determine the optimal adjustment of at least one of the manipulated variables (MVs) (e.g., one or more of the three flow streams described above) to maintain the CV at its target at a specified future time point. In other words, one or more control loops are provided to control substrate concentration, working volume, and VCD (jointly or independently) by manipulating feed streams, permeate streams, and bleed streams, at least one of which uses a model predictive controller. For example, a control loop with a model predictive controller can be used to control substrate concentration by manipulating feed streams, and two independent P / PI / PID controllers can be used to control working volume by manipulating permeate streams and VCD by manipulating bleed streams, respectively. As another example, all substrate concentrations, working volumes, and VCDs can be jointly controlled by manipulating feed streams, bleed streams, and permeate streams using a model predictive controller that jointly models all of these variables. As another example, substrate concentration and VCD may be jointly controlled by manipulating the feed, purge, and permeate flows using a model predictive controller that jointly models all of these variables.

[0057] In addition, the model predictive controller uses an objective function that prioritizes minimization of adjustments to MV over minimization of errors in CV. This controls the process in a more stable manner than the control methods of the prior art, and is also more stable than a simpler method using three independent conventional controllers (i.e., controllers that do not include a dynamic model of the process to be controlled, such as simple P, PI, PD or PID controllers). In addition, the control method may include an adaptive state space model update. This can further improve the stability of the control method, particularly during long bioprocess runs where, for example, cell physiological changes may occur. When the substrate and VCD are not jointly controlled by the MCP, this may be particularly useful for improving the stability of the controlled process, although in this case, an adaptive state space model (i.e., automatic state space model update) can further improve stability. In an embodiment, the VCD target value can be modified to control the total number of viable cells instead of the VCD. This can further improve the stability of the process by preventing the volume adjustment used to control the VCD. In an embodiment, the method may also include using a control target to maintain a target permeate flow rate. This can reduce the undesirable changes in the permeate flow rate that may cause downstream process problems, thereby achieving integrated upstream / downstream continuous operation.

[0058] Figure 2Schematically illustrates the logic flow in an exemplary control process according to the present disclosure. At each iteration of the control method, a set of parameters of the process is measured or otherwise determined in step 200a. In the illustrated embodiment, the following parameters from the process are obtained during the operation of the process: viable cell density (VCD) (also referred to as viable cell concentration (VCC)), volume, feed flow rate, permeate flow rate, and discharge flow rate, and optionally the concentration of substrate (e.g., glucose). These parameters can be measured or set by an effector (e.g., a valve controlling the flow rate). In an embodiment, one or more of these parameters may not be measured directly, but calculated from other measurements. For example, the volume can be calculated based on the weight from the scale. As another example, one or more flows can be calculated based on the rate of change of weight. One or more of these parameters can be measured continuously or nearly continuously (e.g., at very frequent intervals), or at least measured at each iteration of the control method (step 200a). This can be performed, for example, using an online sensor that measures one or more parameters or determines these parameters based on other measurements performed on the medium or stream during the operation of the bioprocess. In addition, one or more of these parameters can be optionally measured at a low frequency, such as less frequent than each iteration of the control method (step 200b). This can be performed, for example, using an off-line protocol, such as by obtaining a culture medium sample and analyzing it in a laboratory. Therefore, the first group of parameters can be measured at a frequency or frequency set higher than the frequency or frequency set of measuring the second group of parameters. The first group and the second group can overlap, that is, the same parameters can be measured at a first (higher) frequency (e.g., using an online sensor) and a second (lower) frequency (e.g., by off-line analysis). For example, when off-line analysis provides a more accurate measurement than online measurement, this may be useful. Note that measurements 200a and 200b can be collected at each iteration of the control method, in which case, for each measurement variable, measurement 200a can include multiple measurements associated with multiple time points, and for each measurement variable, measurement 200b can include one or more measurements associated with one or more time points, and one or more time points are time points less than multiple time points (i.e., less frequent measurements). Measurements 200a and 200b provide current (or latest measurement) values ​​of one or more controlled variables and one or more manipulated variables of the system.

[0059] Measurement 200a and optional 200b are provided to state observer 210. State observer 210 uses measurement 200a and optional 200b to generate estimates of one or more state variables of the bioprocess. For example, state observer 210 can be used to provide estimates of controlled variables based on measurement 200a, measurement 200b, and state space model (in the illustrated embodiment, these variables are VCD (or total cells) and substrate concentration, although these variables can include any one of VCD / total cells, substrate concentration, medium exchange rate and volume). The function of the state observer will be described in more detail below. The estimate of state observer 210 (in the illustrated embodiment, VCD and substrate concentration) and one or more of the measured variables 200a (in the illustrated embodiment, feed flow, harvest flow, and discharge flow, which are the current values ​​of the manipulated variables of the process) are provided to advanced control method 220, which is a model predictive controller (MPC) in the illustrated embodiment.

[0060] The controller 220 may also take as input one or more parameters 230. The one or more parameters 230 may include operating targets (e.g., set points and optional high and / or low thresholds for one or more controlled variables, in the illustrated embodiment these include targets for VCD / total cells, volume, and medium exchange rate, and optionally targets for substrate (which may replace or supplement the medium exchange rate target) and / or permeate flow). The one or more parameters 230 may include controller parameters (in Figure 2200a) are operably connected to one or more actuators (also referred to as "effectors", such as pumps, valves, etc.) and / or one or more sensors (such as online VCD sensors, volume sensors, etc.). Such control units are known in the art, and a detailed description of these control units is beyond the scope of this disclosure. The control method can be implemented using an initialization phase, in which the controller 220 is not used for one or more iterations of the control method. This enables the state observer 210 to be initialized. For example, an initial period can be used to collect enough measurements to obtain good predictions from the Kalman filter. Typically, only a few measurements are sufficient to have a good Kalman filter estimate, such as 5 or 6 iterations (measurements). Alternatively or in addition, the initial time period can be set to a period that allows the cells to reach a density that makes the calculated cell-specific perfusion rate (cell specific perfusion rate, CSPR) higher than the minimum feed rate (wherein the minimum feed rate can be set to ensure that there is a feed flow). Then, the feed can be set based on the expected cell density and / or the desired substrate concentration. For example, in the first iteration, the first set of measurements 200a (and optional 200b) can be used together with the initial (user-defined) values ​​of one or more states of the state-space model that cannot be directly measured. As further explained above and below, the state-space model can be used by both the state observer 210 and the model predictive controller 220. These values ​​are used to integrate the state-space model to predict the values ​​of the state-space variables until the next set of measurements 200a (and optional 200b) are received. In the next iteration, the state-space observer (e.g., Kalman filter) is used to calculate new values ​​of the state-space variables using the latest set of measurements 200a (and optionally 200b). These are used again to integrate the state-space model to predict the values ​​of the state-space variables until the next set of measurements 200a is received. This can be repeated for one or more iterations, which together form an initialization cycle. This produces multiple estimates of the state-space variables (also called "system states"), which can be used by the state-space observer (e.g., Kalman filter) to obtain improved predictions of the state-space variables in future iterations.After the initialization phase, the state-space observer (e.g., Kalman filter) is still used to calculate new values ​​of the state-space variables at each iteration using the latest set of measurements 200a (and optionally 200b), but this is then used by the model predictive controller to determine a first control action for one or more manipulated variables. The model predictive controller integrates the state-space model using the estimates of the state-space variables from the state-space observer to determine the control action to be taken that is optimal over the prediction horizon. The integration may be performed at a particular frequency until a new set of measurements 200a (and optionally 200b) is obtained, at which point a new iteration is started and new estimates of the state-space variables are obtained by the state observer 210. Model Predictive Controller

[0061] In the context of the present disclosure, model predictive control (MPC) is a process control method that involves predicting the future trajectory of a parameter to be controlled (e.g., medium exchange rate or substrate concentration, VCD or total viable cells and volume) to determine the best adjustment to be made to the manipulated variable (e.g., flow stream) to maintain the controlled variable at the desired target at a specified future time point. This uses a model representing the behavior of the process, referred to herein as a "state space model" (described below). Such a model can predict changes in the dependent variables (including controlled variables) of the modeled system caused by changes in the independent variables (including manipulated variables) of the modeled system. MPC control involves obtaining measurements indicating the current state of the biological process at time t, and then using an internal dynamic model of the process to simulate one or more states of the system within a time range. These are used as variables of the cost function on the time range [t, t+T] (also referred to herein as "control objectives", as further described below), and an optimization algorithm is used to identify a control input strategy that minimizes the cost function on the time range [t, t+T]. The behavior of the system is usually predicted at multiple time points included in the prediction range, for example, time points between t and t+T separated by an interval t1 (e.g., [t, t+t1, t+2t1, t+3t1, ..., t+T]). Typically, the first step (or any step corresponding to the time point between the measurements of the state of the bioprocess) of the control input strategy (e.g., the value of the manipulated variable at t+t1) is implemented, and the calculation is repeated each time a new set of measurements of the current state of the bioprocess is obtained. In particular, the calculation can be performed each time a new set of one or more online measurements of the current state of the bioprocess is obtained. At each calculation step (also referred to as "iteration of the control loop" or simply "iteration" in this article), the result of the calculation may include the value of one or more manipulated variables (e.g., feed flow rate) and the value of one or more controlled variables (e.g., glucose concentration), which is optimal according to the control target including the set point of the controlled variable within the time range. The time range [t, t+T] has a length T, which can be selected to be long enough to capture the complex dynamics expected to exist to ensure convergence to the optimal solution. For example, the length T of the time horizon may be selected to extend to the time required for the system to reach steady state. Alternatively or in addition, the length of the prediction horizon may be determined using one or more factors selected from the following: reactor residence time, availability of model-based estimates as a safety feature in the event of a sensor outage or failure, and computing resources. Control Target

[0062] The control solution is found by finding a set of adjustments in the manipulated variables that minimizes the control objective. The control objective is a mathematical expression that quantifies the desirability of the operation. Various forms can be used. A general example of a quadratic control objective can be of the form:

[0063]

[0064] where J is the cost function to be minimized, x i is the ith controlled variable (e.g., medium exchange rate, substrate concentration, VCD, total viable cells, volume), r i is the set point of the ith controlled variable, u i is the ith manipulated variable (e.g. feed flow, harvest flow, discharge flow), and w is the controlled variable (w xi ) and penalize the manipulated variable (w ui ). Note that in each control objective described herein, references to the values ​​of the controlled and manipulated variables may refer to those values ​​at multiple points in time (e.g., predictions of the system state within the prediction horizon and the values ​​of the manipulated variables in the corresponding control strategy, respectively). For example, in the equations above, each term of and may be repeated for n time steps (e.g., corresponding to n iterations of the control loop), with the value of the system internal state at each of these time steps being predicted using a state-space model (and optionally also a state-space observer) as further described herein. Depending on the control strategy used, only the first control step (Δu i corresponds to the first time step in the prediction horizon), and the simulation and optimization can be repeated at the next iteration of the control method using new values ​​of the measured variables of the system.

[0065] According to the present disclosure, the control objective is to minimize perturbations to the process by minimizing adjustments to the manipulated variables while keeping the controlled variables close to the target. An exemplary control objective takes the form in equation (1). in ΔF f =|F f,new -F f,current | (2) ΔF h =|F h,new -F h,current | (3) ΔF b =|F b,new -F b,current| (4) or ΔF f =|F f,new -F f,current | 2 (5a) ΔF h =|F h,new -F h,current | 2 (6a) ΔF b =|F b,new -F b,current | 2 (7a)

[0066] In equations (1) to (4), f obj is the objective function to be minimized; is the estimated future VCD; x v,set is the required VCD; p x It is a penalty for deviations in VCD; is the estimated future working volume of the bioreactor; V set is the desired working volume; p V is the penalty for working volume deviation; is the estimated future substrate concentration; s set is the required substrate concentration; p s is the penalty for deviation in substrate concentration; is the estimated future medium exchange rate (ratio of constant flow target or total cells); m set is the expected medium exchange rate; p m is the penalty for medium exchange rate deviation; F h,set is the desired permeate flow rate; p m is the penalty for permeate flow rate deviation; F f is the feed flow rate; F h is the permeate flow rate; F b is the discharge flow rate; ΔF f is the difference between the current feed flow rate and the proposed new feed flow rate (the proposed feed flow rate change); ΔF h is the difference between the current permeate flow rate and the proposed new permeate flow rate (the proposed permeate flow rate change); ΔF b It is the difference between the current release flow rate and the proposed new release flow rate (the proposed release flow rate change).

[0067] The state-space model is used to predict the future values ​​of controlled variables (CVs), which in this example include as well as An example of a state space model is provided below. The future value of CV depends on the feed flow, harvest flow, and discharge flow. In the objective function (1), the manipulated variable (MV) is ΔF f , ΔF h , and ΔF b In embodiments, the substrate and / or medium exchange term (i.e., and ) may not be included in the control target. In embodiments excluding these two items, the user may set the feed flow rate or the permeate flow rate to a specified value.

[0068] The medium exchange rate can be expressed in one of three forms as shown in equations (8a) to (5c).

[0069] In the first medium exchange rate case, as shown in equation (8a), the target is a simple constant value. In the second case (8a), the target is the ratio of the feed flow to the target working volume. In the third case (8a), the exchange rate is scaled based on the number of viable cells. The third case can be called a cell specific perfusion rate (CSPR).

[0070] In an embodiment, the control objective may include terms intended to maintain a total viable cell target, but not terms intended to maintain a viable cell density target. The objective described in equation (1) includes a penalty for deviations of the VCD from its target. Maintaining a desired cell concentration is typical during perfusion. Modifying the objective to maintain a desired number of cells in the bioreactor separates the control of cells from the control of volume, further improving the stability of the controller. This prevents the controller from increasing volume, thereby diluting the cell concentration, if the VCD is above its target, or from decreasing volume, if the VCD is below its target. Instead, the controller should select a control action that maintains the desired number of total cells. Thus, an enhancement to the control objective of equation (1) is shown in equation (6).

[0071] In equation (6), except is the estimated total number of cells in the future, x v,set is the expected total number of cells, and p xIn addition to the penalty for deviation of the total number of live cells, the other terms have the same meaning as above. Note that when the volume relative to the predetermined target and the total number of cells relative to the predetermined target are controlled simultaneously, the live cell density relative to the predetermined target can be controlled. Therefore, even when using an embodiment that maintains the total number of cells, the user can simply specify the target volume and target VCD, and these can be used in the objective function to obtain the term that penalizes deviation from the target total number of cells (e.g., equation (6)). However, the use of a control target that includes a term that penalizes deviation from the predetermined target volume and a term that penalizes deviation from the predetermined target number of cells ensures that if other actions can be taken, the controller will not optimize the objective function by manipulating the volume to achieve the target live cell density. In fact, in the absence of a term that penalizes deviation from the predetermined target number of cells, the controller can "sacrifice" volume regulation by selecting a control action that reduces the volume to achieve the target live cell density. When using a control target that includes a term that penalizes deviation from the target total number of cells instead of a term that penalizes deviation from the target live cell density, it is unlikely to select such a "simple" control action because the control action will not achieve the goal of making the total number of cells closer to its target. This is in contrast to the simplest goal of maintaining a target viable cell density, which can be achieved by reducing the volume.

[0072] In an embodiment, the control objective is expanded to include an additional penalty to the objective function that penalizes deviations from set minimum and maximum values ​​of a particular set point (also referred to as a "threshold" or "set point threshold"), as shown in equation (7). This can further improve process stability.

[0073] In equation (7), f obj is the objective function to be minimized, such as the objective function provided in equation (6); f exp is an extended objective function including minimum and maximum thresholds; is the estimated future total cell count or VCD; x v,hi 、x v,lo is the total cells or VCD low and high thresholds; p x,hi 、p x,lo is the penalty for deviations in total or viable cell concentration below a low threshold / above a high threshold; is the estimated future working volume of the bioreactor; V hi 、V lo are the lower and upper thresholds of the desired working volume; p V,hi 、p V,lo is the penalty for working volume deviations below the low threshold / above the high threshold; is the estimated future substrate concentration; s hi 、s loare the lower and upper thresholds of required substrate concentration; p s,hi 、p s,lo is the penalty for substrate concentration deviations below a low threshold of desired substrate concentration / above a high threshold of desired substrate concentration; is the estimated future medium exchange rate (ratio of constant flow target or total cells); m hi 、m lo are the lower and upper thresholds of the required medium exchange rate; p m,hi 、p m,lo is the penalty for medium exchange rate deviations below the low threshold / above the high threshold. For example, in the case where there is no desired permeate flow rate, or in the case where there is no low or high threshold for any of the above variables, any term in equation (7) can be omitted.

[0074] The controller can be adjusted (i.e., the parameters of Equation 7 or any equivalent equation can be adjusted) so that the penalty for the high and low thresholds is greater (preferably much greater) than the penalty for deviations from the desired target setting. As an example, V Set to much lower than p V,hi and p V,lo The value of will configure the controller to perform minimal control action unless it is predicted that the working volume will exceed the high threshold or the low threshold. The controller tuning is configured so that the high penalty and the low penalty are large enough to convert the high threshold and the low threshold into soft constraints. This method can be used, for example, to control volume in a bioreactor so that the control process can adjust the volume as needed to maintain other controlled variables at their set points while preventing such adjustments from placing the volume outside a safe range (for example, in terms of the risk of container overflow). This combination of allowing flexible adjustments to maintain the set point while including stronger constraints advantageously balances the goals of stability of the bioprocess and compliance with constraints that may be set by the physical or biological characteristics of the bioprocess. In extreme settings, if it is predicted that remains between the high threshold and the low threshold, then p V =0 will produce a deadband (where no control action is taken). A second benefit of thresholds is the ability to provide multi-mode types of actions. For example, there are usually minimum specifications for medium exchange rate and glucose level. The controller can be adjusted to target the desired glucose concentration while ensuring that the minimum medium exchange rate is maintained.

[0075] In an embodiment, the control objective may include a term that aims to maintain a consistent harvest rate. A perfusion cell culture process is often connected to a downstream purification system to create an integrated continuous system. The input to the downstream unit is the harvest flow. Therefore, efficient continuous operation of the downstream process requires a consistent permeate flow rate. Maintaining a consistent permeate flow rate can be achieved by adding the term in equation (8) to the control objective, where the term f obj Can be f exp replace.

[0076] In equation (8), f obj is the objective function to be minimized, such as the objective function provided in Equation (6) or Equation (7), F h,set 、F h,hi 、F h,lo are the desired permeate flow rate and the lower and upper thresholds of the desired permeate flow rate, p h 、p h,hi 、p h,lo is a penalty for the permeate flow rate to deviate from the target and to be below a low threshold and / or above a high threshold. In some embodiments, any of the harvest terms in equation (8) may or may not be present. Thus, the objective function according to any embodiment described herein may include any one or more of the following (e.g., in particular, one, two, or all of the following): a term (F) that penalizes deviations from a predetermined target for the permeate flow h,set ), a term that penalizes deviations from a predetermined high threshold of permeate flow (F h,hi ), and a term that penalizes deviations from a predetermined low threshold of permeate flow (F h,lo ).

[0077] In any of the above equations (1), (6), (7) and (8), for example, in the case where the controller is used to control a subset of the controlled variables using a subset of the manipulated variables, any of the controlled variables and the manipulated variables can be omitted. For example, a controller that controls the substrate concentration (controlled variable) by controlling the feed flow (manipulated variable) can use a control target that contains only terms of the substrate and the feed flow. In addition, any of the controlled variables can be associated with a term that penalizes deviations from the target, and is associated with one, two, or none of the terms that penalize deviations from the low threshold and the high threshold. For example, one or more of the controlled variables can be associated with a term that penalizes deviations from the corresponding target, but not with a term that penalizes deviations from the high / low threshold. Another one or more of the controlled variables can be associated with a term that penalizes deviations from the corresponding target and a term that penalizes deviations from the corresponding high threshold or low threshold. Another one or more of the controlled variables can be associated with a term that penalizes deviations from the corresponding target, a term that penalizes deviations from the corresponding high threshold, and a term that penalizes deviations from the corresponding low threshold.

[0078] A control objective can balance multiple objectives, and not all objectives can be met simultaneously. For example, when controlling three manipulated variables (e.g., feed flow rate, harvest flow rate, and discharge flow rate), it is impossible to identify the value of the manipulated variable that can simultaneously cause all controlled variables (e.g., volume, VCD, and substrate concentration) to reach any arbitrary target value. Therefore, the objective function can, for example, balance the corresponding control objectives by assigning weights to each control objective so that some control objectives take precedence over other control objectives. This is achieved in the above equation by setting the relative value of the coefficient p to reflect the priority order of the corresponding control objectives. In an embodiment, the use of relatively small adjustments may be more important than whether a particular variable is close to its target, and p x 、p v 、p S and p m One or more of the above may be set to be lower than p F 、p H and p B The controller can be adjusted (i.e., the parameters of equations (1), (6), (7), and (8), or any equivalent equations, can be adjusted) so that the penalty for adjusting the manipulated variable is equal to or greater than the penalty for deviation from the desired target setting. As an example, p S The value is set to be equal to or less than p FThe value of will configure the controller to preferentially make small adjustments to the feed flow rate relative to reaching the substrate target. Of course, the actual value of each item still depends on the deviation value between the target and the measured / predicted substrate concentration and the proposed step change to the manipulated variable, so that when the substrate concentration is further away from its target and then when the substrate concentration is closer to its target, the controller will choose a larger step change to the manipulated variable. Various methods can be used to set the value of the corresponding weight to achieve the goal. In an embodiment, the control method can be implemented in a test process and / or a simulation process, and when multiple candidate value sets of the weights in the objective function are used, the behavior of the system can be compared. One of the candidate value sets can be selected for subsequent use, or to obtain a value set for subsequent use. For example, the behavior of the system in one or more of the following aspects: the ability of the control method to make the controlled variable close enough to its target (wherein, when the controlled variable is within a predetermined range around the target of the predetermined part of the operation of the bioprocess, the controlled variable can be considered to be close enough to its target), the ability of the control method to avoid oscillating behavior in the setting of one or more manipulated variables, and the ability of the control method to avoid overcompensation behavior in the setting of one or more manipulated variables. Overcompensation behavior can be identified as a local minimum or maximum in the trajectory of the manipulated variable, the local maximum / minimum having one or more predetermined characteristics. One or more characteristics can be, for example, a height to width ratio of a local extreme value in the manipulated variable that exceeds a predetermined value. The height of a local extreme value of a manipulated variable can be the highest step change between the value of the extreme value and the closest value at which the manipulated variable does not increase / decrease. The width of a local extreme value of a manipulated variable can be the time between the first point when the manipulated variable does not increase / decrease near the local extreme value. Preferably, the value of the corresponding weight is adjusted to penalize large changes to the manipulated variable, as this may destabilize other parts of the system. Typically, penalizing changes in the manipulated variable adjusts the controller to slowly guide the controlled variable to its target. Assuming that for a cell culture process, maintaining a stable process takes precedence over removing small deviations of the controlled variable from its target, the controller operates to minimize changes in the MV while keeping the CV "close" to its target (rather than the more common goal of minimizing the difference between the CV and its target). A model predictive controller using a control objective that penalizes changes in the manipulated variable is unlikely to display oscillatory behavior unless there is a mismatch between the model and the system. Therefore, it is beneficial for the controller to further include a feature of self-updating of model coefficients, such as automatic updating of a specific consumption rate of a selected nutrient (e.g., glucose) and a specific growth rate of a cell, as further described herein, as this further enhances the stability of the control method. The inventors have found that the models described herein are very stable and can be transferred to a variety of different biological processes with limited changes.Thus, the parameters in any of equations (1), (6), (7) and (8), and in particular the weights in these equations, can be set as described above for one bioprocess and reused for a different bioprocess. In addition, combinations of set points for controlled variables can be set within operating windows that have been identified for the system (e.g., ranges of values ​​of controlled variables that can be achieved within the system and / or that can be achieved with stable behavior in the system). Within these operating windows, the relative values ​​of the coefficients p can be adjusted by the user according to their specific requirements, e.g., the user may wish to keep glucose constant in all cases, even if this means a deviation in another parameter. In this case, the coefficient p is weighted more than the other weighting coefficients. S is set to a high value. The operating window can be identified by simulating the behavior of the system.

[0079] The values ​​of the weights in equations (1), (6), (7) and (8) are typically set to corresponding values ​​that are constant during the operation of the bioprocess. In an embodiment, the values ​​of one or more of the weights in any of equations (1), (6), (7) and (8) can be set to a first corresponding value at a first time during the operation of the bioprocess, and set to a second (or other) corresponding value at a second (or other) time during the operation of the bioprocess. In other words, the corresponding importance of the control objectives set forth in equations (1), (6), (7) and (8) can change during the operation of the bioprocess. For example, this may be advantageous when the state of the cells and / or the state of one or more parts of the bioreactor system can change over time. For example, different cell culture phases can be controlled using differently adjusted control objectives (e.g., a process can include a growth phase followed by a static perfusion phase, and these phases can be optimized separately and / or follow different trajectories of set points). Similarly, in embodiments, the values ​​of one or more of the targets (set points) and / or high / low thresholds in any of these equations may be set to a first corresponding value at a first time during the operation of the bioprocess, and to a second (or other) corresponding value at a second (or other) time during the operation of the bioprocess. In other words, the values ​​of the set points and / or thresholds used in the control targets set forth in equations (1), (6), (7), and (8) may vary during the operation of the bioprocess. This may be advantageous, for example, when the state of the cells and / or the state of one or more parts of the bioreactor system may vary over time. For example, when it is expected that the cell culture will undergo one or more growth phases during the operation of the bioprocess, the target VCD may be adjusted accordingly. For example, the substrate concentration target may be set to a higher level in a first phase (e.g., a growth phase to promote growth) and then to a lower level in a second phase (e.g., a steady-state culture). As another example, the target VCD may be set to a first level in a first growth phase (e.g., until the target VCD is reached) and then to a different level in a later growth phase to reflect the natural tendency of the health of the cell culture to degrade over time.

[0080] Any term of equations (1), (6), (7) and (8) can be removed to reflect the controlled variable and / or manipulated variable being controlled in the same control loop. Other manipulated variables in one or more independent control loops can be used to control other controlled variables. Therefore, the method may include using multiple independent control loops, each control loop using different one or more manipulated variables to control different one or more controlled variables. At least one of the control loops may use a model predictive controller as described herein. Any one or more additional control loops may use standard controllers known in the art, such as proportional (P) controllers, proportional derivative (PD) controllers, or proportional integral derivative (PID) controllers. Therefore, in an embodiment, a model predictive controller may be used to control the value of a single controlled variable using a single manipulated variable. For example, a model predictive controller may be used to control the concentration of a substrate using a feed flow rate as a manipulated variable. This control method may use a control objective of the form given in equations (1a) or (7a):

[0081] Wherein, equations (1a) and (7a) can also be expressed as equations (1b) and (7b) respectively:

[0082] Where k is the current iteration and j is the number of steps in the prediction horizon from k to n (for state variables) or m (for controller output). In such an embodiment, the volume and viable cell density can be controlled using harvest rate and discharge rate, respectively, by independent control loops having, for example, a PID controller. In other embodiments, the model predictive controller can be used to control the values ​​of two controlled variables using two or more manipulated variables. Thus, as another example, the model predictive controller can be used to control the values ​​of two controlled variables (e.g., medium exchange rate and substrate concentration) using two manipulated variables (e.g., feed flow rate and discharge flow rate) or three manipulated variables (e.g., feed flow rate, harvest flow rate, and discharge flow rate). In such an embodiment, the control method can use a control objective of the form given in equation (1c) or (7c):

[0083] This may be useful, for example, when it is desired to maintain a minimum medium exchange rate while maintaining the substrate (e.g., glucose) concentration at a predetermined set point. Thus, it may be possible to define f in equation (1c) without a term for the maximum medium exchange rate and / or without a term for f defined in equation (1c)obj Equation (7c) is used when the term for setting the medium exchange rate is used.

[0084] As another example, the feed flow rate, harvest flow rate, and bleed flow rate can be used as manipulated variables to control viable cell density, perfusion rate (media exchange rate), and volume. In such an embodiment, the control method can use a control objective of the form given in equation (1d), (6d), or (7d):

[0085] Note that the model can be expanded to include, for example, substrate control (according to equations (1), (6), (7)) or reduced, for example, by removing the medium exchange rate term (e.g., if there is no target medium exchange rate).

[0086] As yet another example, the substrate concentration (e.g., glucose concentration) can be controlled simultaneously with the viable cell density. In such an embodiment, the control method can use a control target of the form given in equation (1e), (6e), or (7e):

[0087] The combined control of substrate concentration and viable cell density (whether or not including one or more additional control targets related to volume control, culture medium exchange rate control and permeate flow rate control) can advantageously reduce the reliance on substrate concentration and viable cell density measurement. In particular, a model predictive controller that uses a joint prediction of VCD and substrate concentration to control substrate concentration and viable cell density (or total number of cells), and a control method that regulates a process based on the measurement of both VCD and substrate, even if there is no update measurement for one of substrate or VCD in a particular iteration, can also be able to determine appropriate control actions. This advantage is also present in any control method using MPC, which jointly predicts two controlled variables and regulates a process based on the measurement of these two variables. In this case, compared with a control method that uses a conventional controller to independently control two variables, the control of the two variables is more robust to the failure of the measurement system for measuring any one of the two variables. This may be particularly advantageous when one of the measurements is difficult to obtain or difficult to obtain using a sensor system that is prone to failure. For example, the measurement of substrate / metabolites may be more difficult to obtain than the measurement of viable cell density. Therefore, as described herein, coupling regulation of substrates / metabolites with regulation of VCD may improve the robustness of the substrate / metabolite regulation process. State Observer

[0088] In the context of the present disclosure, one or more state observers can be used to estimate the value of one or more variables of a biological process, such as the value of an independent variable of a state space model used by a model predictive controller. A state observer is a model that provides an estimate of one or more internal states of a system (in this example, a biological process) based on measurements of the input and output of the system (wherein the internal state and output can overlap, such as substrate concentration can be the internal state and output of the system). In particular, a state observer can be used to estimate the value of VCD, substrate concentration, and even volume. There are many benefits to using a state observer. In particular, a state observer can be used to provide state estimates between online measurements or offline measurements. This allows control actions to run at a higher frequency than state measurements. As another example, a state observer can be used to combine multiple measurements of the same parameter. This may be useful when a continuous soft sensor is combined with a more accurate infrequent offline measurement (e.g., a laboratory measurement). For example, VCD can be estimated via an online conductivity or capacitance-based sensor, but the measurement has a tendency to drift. VCD can also be measured once a day. The state observer can combine these two measurements with an estimate from a state space model to provide the best estimate given the uncertainty in each source. In addition, the state observer is constructed to consider the relative uncertainty in the measurement and model to best handle noisy measurements. As another example, the state observer can be suitable for handling the situation where there is a delay between the sampling time and the result available time. For example, when using a bioreactor with a sensor in the permeate line rather than in the bioreactor itself, there is a certain distance of pipe (tubing) outside the bioreactor, and the permeate needs to pass through this distance before reaching the sensor. This leads to the dead time before the permeate from the bioreactor reaches the sensor. When using the state observer, this can be considered to be an update of the measurement (such as substrate concentration) estimated by the controller. For example, if there is a known 1 minute flow time and a known 1 minute measurement time, there will be a delay of 2 minutes in any measurement. This time delay can be considered in the state observer. For example, the predicted value of the measured variable at the current time k can be obtained based on the most recent measurement (corresponding to kd, wherein d is the dead zone / time delay) and the state space model for modeling the change of the measured variable over time. The time delay parameters in such a model may be provided by the user, e.g. depending on the configuration of the bioreactor system (comprising the bioreactor and sensors for providing the measurements, and possible physical connections between the bioreactor and the sensors), or may be estimated, e.g. by comparing predicted and measured values ​​of state-space variables.

[0089] The state observer can be a linear state observer. The state observer can be a continuous time observer. A linear continuous time observer can obtain a linear system and y = Cx + Du (where x is the true internal state, u is the input, y is the output, and A, B, C, D are the coefficients of the model), such as: and in, is the estimate of the internal state and output in the observer, L is the observer gain, and the observer error e = Satisfy the equation The state observer can be a Luenberg observer. The Luenberg observer uses a dynamic model of the physical system to estimate its internal state. The Luenberg observer is derived by assuming a linear system that satisfies equations (10a) and (10b): X[k+1]=A*X[k]+BU[k](10a) Y[k]=C*X[k]+DU[k](10b)

[0090] Where, at time k, X[k] is the internal state of the process (e.g., volume, concentration of one or more metabolites, and / or one or more cell densities including viable cell density), U[k] is the input to the process (e.g., a manipulated variable such as a feed flow, a harvest flow, and / or a bleed flow), and Y[k] is the output of the process (e.g., volume, concentration of one or more metabolites, and / or viable cell density). The Luenberg observer is derived as:

[0091] The variables represented by “^” are the variables of the observer, so that is the predicted output of the state observer and y(k) is the measured output of the process.

[0092] The state observer may be a Kalman filter (also referred to as a linear quadratic estimate). A Kalman filter is a method for generating an estimate of an unknown variable using a dynamic model of the system, known inputs of the system, and measurements of the system state observed over time by estimating a joint probability distribution on each time variable. The method includes providing an estimate of the current state variable of the system and its uncertainty, and updating these estimates when a new measurement is obtained using a weighted average of the predicted state and the new measurement. Weights are determined to provide more weights to values ​​with lower uncertainty than values ​​with higher uncertainty, and weights are calculated according to covariance. The updated estimate is then used to provide a prediction in the next iteration, and when a new measurement is obtained, the prediction itself is updated. Therefore, the method operates iteratively to provide an improved estimate of the current state of the system. The Kalman filter advantageously handles the uncertainty associated with the noise in the sensor data, providing a better estimate of the internal state of the system than obtained using sensor measurements alone. For example, when a Kalman filter is used to estimate substrate concentration, a model as described in equations (11), (11a), (11b) may be used. The state observer may be a moving range estimate. Moving range estimation is a method for producing estimates of unknown variables using a dynamic model of the system, a set of measurements over a time window (a history of past measurements), and an optimization cost function over the estimation horizon. At each iteration (time t) when a new measurement is obtained, the dynamic model is integrated over the past time horizon ([tT, t]) to identify the state trajectory that minimizes the optimization cost function over the time horizon. The last step of the estimation strategy is then used as an estimate of the current value of the measured variable. The calculation is then repeated at each iteration, moving the horizon forward to a new time t. The optimization cost function can be defined as:

[0093] Among them, x p,i is the ith model predictor variable, is the prior model prediction, x m,i is the ith measured variable, p i is the estimated parameter associated with variable i, w m is the value x m,i The weighting coefficient of the relative importance of is a reflection of the prior model prediction The weighting coefficient of the relative importance of It is a punishment i In the above example of using a state observer to estimate the substrate concentration, the model provided in equations (9) to (10) can be used as the dynamic model of the system, where c A are the estimated and measured state variables, F is the input to the system, and r Ais an estimated parameter. The time range can be set according to the number of iterations. As described above, the time range can be set to have a length long enough to capture the complex dynamics that may be expected to occur. This is usually based on the experience of the system at hand and / or the simulation of the control system to be controlled. As a safe and conservative choice, a prediction range length including the time to reach steady state can be used. Taking into account the computing resources available for calculation, the selection of the length of the prediction range can balance the requirements of capturing the complex dynamics in the system and maintaining the actual useful operating speed of the control loop. Alternatively or additionally, the length of the prediction range can be selected based on the reactor residence time. Methods for calculating the expected residence time or residence time distribution are known in the art. Alternatively or in addition, the length of the prediction range can be selected to be able to use the control algorithm as a safety measure, for example, in the event of a sensor shutdown or failure. In this case, the predicted values ​​of one or more manipulated variables within the range can be used to control the process, and the problem of the sensor can be repaired at the same time. When nonlinearity exists in the system being modeled, moving range estimation may be advantageous. For example, when the dynamic system being modeled uses both VCD and volume as state variables and uses blowdown flow rate and permeate flow rate as inputs, the system of equations modeling the system may not be linear (i.e., it may contain a term that multiplies the two state variables). Any optimization algorithm known in the art may be used to identify a solution that minimizes the cost function for the range of motion estimate. When the range of motion estimate uses a nonlinear dynamic model of the system, the optimization algorithm may be a nonlinear optimizer. State Space Model

[0094] A state-space model is a model that provides a description of the process to be controlled. A state-space model can be used in a state observer to estimate parameter values ​​that characterize the internal state of the system. A state-space model can alternatively or additionally be used in a model predictive controller, where it is used to generate predictions of the internal state of the system over a prediction horizon. A state-space model can be a linear state-space model or a linearized state-space model. A linearized state-space model is a model that includes linear equations that are obtained as an approximation of the behavior of a nonlinear model around a stationary point (also called a "steady state"). For example, consider a system with an internal state x, an input u, and an output y. When a state-space model is used to model substrate concentration, the internal state x of the system can include substrate concentration and consumption rate, the input u can include perfusion rate (feed flow rate), and the output can include substrate concentration. A nonlinear system can be represented as And the fixed point can be expressed as That is, f(x0,u0) = 0. Therefore, the state space equation can be expressed in terms of new variables Δx = x-x0, Δu = u-u0, and Δy = y-y0 as follows: as well as

[0095] The state-space model used in accordance with the present disclosure may depend on the controlled variable to be controlled using the model predictive controller. For example, when using model predictive control to control substrate concentration by manipulating feed flow, the state-space model may include a single equation that expresses the rate of change of substrate concentration (internal state of the system and output of the system, a controlled variable) as a function of feed flow rate (input, manipulated variable), concentration of substrate in the feed (parameter provided by the user or sensor), volume of culture (parameter provided by the user or sensor), and substrate consumption rate (internal state of the system, parameter estimated by solving the system in pseudo-steady state). For example, equation (9) may be used:

[0096] It can also be described in matrix form using equation (10):

[0097] in and and is the rate of change of the substrate concentration and substrate uptake rate in the bioreactor (i.e. and ), x sys,t is the concentration of substrate in the bioreactor at time t (i.e., c A ; t = n is the time with the most recent data) and the substrate uptake rate at time t (i.e., r A ), F is the feed flow rate, c A,0 is the substrate concentration in the feed flow rate, V is the volume of the bioreactor, and r A is the substrate uptake rate of the cell, assuming Further assumption (pseudo-steady state), then it can be determined at any point in time Among them, c can be measured or estimated at the current time point A , F is known, and V, c A,0 is a parameter, and c can be estimated at a future time point by integrating equation (9) A , until a future time point, F is part of the proposed control strategy, and V, c A,0is a parameter. Such a model thus captures the evolution of substrate concentration as a function of the chosen feed rate and estimates the current substrate uptake rate by solving the model at a pseudo-steady state. Thus, the substrate uptake rate does not need to be known before the bioprocess is performed (e.g., determined empirically), and its value can be adjusted during the process in order to reduce the deviation between the model and the process, thereby further increasing process stability. Note that in Eq. (9), effectively, the cell density is an input to the model, since the substrate uptake rate r A Depends on the cell density (see equation (25) below). The harvest flow and the discharge flow can be ignored to the extent that they contribute to substrate loss because they do not contribute to changes in substrate concentration in the reactor and can be excluded from the model by assuming that the volume of the culture is constant (i.e., Ff=Fb+Fh). Alternatively, for example, if the volume of the culture cannot be considered constant, the harvest flow and the discharge flow can be explicitly included in the model. The substrate concentration (e.g., glucose) can be measured online and / or offline, and this can be used by a state observer (e.g., a Kalman filter) to estimate the current value of the substrate concentration (e.g., taking into account uncertainty, noise, and / or possible time delays in the measurement). The model predictive controller can then use the measured or estimated substrate concentration to update the feed rate to maintain the set point of the substrate concentration under the estimated pseudo-steady state of the substrate concentration. In this method, one or more other control loops can be used to control other controlled variables such as volume and / or cell concentration, each control loop using a corresponding controller, which can be, for example, a P, PI, PID, or a model predictive controller. For example, the volume can be controlled using a control loop that manipulates the permeate (harvest) flow rate. The viable cell density can be controlled using a control loop that manipulates the purge flow rate.

[0098] Note that equation (9) assumes that the volume of the culture in the bioreactor does not change, so that Ff = Fb + Fh. Equation (9) can be written in a way that does not require this assumption (equation (9a)):

[0099] As another example, when model predictive control is used to control the viable cell density, volume, and optionally the perfusion rate, the state space model may include a kinetic growth model as further described below, such as Equation (11), Equations (11) to (14), or a simplified form thereof expressed in matrix form using Equation (10a) (see, e.g., Equation (26) below): X[k+1]=A*X[k]+BU[k] (10a)

[0100] Where X is the state x v 、x d 、x l (the concentrations of live cells, dead cells, and lysed cells, respectively), U is the input Fb 、F h and F f (respectively, the discharge flow rate, the permeate flow rate, and the feed flow rate), For sufficiently small sampling times, A is And B is (Note that for any sampling time, these A and B can be converted using standard discretization formulas, and the specific values ​​of the matrix of coefficients A and B depend on the specific equations used for the dynamic model), and effective growth is a parameter that can be estimated by solving the model in a pseudo-steady state in each iteration of the control method, as explained above about the substrate uptake rate of the cell. Effective death rate and cell lysis rate can also be parameters estimated by solving the model in a pseudo-steady state in each iteration of the control method, as explained above about the substrate uptake rate of the cell, or these parameters can be maintained at a predetermined value (that is, not automatically updated based on the mismatch between the model and the measurement). Without wishing to be bound by theory, the inventor believes that the effective growth rate is more likely to change significantly during the biological process, and is more directly related to the live cell density controlled by the method, so that the estimation of the automatically updated growth rate is more important than the estimation of the death and lysis rate. When only equation (11) or similar equations are used, the effective growth rate can capture the contribution of both growth and death processes, that is, the effective growth rate can bring the growth and death rates together. The use of more complex predictive models, such as models that model dead and lysed cells as well as live cells (e.g., a model that includes equations (11) to (14)), can enhance the predictive power of the model.

[0101] For example, a growth model that explicitly models both dead and lysed cells may be able to predict changes in growth dynamics due to changes in the medium exchange rate. In contrast, a model with a single equation that combines growth and death may respond to changes in growth rate only after the growth rate has been affected by changes in the medium exchange rate, by observing a model mismatch (where the state-space model is subsequently updated to account for changes in growth rate). Similarly, any change in a variable that is explicitly modeled in the model of equations (11) to (14) (or is directly - e.g., linearly related to an explicitly modeled variable) will have an effect on the cell-related state variables (i.e., live cell concentration, dead cell concentration, and / or lysed cell concentration), and this will be captured by the model. In contrast, if a variable is not explicitly modeled in this manner, its effect on the cell-related state variables can be captured simply by updating a coefficient that effectively captures its effect (e.g., effective growth rate) a posteriori. As another example, when predictive control is used to control viable cell density, volume, and substrate concentration, the state-space model may include a matrix form of a set of equations, the set of equations including a kinetic growth model (e.g., Equations (11), (11) to (14), or (26)), an equation describing volume change (e.g., Equation (27)), and an equation describing substrate concentration dynamics (e.g., Equation (25) or (25b)). Thus, as further described below, the state-space model may include a kinetic growth model. In an embodiment, the state-space model may include a model describing the growth dynamics of a cell culture process as described in WO2021 / 165480. The parameters of such a model may be determined as described in WO2021 / 165480, for example using a data-driven approach, such as a partial least squares regression model or a machine learning model and / or a Bayesian approach as described therein.

[0102] The term "kinetic growth model" refers to any model that captures the kinetics of a cell population in a bioprocess. Therefore, a kinetic growth model can be used to simulate the number of viable cells (and other culture-related parameters) in a bioreactor, for example to predict the number of cells (e.g., viable cell density) in a bioreactor at a future time point. For example, a kinetic growth model can include one or more differential equations that model the time-dependent behavior of one or more cell population variables. A cell population variable can be a variable that characterizes a viable cell population, a dead cell population, a lysed cell population, and / or a total cell population in a bioprocess. Typical cell population variables include viable cell density (VCD), dead cell density, and lysed cell density, which capture the concentrations of viable cells, dead cells, and lysed cells in a bioreactor, respectively. In an embodiment, a kinetic growth model uses the Monod equation to capture cell growth rate as a function of limiting nutrient concentration. Equations (11) to (14) below provide an example of a kinetic growth model, which describe viable cell density x v , dead cell density x d , total cell density x t , and the lysed cell density x l Variation of as a function of time: x t =x v +x d +x l (14)

[0103] In equations (11) to (14), F b and F h are the release rate and the harvest rate (see above and Figure 1 ), V is the reactor volume, μ eff , μ d , k l are the effective growth rate, effective death rate, and lysis rate, respectively. Equation (11) captures the following assumptions: (i) Living cells grow at an effective growth rate μ eff formed by living cells; (ii) living cells can be discharged through the flow F b Leave the reactor; (iii) living cells can die at an effective rate μ d (iv) no live cells are harvested through the F h exiting the reactor (in other words, in the presence of a harvest stream that comprises a perfect cell retaining filter—which may be a valid assumption when any cells exiting the bioreactor via the harvest stream represent negligible quantities). Calculation of the effective growth rate is critical to the operation of this model and is described in detail below.

[0104] Equation (12) captures the following assumptions: (i) Dead cells die at an effective rate μ d (ii) dead cells form through a first-order process at a rate k l (iii) dead cells can be transformed into lysed cells by the discharge flow F b (if any) exit the reactor; and (iv) no dead cells pass through the harvest stream F h Leave the reactor. The calculation of the effective death rate is detailed below. Equation (13) captures the following assumptions: (i) The lysing cells are released at a rate k l formed by dead cells; (ii) lysed cells can be discharged through the flow F b (if present) leaving the reactor; and (iv) lysed cells can be harvested by flow F h (if present) leaves the reactor. Equation (14) captures the assumption that cells are either alive, dead, or lysed. This can be used to calculate one of the other variables, such as lysed cells (which are usually not directly measurable), by closing the balance between live and dead cells.

[0105] In an embodiment, the death process (by parameter μ d Capture) can be modeled as resulting from a combination of a basal mortality rate and a toxicity factor, for example as provided in equation (15) below: μ d =k d +k t φ t (15)

[0106] In equation (15), k d is the primary (basal) mortality rate, k d is the “toxicity rate”, φ t is a measure of toxicity. The variable φ t Can represent the concentration of one or more components that have toxic effects on cells. In the embodiment, assuming φ t Equal to the concentration of lysed cells x l (i.e. φ t =x l ). In other embodiments, assuming φ t is equal to the concentration of unknown biological material that accumulates in culture as a result of cell growth and is inhibitory to cell growth and / or toxic to cells, which is designated as φ b (so that φ t =φ b ). For example, the following equation (16) can be used to capture the evolution of this variable:

[0107] The above formula assumes that the unknown product is proportional to the viable cell density x v The product is produced at a proportional rate and can be obtained through the discharge stream and the harvest stream (F b 、F h ) leaves the bioreactor.

[0108] In an embodiment, the growth process (by parameter μ eff Capture) is modeled as the growth rate μ under ideal conditions max The product of (assuming growth rate is maximized) and one or more factors that describe the effects of other system variables on growth. In some cases, these factors can take one of three functional forms: substrate limitation η s , quadratic η q or inhibitory i The relationship between these factors and the resulting effective growth rate can be captured in equation (17): μ eff =μ max η s η q η i (17)

[0109] Among them, the correction factor η s Capture N s Contribution of substrate-limiting variable, η q Capture N q The contribution of the quadratic influencing variables, and η i Capture N i Suppress the contribution of the variable. N s Can be equal to 0 (no substrate limiting variable), 1 (one substrate limiting variable), or any natural number. N q Can be equal to 0 (no quadratic influence variable), 1 (one quadratic influence variable), or any natural number. N i Can be equal to 0 (no inhibitory variable), 1 (one inhibitory variable) or any natural number. The above correction factor can be calculated as the product of multiple correction factors, each of which captures the contribution of substrate limitation / secondary effect / inhibitory variable, as shown in the following equations (18) to (20):

[0110] In an embodiment, the inhibition effect is captured using a correction factor of the form provided by the following equation (21):

[0111] Among them, z n is the concentration of the substance with growth inhibitory effect, θ i,n It means zn Parameter of the level above which inhibition occurs. Figure 3A It is shown that for the parameter θ i,n Examples of values ​​of the growth inhibitory factor as a function of the concentration of the growth inhibitory substance for different values ​​of , the effect of which is modeled by the correction factor. The variable φ in the above equations (15) and (16) t can be considered a special case of inhibition, where the concentration of the inhibitory substance depends on the viable cell density (e.g. because the inhibitory substance is produced by or as a result of the presence of cells). t Sometimes it is also possible to use the formula provided in equation (21) for modeling. Therefore, in some embodiments, equation (17) can be written as:

[0112] where θ t (or θ b , as the case may be) is representative of biological material The coefficient of inhibition of growth by accumulation of can be equal to x l or As will be appreciated by those skilled in the art, in some embodiments, more than one substance may be present. in, Each of can be modeled using the corresponding terms in equations (17) and (22) and the corresponding equation (16). Substances with growth inhibitory effects and substances produced by or due to the presence of cells in culture (i.e., substances Examples of substances with growth inhibitory effects that are not necessarily related to viable cell density include substances (e.g. antibiotics) that are included in the culture medium to have the desired effect but may also have a (ideally mild) growth inhibitory effect on the cell culture.

[0113] In an embodiment, a correction factor of the form provided by the following equation (23) is used to capture substrate limitation effects:

[0114] Among them, θ s,n is a parameter that represents the approximate level of the variable. When the approximate level is lower than this, the variable z n (Growth-limiting substrate) begins to have a limiting effect on growth. Figure 3B It is shown that for the parameter θ s,n Examples of values ​​of the substrate limiting factor as a function of the limiting substrate concentration for different values ​​of , whose effect is modeled by the correction factor. In equation (23), the factor 2 is used to give the parameter θ s,n As the approximate concentration zn The intuitive biological significance is that below this approximate concentration z n The limiting effect can be seen when (for example, when z n The value is lower than θ s,n Any other value can be used for this factor, resulting in the same behavior, with the effect that the parameter θ s,n is adjusted accordingly and no longer has the same intuitive interpretation. In particular, this factor can be omitted entirely (i.e., set to 1). Similarly, in equations (21) and (22), the cubic term (i.e., z n / θ i,n ) can include giving the parameter θ i,n As the approximate concentration z n The coefficient of intuitive biological significance is higher than the approximate concentration z n The limiting effect can be seen when (for example, when z n The value reaches θ i,n , for example, 0.37, when the inhibition function crosses the threshold value of ˜0.95). Examples of substances with substrate-limiting effects include nutrients such as glucose, amino acids, and the like.

[0115] In an embodiment, a correction factor of the form provided by the following equation (24) is used to capture the quadratic effect:

[0116] Among them, μ q,n is a parameter representing the target value (i.e., the value at which maximum growth occurs), and θ q,n is a parameter that represents the “spread” of the effect. A factor of 1 / 25 is used to give the parameter θ q,n Intuitive meaning, where θ q,n = 1 means that the quadratic effect is at the target value μ q,n Any other value can be used for this factor, resulting in the same behavior, with the same effect: the parameter θ q,n is adjusted accordingly and no longer has the same intuitive interpretation. In particular, the factor can be omitted entirely (i.e., set to 1). s,n and θ q,n ) can be advantageous because it can make it easier for a user to set these parameters (using, for example, biological knowledge or assumptions) or realistic bounds for these parameters. Figure 4A It is shown that for the parameter μ q,n Different values ​​of (θ q,n =1), examples of values ​​of the quadratic effect factors as functions of the concentrations of substances whose effects are modeled by the correction factors. Figure 4BIt is shown that for the parameter θ q,n Different values ​​of (μ q,n =5), examples of values ​​of the quadratic effect factors as a function of the concentration of the substance whose effect is modeled by the correction factor.

[0117] As will be appreciated by those skilled in the art, other equations may be used to replace or supplement the above equations to model cell population variables and factors affecting these variables. Together, these equations may form a state space model because these equations are based on a series of state variables x v 、x d 、x t 、x l The evolution of the state of the cell culture (also referred to herein as the "cell state") is described as a function of the system inputs (including, for example, the concentrations of various substances that affect the cell state).

[0118] Thus, the state-space model may comprise a matrix form of a system of equations comprising a kinetic growth model and / or one or more equations that capture the evolution of the concentration of one or more metabolites (specifically including one or more nutrients / substrates, byproducts and / or desired products) in a bulk culture, as described below (e.g., Eq. (25)). Note that the models provided in Eqs. (9) (or 9(a)) and (10) are examples of models that include a single equation that captures the evolution of the concentration of a single metabolite (in this case a substrate) in a bulk culture. The flow of the metabolite may be expressed as a mass flow or a molar flow (because the latter can be converted to the former using molar mass and vice versa, such that conservation of mass expressed in Eq. (25) is verified regardless of the units chosen), and the skilled person will be able to convert one to the other. Thus, references to mass flow are intended to encompass the use of the corresponding molar flow, with corresponding adjustments made for consistency of units within the equations. Similarly, references to concentration may refer to either mass or molar concentration. The flow of metabolites entering the bioreactor depends on the feed flow F F The value of and the concentration of metabolites in this flow. The metabolite flow out of the bioreactor depends on the permeate flow F H The value and outflow F B The values ​​of and the concentrations of metabolites in these corresponding streams. The consumption and secretion of metabolites by cells in a bioreactor depends on the viable cell density in the reactor and a variable called the "specific transport rate" (sometimes also called the "metabolic rate"), which can also be called the "specific consumption rate" of the metabolite by the cells (usually, if it is negative, the metabolite is being consumed by the cells) or the "specific secretion / production rate" (usually, if it is positive, the metabolite is being produced by the cells). Therefore, the material balance of metabolite i can be calculated for a general system (e.g., Figure 1As shown) is written as the following equation (25):

[0119] This equation expresses the conservation of mass of the system at any time point t. In equation (25), δ m,i is the specific transport rate of metabolite i by cells in culture, m i is the concentration of metabolite i in the reactor, V is the volume of the culture in the bioreactor, m F,i is the concentration of metabolite i in the feed stream, m H,i is the concentration of metabolite i in the permeate flow, m B,i is the concentration of metabolite i in the discharge stream, x v is the viable cell density in the reactor, F F 、F H 、F B are the volumetric feed flow rate, harvest flow rate, and drain flow rate, respectively (although mass flow rates may also be used with appropriate coefficients corresponding to the density of the flow). m,i *x v Available items Instead, ε is a constant chosen to ensure that m is below the detection limit of the metabolite. i The value of ε does not result in an error in the estimate of a particular transport rate. Typically, ε is chosen to be approximately equal to the detection limit of the metabolite (e.g., when the metabolite concentration is normalized, it may be chosen to be 0.05). Equation (25) assumes that permeate stream 28A contains the only material that leaves the system via auxiliary harvest stream 28C (i.e., the auxiliary harvest stream and the return stream do not need to be included in the model since metabolites leave the system only via the permeate stream), and that cell retention device 28 functions such that permeate stream 28A may be assumed to contain no cells. Equation (25) may be adapted to include auxiliary harvest stream 28C (and, if mass flow rate is used, the corresponding m A,i and density ρ A ) and return flow 28B (and corresponding m R,i and ρ R). In addition, equation (25) can be modified to simulate the removal of some cells by osmotic flow. In other words, additional terms can be added to equation (25), and some terms can be removed depending on the setting of the biological process and the assumptions made. Equation (25) (referred to herein as a "material balance model" or "bulk metabolite concentration model") captures the relationship between the extracellular flux of metabolites and the concentration of metabolites in the culture medium. The model does simulate intracellular metabolic fluxes, which can be captured using metabolic models that simulate the fluxes of reactions that form the cellular metabolic network together, and are significantly more complex (and therefore more difficult to solve and require a large amount of data and / or assumptions to parameterize). Therefore, the model used herein advantageously provides information about the metabolic state of the cell while keeping the solution and parameterization relatively simple, allowing important system state variables, such as the specific transport rate of metabolites (as will be further explained below) to be obtained in a simple and efficient manner.

[0120] Furthermore, equation (25) can be simplified by making some assumptions. For example, it is assumed that the metabolite concentration is the same everywhere in the medium in the bioreactor, and therefore the same in the permeate and effluent streams (in other words, it is assumed that the concentration gradient within the reactor is negligible, so that m B,i =m H,i =m i ), and the number of cells lost in the discharge flow and permeate flow is negligible, equation (25) can be written as:

[0121] Using the form of equation (25), equation (25a) corresponds to equation (9a).

[0122] Assume further that the volume of the culture is constant (i.e., F F =F H +F B ), the flow is constant, and using the first-order finite difference approximation of the derivative, for time t k The specific consumption / secretion rate of the metabolite at , equation (25a) can be solved as:

[0123] Note that equation (9) is also a simplification of equation (25), which considers that the volume of the culture is constant, so that Ff = Fb + Fh. Therefore, assuming that the volume of the culture is constant, equation (25a) can be rewritten as equation (25b), which corresponds to equation (9):

[0124] where, in equation (9), the viable cell density and the specific cell uptake rate are combined in an estimated single coefficient r A When the viable cell density is instead modeled explicitly, for example using a kinetic growth model such as equation (11), it may be advantageous to use equation (25b) instead of equation (9). For example, the state-space model may include equations that capture changes in metabolite (e.g., substrate) concentration, such as equations (25), (25a), or (25b), and one or more equations that capture changes in cell density, such as equation (11) or equations (11) to (14). In such an embodiment, the substrate concentration and viable cell density may be measured at each iteration, and this may be used by the state observer to obtain estimates of the substrate concentration and viable cell density as well as estimates of the cell-specific uptake rate and effective growth rate by integration of the state-space model. The model predictive controller may use these estimates to identify a control strategy that jointly controls the viable cell density and substrate concentration.

[0125] Any method for calculating integrated viable cell density can be used in the methods described herein. For example, IVCD can be calculated using equation (27): k : IVCD k =(α x v,k +β x v,k+1 )*(t k+1 -t k ) (27)

[0126] Wherein, coefficients α and β weight the relative influence of two viable cell density values, and make α+β=1. For example, these two values ​​can be weighted equally, i.e., α=β=0.5. In an embodiment, α and β are selected so that α>β (e.g., α=0.6 and β=0.4). These coefficients can be selected to reflect the observed cell growth behavior and can be selected independently for each time point. In the case where exponential growth can be assumed, a logarithmic transformation can be used to calculate the integrated viable cell density. For example, the integrated cell density can be calculated using equation (27a): in,

[0127] As mentioned above, δ at time k m,iThe equation can be solved using known (usually measured) biomass and metabolite concentrations at time k and k+1 to obtain the metabolite transport rate at each time point value available for the above measurement. In addition, this can be performed separately for each measured metabolite. The resulting metabolite transport rate is expressed as the amount (mass or mole) of metabolites per unit maturity (i.e., usually per unit time) per cell. Note that in the equation for specific transport rate, the signs of all terms can be reversed, depending on whether the negative rate refers to cell consumption of metabolites, the positive rate refers to cell production of metabolites (i.e., rate from the perspective of culture medium), or the opposite (i.e., positive rate refers to cell consumption of metabolites, and negative rate refers to cell production of metabolites, in other words, rate from the perspective of cell compartments).

[0128] The state-space model can be an adaptive state-space model. An adaptive state-space model refers to a state-space model that updates one or more coefficients in the model during operation of the bioprocess based on one or more measurements of state-space variables collected during operation of the process. This is in contrast to, for example, simply using constant values ​​of these coefficients throughout the operation of the bioprocess, or even using different values ​​of these coefficients provided by the user for different iterations of the control loop. The use of automatically updated coefficients in the state-space model further improves the stability and reliability of the model predictive control because the model more accurately reflects the current state of the bioprocess. This is particularly important in the context of perfusion bioprocesses, where cells can be maintained in culture for extended periods of time because the metabolism of the cells themselves can change over that time (resulting in, for example, different growth rates, different substrate consumption rates, etc.), as well as related characteristics of the bioreactor system (e.g., performance of the filtration system of the permeate). For example, the state-space model can include kinetic coefficients representing specific growth rates and / or specific substrate consumption rates. The control method can compare predicted values ​​of VCD and / or substrate concentration with measurements collected from the process. The deviation between the predicted value and the measured value can be used to generate an optimal update to the predicted value given the measurement noise and model uncertainty, such as using a state observer (e.g., a Kalman filter as described above). Alternatively or in addition, the deviation between the predicted value and the measured value can be used to update the dynamic coefficients in the state-space model to continuously improve the prediction of future process states. The term "process state" can refer to a state defined as a state in a state-space model. Therefore, the above-mentioned state-space model can be updated at regular intervals, such as every iteration, every x iterations, or every iteration of a control loop that meets one or more criteria (e.g., every iteration that meets the criteria of having a more accurate measurement of one or more variables of the state-space model (compared to measurements obtained at all iterations), such as offline measurements). Updating the state-space model can include updating the value of one or more coefficients of the model, such as one or more dynamic coefficients. This can be achieved by considering the coefficients of the model to form a part of the state-space variables to be estimated at each iteration where the model will be updated. In other words, instead of being fixed to a predetermined value provided by a user, one or more coefficients of the state-space model can be considered to represent the state-space variables estimated by the state observer. The model predictive controller then uses the updated values ​​of these coefficients to predict the process trajectory within the prediction horizon and thus determine the optimal control strategy. For example, in the model of equations (9) and (10), the substrate concentration c A The comparison between the predicted value and the measured value is used to update r A For example, the process can proceed as follows, where k refers to an iteration of the control method (e.g., when a new online glucose measurement is received). When k=1, using the initial measurement and rA This is used to integrate equation (9) to predict the c between substrate measurements. A and r A When k = 2, the Kalman filter is used to calculate a new (most recent) estimate of the system state, i.e., c A and r A These are used to integrate equation (9) for the upcoming interval. This is repeated for a number of iterations, for example about 5 iterations, in order to obtain the system state c A and r A to obtain the best performance of the Kalman filter. At k=i (the number of iterations typically set by the user), the model predictive controller is activated to determine the first control action for the manipulated variable (e.g., feed flow rate). At k=i+1, new Kalman filter estimates of the system state are obtained. These are used as the basis for integrating equation (9) at the beginning of the next interval to determine the control action taken on the manipulated variable via the model predictive controller by integrating the ODE model at some frequency until the next online measurement is received at k=i+2. As another example, in the model of equations (25) / (25a), one can i The comparison between the predicted value and the measured value is used to update δ m,i As another example, in the model of equations (11) to (14), the effective growth rate, effective death rate, and lysis rate (μ eff , μ d , k l ) can be based on the viable cell density x v , lysed cell density x l , and the dead cell density x d The effective growth rate (μ) is updated by comparing the predicted value (if any) with the measured value. In an embodiment, in the model of equations (11) to (14), the effective growth rate (μ eff ) can be based on the viable cell density x v In such an embodiment, equation (14) and the state observer can be used to update the live cell density x v The dead cell density and lysed cell density are updated by comparison between the predicted and measured values.

[0129] The simplified versions of equations (11) to (14) combine all the effects of growth rate and death rate into a single variable μ tot (Equation (26)). In this form, taking into account the volume change, we can write a new set of equations, including equation (26) and equations (27) to (28):

[0130] Note that equation (26) can also be interpreted as assuming that no volume change is expected (i.e., F f =F b +F h ). However, allowing for volume changes by including equation (27) or its equivalent that simulates volume changes enables volume control to be performed in conjunction with control of other variables, such as viable cell density in the example using equations (26) to (28). Equation (27) can also be used with a kinetic growth model that does not make the simplifications in equation (26) (e.g., equation (11) or equations (11) to (14)), and / or with a model that captures the rate of change of concentration of one or more metabolites (e.g., equation (25) or (25a)). This enables joint control of volume and cell density (e.g., where equation (27) is combined with equation (11) or equations (11) to (14)) and concentration of one or more metabolites (e.g., where equation (27) is combined with equation (25) or (25a)), or all of the above (where equation (27) is combined with (i) equation (11) or equations (11) to (14) and (ii) equation (25) or (25a)), respectively.

[0131] Using any of these sets of equations, linearized around steady-state values ​​determined for a given perfusion rate, viable cell density, and volume, the system can be approximated in the typical linear form: y=Cx(10b') Where, when using equations (26) to (28), A, B, and C are given by: After discretization (see equation (10)), equations (10a) and (10b) can be used for the standard Luenberger observer:

[0132] Note that the pole of the observer (A-LC) can be tuned by adjusting L to emphasize updating the estimated coefficients (in the example above, the overall growth / death rate) while supporting (to a user-defined degree) measurement of the process state (in the example above, viable cell density and volume).

[0133] Updating a state-space model may also be referred to as "parameterizing" or "reparameterizing" the state-space model. Thus, methods of any aspect may include parameterizing a state-space model. Parameterizing the state-space model may include obtaining measurements of state variables corresponding to a biological process, predicting values ​​of one or more state variables of the biological process using a state-space model having a first set of parameters, and determining whether the measurements are within a range of values ​​predicted by the state-space model having the first set of parameters. Parameters of the state-space model may include coefficients associated with the state-space model, such as any of equations (9) to (25) / (25a). The method may also include providing a second set of parameters based on a difference between the measurements and the values ​​predicted by the state-space model using the first set of parameters. system

[0134] Figure 5 An embodiment of a system for controlling a bioprocess according to an embodiment of the present disclosure is shown. The system includes a computing device 1, which includes a processor 101 and a computer readable memory 102. In the embodiment shown, the computing device 1 also includes a user interface 103, which is shown as a screen, but can include any other means of conveying information to a user, such as through auditory or visual signals. The computing device 1 is operably connected to a bioprocess control system, such as through a network 6, which includes a bioreactor 2 (e.g., Figure 1 As shown), one or more sensors 3 and one or more effectors 4. The computing device 1 can be a smart phone, a tablet computer, a personal computer or other computing device. The computing device 1 is used to implement a method for controlling a biological process, as described herein. In an alternative embodiment, the computing device 1 is used to implement a part of the method for controlling a biological process, and communicates with a remote computing device (not shown) to implement other parts of the method for controlling a biological process, as described herein. For example, the computing device 1 can be a distributed control unit and can communicate with a remote computing device that implements the functions of one or both of a state observer and a model predictive controller. The communication between the computing device 1 and the remote computing device can be through a wired or wireless connection, and can occur through a local or public network (e.g., through the public Internet). Each of the sensors 3 and the optional effectors 4 can be wired to the computing device 1 (or the remote computing device, if present), or can be able to communicate through a wireless connection (i.e., through a network 6) (e.g., through WiFi), as shown. The connection between the computing device 1 and the effector 4 and the sensor 3 can be direct or indirect (e.g., through a remote computer). One or more sensors 3 are used to obtain data related to the biological process performed in the bioreactor 2). One or more effectors 4 are used to control one or more manipulated variables of a bioprocess carried out in the bioreactor 2 .

[0135] One or more sensors 3 can each be an online sensor (sometimes also referred to as an "online sensor") that automatically measures the properties of a bioprocess while the bioprocess is ongoing (with or without the need to extract a sample of the culture), or an offline sensor (a sample is obtained manually or automatically, and then processed to obtain a measurement). Each measurement from a sensor (or a quantity derived from such a measurement) represents a data point associated with a time (or corresponding maturity) value. One or more sensors 3 can include a sensor for recording the biomass in the bioreactor 2, referred to herein as a "biomass sensor". This is typically in the form of a parameter from which viable cell density or viable cell density can be estimated. A biomass sensor can record a physical parameter, from which the biomass in the bioreactor can be estimated (usually in the form of total cell density or viable cell density). For example, biomass sensors based on optical density or capacitance are known in the art. One or more sensors can also include one or more sensors that measure the concentration of one or more metabolites (wherein the term "metabolite" used herein includes substrates of cell metabolism (e.g., glucose) and products of cell metabolism in the bioreactor), referred to herein as a "metabolite sensor". Metabolite sensors can measure the concentration of a single or multiple metabolites (e.g., from a few metabolites to hundreds or even thousands of metabolites) in a culture as a whole, a culture medium compartment, a biomass compartment (i.e., a cell as a whole), or a specific cell compartment. Examples of metabolite sensors are known in the art and include NMR spectrometers, mass spectrometers, enzyme-based sensors (sometimes referred to as "biosensors", e.g., for monitoring glucose, lactic acid, etc.), etc. Most commonly used metabolite sensors measure the concentration of metabolites in the culture medium. Therefore, unless otherwise stated, reference to the concentration of a metabolite refers to the concentration of a metabolite in the culture medium in a bioreactor.

[0136] As used herein, sensor 3 (e.g., metabolite and biomass sensor) can also refer to a system that estimates the concentration of metabolites or the amount of biomass from one or more measured variables (e.g., provided by other sensors). For example, a metabolite sensor can actually be implemented as a processor (e.g., processor 101) that receives information (e.g., physical / chemical properties of a measurement system) from one or more sensors and estimates the concentration of metabolites from the information using one or more mathematical models. For example, a metabolite sensor can be implemented as a processor that receives spectra from a near-infrared spectrometer and estimates the concentration of metabolites from these spectra. Such sensors can be referred to as "soft sensors" (by reference to "measurements" obtained using software rather than by direct measurement). One or more sensors 3 can also include one or more sensors that measure other process conditions, such as pH, the volume of the culture, the volume / mass flow rate of materials entering and leaving the bioreactor, medium density, temperature, etc. Such sensors are known in the art. Whether one or more sensors 3 that measure other process conditions are necessary or advantageous can depend at least on the operating mode and model used in the state observer and / or controller. For example, it may be advantageous to include one or more sensors that measure the amount and / or composition of the flow entering and / or leaving the bioreactor. In addition, the one or more sensors may include a sensor that measures the volume of liquid in the bioreactor (e.g., a level sensor or a weighing scale). The measurements from the sensors 3 are transmitted to the computing device 1, which may store the data permanently or temporarily in the memory 102. The computing device memory 102 may store one or more state observer models and / or one or more controller models as described herein. The processor 101 may execute instructions to use these models and data from the one or more sensors 3 and / or simulated data to provide targets for the manipulated variables (feed flow rate, harvest flow rate, and drain flow rate) as described herein (e.g., by reference to Figure 2 , 3 and 4).

[0137] The control methods and systems described herein have many benefits over the prior art. For example, the control methods and systems described herein achieve improved continuous processing by stabilizing the flow stream. Stabilizing the flow stream, especially the permeate flow, is important for achieving integrated upstream / downstream continuous operation. The harvest stream can be connected to a downstream process, such as a purification process, which can depend on a consistent permeate flow rate. In addition, the methods and systems described herein can improve process efficiency and quality by ensuring that sufficient nutrients are provided to cells by controlling substrates (e.g., glucose). This strategy can also be used to prevent overfeeding from causing waste of culture medium or even metabolic overflow in the presence of excess nutrients. Control to a specific glucose concentration has been shown to have a positive effect on metabolism, including affecting product quality. The methods and systems of the present invention also minimize process disturbances by minimizing adjustments in the flow stream. This stabilizes the process, resulting in improved battery performance, because batteries generally perform better in a stable environment. This also has a beneficial stable quality for other key process parameters of the controller, such as dissolved oxygen (DO), pH. Achieving stable perfusion operation in perfusion mode is an important and unmet challenge in this field. Example

[0138] Exemplary methods of controlling a perfusion flow bioprocess will now be described. Example 1 Introduction

[0139] Continuous bioprocessing is becoming increasingly popular in the industry. For example, in upstream bioprocessing (i.e., all parts before the fermentation step, where cells are used, e.g., to produce a desired product), perfusion processes are often used to achieve high viable cell concentrations (VCC; >30·10 6 c mL -1 ). These can then be maintained for extended periods of time (>30 days) during such perfusion processes during the production phase. Accurate and robust control of substrate concentration is a major goal of such processes, as it helps to ensure stable and reliable process performance in terms of cell growth and productivity. Therefore, at least the feed flow rate needs to be controlled, as this determines how much cell culture medium is provided per unit time. Currently, there are different methods of varying technical complexity and varying precision to control the feed flow rate.

[0140] The simplest way to control the feed flow rate is to define a ratio of feed flow rate to VCC to be maintained. For example, for 20·10 6The flow rate can be set to 1 liter / day with a VCC of 10 cells / ml. As the cells grow (increasing VCC), the ratio of these two quantities can be kept constant. As mentioned above, this is often referred to as a "cell specific perfusion rate" (CSPR) control. In addition to the disadvantages already mentioned above, this method requires reliable VCC data, and its performance depends on how often such reliable VCC data is obtained.

[0141] A slightly more complex approach combines the use of an online biomass sensor and an online sensor for a substrate (e.g. glucose). This enables independent control of VCC and glucose concentrations, wherein the feed flow rate can then be controlled according to a defined substrate concentration set point by using a standard control algorithm (e.g. PI or PID). This approach still has disadvantages, at least in that these methods cannot take into account changes in cell size (i.e. viable cell volume) if performed in single-frequency mode and if the online value is not referenced to an offline measurement. In fact, online measurements of VCC typically use a capacitive sensor with a single frequency, which measures a signal indicating viable cell volume rather than cell number. Note that this is also the case when these measurements are used in CSPR control as described above. Solutions have been proposed that attempt to correct this by using multi-frequency scanning capacitive sensors, but these solutions still require appropriate empirical data and corresponding data analysis for each biological process to be controlled. Relatively few methods have been described for the joint control of substrate and biomass. For example, Abbate et al. (Experimental Validation of a Cascade Control Strategy for Continuously Perfused Animal Cell Cultures. Processes 2020, 8, 413) describe a cascade control structure for regulating biomass and glucose concentrations, including an inner loop for implementing feedback linearization using online estimates of biomass growth rate and glucose uptake rate, and an outer loop for controlling the linearization process using two PI controllers (one for biomass inner loop input and one for glucose inner loop input). This method uses only the output of the PI controller to control the feed rate. No other variables can be controlled by this model. Due to its basic model and related control loops, this is a relatively complex method, which means that the method is not easily transferred to different bioreactor systems. On the contrary, the method needs to be redesigned and adjusted for each system. In addition, the method does not consider the potential measurement noise and delay of the substrate sensor, which may affect the reliability and stability of the controlled process. In addition, the method cannot include restrictions on possible step changes (possible stepchange) and step change width (step change width) of the feed flow rate. Such step changes may also be detrimental to the stability and reliability of the controlled process. Finally, this approach also fails to account for potential physiological and metabolic changes in long-term cultures and requires reliable and frequent VCC data.

[0142] Therefore, the inventors set out to provide a more sophisticated method that meets the operator's needs in terms of process efficiency, reliability and robustness and can be implemented with reasonable effort independent of the bioreactor and biological system. General Methods for Controlling Perfusion Bioreactors

[0143] This example describes a method for operating a perfusion bioreactor using independent control loops: (i) working volume / level, (ii) VCC, and (iii) substrate concentration. Volume is controlled based on measured bioreactor weight by controlling permeation using PID control. VCC is controlled based on online biomass measurement via control of the effluent stream using PID control. Substrate concentration is controlled based on online measurement of substrate by controlling the feed stream using an advanced perfusion control (APC) algorithm.

[0144] The bioreactor used in this example is a bioreactor with a cell retention device connected to a control tower for controlling process parameters such as pH, DO, temperature, and agitation and individual pumps for controlling permeate flow rate, effluent flow rate, and feed flow rate. The bioreactor is also equipped with an on-line probe to measure VCC (using PID control to control the effluent flow rate to maintain a defined VCC set point) and to measure substrates such as C or N sources (using an APC algorithm to control the feed flow rate to maintain a defined concentration set point for the substrate in the bioreactor). Improved predictive control of feed flow rate

[0145] Before starting the APC algorithm and thus controlling the feed flow at the initiation / start of the perfusion culture, the following parameters were provided to the algorithm: - mathematical models describing the cellular utilization of the substrate (state-space models), - a concentration set point for this substrate that is relevant to the process performance, - the concentration of the substrate in the fresh perfusion medium supplied, - initial substrate uptake rate, - the working volume of the culture, - The measurement interval of the in-line probe measurement substrate, - Initial constant feed flow rate, - the minimum possible feed flow rate and the maximum possible feed flow rate (i.e. the low and high thresholds for the feed flow rate), - Minimum and maximum increments in feed flow rate (ie the largest expected step in feed flow rate).

[0146] In the first phase, perfusion is started using the provided initial constant feed flow rate, and the substrate is continuously measured with a substrate online probe at specific and defined time intervals during the process. This initial period is used to collect enough measurements to obtain a good prediction from the Kalman filter. Typically, only a few measurements are sufficient to have a good Kalman filter estimate, such as 5 or 6 iterations (measurements).

[0147] After this initial startup phase, the control algorithm is activated. For each new measurement of the substrate, an estimate of the measurement is calculated using a Kalman filter as further described below to take into account potential measurement errors. The estimate of the measured concentration is used to calculate the change in feed flow rate using a prediction model, which needs to maintain a previously defined substrate concentration set point for an upcoming measurement interval (see model predictive control below). The feed flow rate is then adjusted according to the predicted change required for maintaining the previously defined concentration set point of the substrate in the next measurement interval. The prediction model is used to simulate the process of substrate concentration until the next measurement of the substrate is obtained. This is used by the model predictive controller to identify the optimal control strategy within the prediction range.

[0148] The described method includes an APC algorithm for feed flow control that addresses current obstacles to efficient and accurate perfusion control by: (i) using three completely independent control loops for permeate flow rate, effluent flow rate and feed flow rate, (ii) providing a control method that is applicable to many different bioreactor systems and cell types, e.g., a plug-and-play solution with minimal prior knowledge required for rapid practical feasibility, (iii) compensating for measurement errors (e.g., random noise) as well as accounting for measurement dead time of an online substrate probe (within the APC, used as input to the APC to perform feed control), (iv) being able to predict changes in feed rate required for multiple upcoming intervals to maintain the corresponding target concentration (i.e., increasing flexibility in setting the target substrate concentration), and (v) providing a control solution that is robust to potential technical short-term failures that deviate from a single measurement, since the feed flow rate required for the upcoming interval has been predicted. Furthermore, when controlling the feed based on substrate concentration, the control method ensures optimal medium consumption, ensuring that there is no over- or under-feeding. Finally, the behavior of the system in terms of simulated substrate concentration and uptake rate between two measurements can be displayed to the user, e.g., for monitoring purposes. Proof of concept: APC for glucose control

[0149] Figure 6 The setup for this proof-of-concept experiment is shown in RM perfusion was performed in bioreactor 700. Separate control loops were used to control the following parameters: level, VCC and glucose as substrate.

[0150] The level (volume) is controlled by adjusting the permeate flow 610. The internal perfusion membrane of the RM perfusion bag serves as a cell retention device. Filtrate 610 is removed from the bioreactor to maintain a constant working volume using a gravimetric PID flow controller 630, which uses The bioreactor weight of the RM (from loadcell 640) is collected as input via the distributed control unit 650 (control tower).

[0151] The VCC is controlled by adjusting the bleed flow 660. A biomass sensor 660 (from Sartorius Biomass is measured online using ViaMass. This is used to keep VCC constant (via bleed F2660) using a PID controller 670.

[0152] The glucose concentration is controlled by adjusting the feed flow 680. Within the permeate 610, a glucose sensor 690 (specifically, a 1000nm FTIR RT-PCR system from Sartorius) is installed. This is transmitted to the computing device 620, where the measurement signal is transmitted via the OPC interconnect from The Trace software was transferred to MFCS / win 3.1 to MATLAB, which was deployed to run the advanced perfusion control (APC) algorithm for controlling glucose concentration. The APC algorithm consists of three subunits: 1) ordinary differential equation (ODE) model, 2) Kalman filter, and 3) model predictive control (MPC), which are described in detail below. At the beginning of the APC algorithm, the variables and parameters listed in Table 1 below are created and defined to initialize the algorithm. Table 1 - Variables defined for initializing the glucose control APC. Variables with a subscript "t" are updated with each new iteration, ie a new online measurement is made every interval n (h = hours).

[0153] Using the values ​​listed in Table 1, the ODE model of the reaction rate in the continuous bioreactor was repeatedly integrated between online glucose measurements. This allowed the calculated glucose concentration to be consistently obtained through numerical simulations of the process. The model used in this example includes the following equation (9): It can also be described in matrix form using equation (10):

[0154] in, and is the rate of change of substrate concentration in the bioreactor and the substrate uptake rate, x sys,t is the concentration of substrate in the bioreactor at time t (t = n is the time with the most recent data) and the substrate uptake rate at time t, F is the feed flow rate, c A,0 is the substrate concentration in the feed flow rate, V is the volume of the bioreactor, and r A is the substrate uptake rate of the cell. For the cell line and culture medium used, r A The initial value of is set to a "realistic" biological value that can be obtained from previous experiments. At this point, its exact value is considered to be of little concern within reasonable limits, as it is updated quickly using the Kalman filter's estimate.

[0155] In fact, with each new glucose measurement, a new estimate of the system state Glucose concentration and glucose uptake rate were calculated using the Kalman filter (KF) described in equation (11):

[0156] Among them, K T is the Kalman gain, defined as K T =P·C T ·(C·P·C T +R) -1 (Equation (11a)), is a vector of system state estimates (i.e., an estimate of the glucose concentration in g / l and an estimate of the glucose uptake rate in g / lh), C and R are parameters set by the user as explained in Table 1, and P is the covariance of the state, which is adjusted at each iteration according to K and based on the previous value of P using P t=(IK·C) (Equation (11b)). Therefore, when a new online measurement is received, a new Kalman gain is obtained by comparing the new measurement with the system state obtained by integrating the ODE model (Equation (9)) at the sampling time point. This is then used to calculate the new system state and update the variance-covariance matrix P. The model predictive controller then takes over to calculate the system estimate using equation (10) to calculate the control action that minimizes the control objective J. Equation (11) estimates the system state based on a weighted measurement error by comparing the latest ODE prediction value (the value obtained by integrating equation (10)) and the latest measurement value. Therefore, the Kalman gain K is used to weight the deviation between the online measurement and the state vector at the sampling time point to update / calculate the new system state.

[0157] Using a continuous-time discrete KF allows the measurement dead time (potential dead volume in the pipeline and measurement processing time) to be taken into account by calling the corresponding simulated glucose values ​​derived from the ODE model. In other words, if the expected dead time is d seconds, then the x used is sys,t The value of may be a value associated with a time d seconds before the current measurement time, which is obtained by simulating the ODE model according to the previous measurement time.

[0158] The glucose concentration estimate obtained as the output of the Kalman filter is then used as the input to a model predictive controller that solves the quadratic optimization problem of identifying the value of the desired change Δu between two steps that minimize the cost function J defined by Eq. (12) k , taking into account explicit constraints on step variation and width. The control variable u (feed flow rate) can then be adjusted accordingly.

[0159] In equation (12), u is the manipulated variable (in this case, the feed flow rate in l / h), Δu is the increment between two values ​​of the manipulated variable, and y ref is the reference trajectory of the controlled variable (in this case, the set point of glucose concentration in g / l), J k is the cost function that is minimized at each iteration of the control method (i.e., J kis the value of the function at iteration k) y is an estimate of the manipulated variable (in this case the glucose concentration in g / l, provided by the Kalman filter), Q is a weighting matrix for the controlled variable penalties, R is a weighting matrix for the manipulated variable (controller output) penalties, k is the current time point, and k+j refers to one of the multiple time points (prediction horizon) over which the function is optimized. In this example, the following values ​​are used for Q and R: for deviations in glucose, a weighting factor of 1 is used (Q), and for deviations in the control action, a weighting factor of 100 is used (R).

[0160] At the end of each iteration, the new feed flow rate is transferred from Matlab to MFCS / win 3.1 (i.e., in computing device 620) to the bioreactor control tower 650, e.g., from Sartorius B-DCU, which is operated to control the pump rate of the perfusion medium 680 accordingly. Experimental run showing the functionality of the concept model

[0161] The above concepts were used to control Glucose concentration in the RM perfusion bioreactor. These two experiments were designed to simulate the presence of a disturbance (change in the VCC set point - Run 1) and to test the performance of the method in the presence of a change in the control behavior (change in the glucose set point - Run 2).

[0162] Run 1: Set VCC setpoint to 20.10 6 cells / ml until day 7 and thereafter allowed to grow to 40.10 6 cells / ml. The glucose set point was set to a constant 5 g / l. Fig. 7A As shown, at a perfusion rate of 1 vvd (total medium exchange rate, i.e., harvest / feed rate, Fig.7D ) with a value of about 2.5·10 6 The APC algorithm was initialized after about 56 hours with an online glucose measurement rate per hour (Phase 2). Soon after, a target glucose concentration of 5 g / l was activated, causing the APC algorithm to reduce the feed flow rate from 1 vvd to 0.5 vvd ( Fig.7D ). After 72 hours, once VCC is maintained at 20·10 6 The glucose concentration was maintained at 5 g / l until day 10 ( Figure 7B ). When VCC set point is 20·10 6 cells / ml until 168 hours, the average glucose uptake rate was 0.2 g (Lh)-1 ( Figure 7C ) and slightly varying feed flow rates ( Fig.7D )(mainly lower than 41.67 ml / h), i.e. using 1 vvd. After 168 hours, change the VCC set point to 40 10 6 cells / ml increases the glucose uptake rate (see Figure 7C ), in order to maintain the glucose set point, the feed flow rate is increased accordingly (see Fig.7D This experiment demonstrated the ability of the controller to control the glucose set point at different VCC set points and during the growth period between set point changes (see Figure 7B The remarkable stability of Fig. 7A target steps on the graph and the corresponding growth-related changes in the VCC).

[0163] Run 2: Set VCC setpoint to a constant 40.10 6 cells / ml, the glucose set point was set to 5 g / l until day 8 and to 4 g / l thereafter. Therefore, the purpose of this run was to demonstrate the ability of the control method to cope with changes in the glucose set point during the culture. In addition, the feed flow rate was not started at 1 vvd as in Run 1. Instead, the APC algorithm was used from the beginning to control the feed flow rate to maintain a glucose concentration of 5 g / l ( Figure 8B ). Therefore, the initial flow value is 10.42 ml / h, i.e. 0.25 vvd ( Fig.8D ). When the culture reached 40·10 6 When the target VCC is 1 cell / ml ( Fig. 8A ), the feed flow rate automatically increases ( Fig.8D ), and the glucose uptake rate calculated by the algorithm also increased ( Figure 8C The 5 g / L glucose set point was effectively maintained for 200 hours ( Figure 8B ), the average glucose uptake rate was 0.35 g / lh( Figure 8C ), the feed flow rate is about 60 mL / h ( Fig.8D Then, the glucose set point was changed to 4 g / l and the feed flow rate was automatically reduced by the APC algorithm ( Fig.8D ). This second set point is then effectively maintained until the process is terminated after 264 hours ( Figure 8B ). Example 2 Introduction

[0164] In this example, a control approach was used to maintain stable operation of a perfusion monoclonal (mAb) process throughout all stages of the process (ie, starting from inoculation), using a controller that jointly controls VCD and volume. method

[0165] The process is carried out in three stages: 1. Inoculation (Day 0-3): No control measures are taken, and the state observer is updated in real time to monitor the combined growth / death rate. Model predictions are provided to the operator. 2. Growth (Days 3-7): Feed and harvest rates used to stabilize volume and achieve target cell specific perfusion rates. 3. Production (Days 7-31): Feed rate, harvest rate and discharge rate were manipulated to achieve target set points for viable cell density, volume and perfusion rate.

[0166] Using CHO cells in a 2 L Univessel TM The experiment was performed in a perfusion vessel. The flow rate was adjusted by adjusting the pump speed based on a calibrated peristaltic pump. The calibration was frequently updated based on the vessel weight that changes over time. The retention of cells in the harvest line was achieved using an alternating tangential flow (ATF) filtration device. In this experiment, glucose was manually controlled to maintain appropriate glucose levels by bolus additions made once per day as needed.

[0167] In all phases except the inoculation phase, the control actions are obtained by numerically solving the following minimization problem with a discrete control frequency of 2 h: V-s1≤Vmax (29) V+s2≥Vmin (30) s1,s2≥0 (31)

[0168] ODE (Ordinary Differential Equation) constraints are implemented by discretizing the range using orthogonal collocation.At each sampling time, initial candidate feed rate, drain rate and harvest rate are implemented on real device.

[0169] Numerical optimization in Microsoft Azure TM The computations are performed in Python on the virtual machine and passed to the physical equipment via the OPC-UA protocol. User input from control engineers and lab technicians is implemented through a web API and a web-based graphical user interface.

[0170] The control tuning values ​​used in this experiment (normalized to account for the measurement units so that the values ​​represent relative importance in the objective function) are shown in Table 2. <![CDATA[p x ]]> 3 <![CDATA[p v ]]> 2 <![CDATA[p p ]]> 2 <![CDATA[p f ]]> 1 <![CDATA[p h ]]> 3 <![CDATA[p b ]]> 1 <![CDATA[p VB ]]> <![CDATA[1x10 8 ]]> Table 2. Weights of the control objective function (Equation (1f)) used in this example.

[0171] Note that this adjustment will seriously affect the container P VB In addition to this severe penalty, note that the penalty for setpoint adjustment is of the same magnitude as the penalty for input movement inhibition. Therefore, the control objective strongly favors a smooth, stable input to the process. This promotes an ideal environment for bioproduction compared to traditional control methods, which place more emphasis on setpoint tracking than on input movement inhibition.

[0172] Fig. 9A and Fig. 9B Viable cell density and volume curves achieved during a 31-day run compared to the set-point target are shown. Set-point tracking performance was demonstrated by introducing a VCD set-point change at day 24. Fig. 9C The feed rate, harvest rate and drain rate that are prohibited by the controller are shown. The high penalty for perturbations in the harvest rate and feed rate can be observed by the smoothness of the corresponding curves. Fig.9D The estimated growth / death rates μ are plotted tot (Calculated using the Luenberg observer). Equivalents and scope

[0173] All documents mentioned in this specification are incorporated herein by reference as a whole. Unless the context otherwise dictates, the description and definition of the features set forth above are not limited to any particular aspect or embodiment of the invention, and are equally applicable to all aspects and embodiments described. The features disclosed in the foregoing description, or in the appended claims, or in the drawings, are expressed in their specific form or according to the device for performing the disclosed function, or the method or process for obtaining the disclosed result, as the case may be, and can be used to implement the invention in its different forms alone or in any combination of these features. Although the present invention has been described in conjunction with the above exemplary embodiments, many equivalent modifications and variations will be apparent to those skilled in the art when the present disclosure is given. Therefore, the exemplary embodiments of the present invention set forth above are considered to be illustrative rather than restrictive. Various changes may be made to the described embodiments without departing from the spirit and scope of the invention as defined by the appended claims. Any section headings used herein are for organizational purposes only and should not be interpreted as limiting the subject matter described. Any theoretical explanations provided herein are intended to enhance the reader's understanding. The inventor does not wish to be bound by any of these theoretical explanations. "And / or" used herein should be considered as a specific disclosure of each of the two specified features or components with or without the other. For example, "A and / or B" should be considered as a specific disclosure of each of (i) A, (ii) B, and (iii) A and B, just as each is set forth separately herein. Unless the context clearly dictates otherwise, as used in the specification and the appended claims, the singular forms "a", "a", and "the" include plural indicators. Ranges may be expressed herein as from "about" a particular value and / or to "about" another particular value. When such a range is expressed, another embodiment includes from a particular value and / or to another particular value. Similarly, when a value is expressed as an approximate value by using the antecedent "about" or "approximately", it will be understood that the particular value forms another embodiment. The term "about" or "approximately" with respect to a numerical value is optional and means, for example, + / -10%. Throughout the specification including the claims, unless the context requires otherwise, the words "include" and "include" and variations such as "include", "include" and "includes" will be understood to imply the inclusion of the stated integer or step or group of integers or steps, but do not exclude any other integer or step or group of integers or steps. Unless the context indicates otherwise, further aspects and embodiments of the present invention provide the above-described aspects and embodiments wherein the term "comprising" is replaced by the term "consisting of" or "consisting essentially of.

Claims

1. A computer-implemented method for controlling a biological process comprising culturing cells in a bioreactor, wherein: The bioprocess is operated as a perfusion bioprocess, the method comprising: controlling the value of one or more controlled variables selected from the group consisting of: the number or density of viable cells in the bioreactor, the volume of the culture in the bioreactor, and the concentration of one or more metabolites in the bioreactor using one or more control loops, the one or more control loops each being configured to control a non-overlapping subset of the controlled variables by setting the value of one or more manipulated variables selected from the group consisting of the feed flow rate, the effluent flow rate, and the permeate flow rate, wherein at least one of the control loops uses a controller that uses predictions of the values ​​of the subset of the controlled variables to identify values ​​of the one or more manipulated variables that optimize a control objective, the predictions of the values ​​of the subset of the controlled variables being derived from a dynamic model of the biological process that describes the rates of change of the one or more controlled variables, wherein the method comprises receiving measurements of the values ​​of the one or more controlled variables or measurements from which the values ​​of the one or more controlled variables can be derived, and automatically updating the values ​​of one or more terms of the dynamic model of the biological process using the measurements or estimates of the values ​​derived from the measurements before predicting a state trajectory of the biological process.

2. The method according to claim 1, wherein: The method is repeated each time a new measurement is received and / or wherein said estimate of said value is obtained using a state observer, and / or wherein said method comprises updating the values ​​of said one or more terms selected from cell growth rate and substrate uptake rate of said dynamic model of said biological process.

3. The method according to claim 1 or claim 2, wherein: Controlling the value of the one or more controlled variables includes controlling the value of: the number or density of viable cells in the bioreactor, the volume of the culture in the bioreactor, and The concentration of one or more metabolites in the bioreactor; and / or Wherein, controlling the value of the one or more controlled variables includes setting the values ​​of: the feed flow rate, the blowdown flow rate, and the permeate flow rate.

4. A method according to any one of the preceding claims, wherein: The control objective is to penalize the following expression: the difference between the prediction of the values ​​of the subset of the controlled variables and the corresponding predetermined target values, and A change in the value of the one or more manipulated variables.

5. A method according to any one of the preceding claims, wherein: The control objective is used to: more strongly penalize changes in the values ​​of the one or more manipulated variables than the difference between the prediction of the values ​​of the subset of the controlled variables and the corresponding predetermined target values, and / or wherein the control objective is used to prioritize the stability of the manipulated variables, and / or wherein the control objective at least equally weights the term that penalizes the change in the value of the one or more manipulated variables and the term that penalizes the difference between the prediction of the values ​​of the subset of the controlled variables and the corresponding predetermined target values.

6. A method according to any one of the preceding claims, wherein: The control objectives include: penalizing at least one term of a predicted value of a controlled variable below a predetermined first threshold, optionally wherein the term of a predicted value of a controlled variable below a predetermined first threshold penalizes the difference between the predicted value of the controlled variable and the predetermined first threshold if the predicted value is below the predetermined first threshold; and / or At least one term that penalizes a predicted value of a controlled variable that is above a predetermined second threshold, optionally wherein the term that penalizes a predicted value of a controlled variable that is above a predetermined second threshold penalizes a difference between the predicted value of the controlled variable and the predetermined second threshold when the predicted value is above the predetermined second threshold.

7. A method according to any one of the preceding claims, wherein: The one or more controlled variables include a viable cell density, and the control target uses a corresponding total cell number instead of the viable cell density as a controlled variable, Optionally, the control target includes a term that penalizes the difference between a predicted value of the total cell count in the biological process and a corresponding predetermined target value and / or a term that penalizes the difference between a predicted value of the viable cell density in the biological process and a corresponding predetermined target value.

8. A method according to any one of the preceding claims, wherein: The method comprises using a state observer to provide an estimate of the value of the one or more state variables of the biological process, the one or more state variables of the biological process including the one or more controlled variables, using one or more measurements of state variables of the biological process and a dynamic model of the biological process that describes the rate of change of the state variables, Optionally, wherein the state observer provides an estimate of the value of the one or more state variables of the biological process using a plurality of measurements of at least one of the state variables of the process, wherein the plurality of measurements comprises a first measurement and a second measurement, wherein the first measurement is taken more frequently than the second measurement, and / or Optionally, wherein the state observer provides an estimate of the value of the one or more state variables of the biological process using measurements acquired with a time delay, and wherein the state observer provides an estimate of the value of the one or more state variables of the biological process taking into account the time delay.

9. A method according to any one of the preceding claims, wherein: The method includes identifying one or more values ​​of the one or more manipulated variables that minimize the control objective over a period of time, and controlling the biological process to use one of the one or more values ​​for each of the one or more manipulated variables, and / or wherein a controller that identifies the values ​​of the one or more manipulated variables that optimize a control objective controls the two or more controlled variables using predictions of the values ​​of the subset of controlled variables from a dynamic model of the biological process that collectively describes the rates of change of the two or more controlled variables, and measurements of the values ​​of the two or more controlled variables or estimates of the values ​​of the variables obtained from the measurements.

10. A method according to any one of the preceding claims, wherein: Identifying values ​​of the one or more manipulated variables that optimize a control objective comprises, optionally, using the dynamic model of the biological process to predict a state trajectory of the biological process via one or more candidate values ​​of the one or more manipulated variables by finding values ​​of one or more state-space variables that represent a solution of the dynamic model at one or more future time points, and using the predictions of the values ​​of the subset of the controlled variables in the state trajectory as variables of the control objective, optionally wherein the method comprises selecting and comparing candidate values ​​using an optimization algorithm.

11. A method according to any one of the preceding claims, wherein: The state observer is a Kalman filter, a Luenberg observer, or a moving range estimate, and / or Wherein, the controlled variables include the viable cell density, the volume and concentration of one or more metabolites, and / or Wherein, the manipulated variables include the feed flow rate, the permeate flow rate, and the discharge flow rate, and / or Wherein, the one or more control loops include: using a control loop of a controller that identifies values ​​of the one or more manipulated variables that optimize a control objective using predictions of the values ​​of the subset of controlled variables from a dynamic model of the biological process that describe rates of change of the one or more controlled variables; and One or more other control loops, optionally wherein the one or more other control loops do not use a dynamic model of the biological process, and / or wherein the one or more other control loops use a controller selected from a proportional controller, a proportional-integral controller, and a proportional-integral-derivative controller.

12. A method according to any one of the preceding claims, wherein: The manipulated variable includes the permeate flow rate, and the control target includes a term that penalizes a difference between a candidate permeate flow rate and a corresponding predetermined target value, a term that penalizes a candidate value of the permeate flow rate that is lower than a predetermined first threshold, and / or a term that penalizes a candidate value of the permeate flow rate that is higher than a predetermined second threshold, and / or Wherein, the control target includes an item that penalizes the difference between the candidate medium exchange rate and the corresponding predetermined target value, an item that penalizes the candidate value of the medium exchange rate that is lower than a predetermined first threshold, and / or an item that penalizes the candidate value of the medium exchange rate that is higher than a predetermined second threshold.

13. A method according to any one of the preceding claims, wherein: The controller identifies values ​​of the one or more manipulated variables that optimize a control objective using predictions of values ​​of the subset of controlled variables from a dynamic model of the biological process that describe rates of change of the one or more controlled variables, the subset of controlled variables controlled by the control loop using the controller comprising: (i) concentration of one or more substrates, optionally wherein the one or more manipulated variables include a feed flow rate, and / or wherein the one or more control loops further comprise a control loop for controlling the volume as a controlled variable using the permeate flow rate as a manipulated variable, the control loop optionally using a P, PI, or PID controller, and a control loop for controlling the viable cell density as a controlled variable using the effluent flow rate as a manipulated variable, the control loop optionally using a P, PI, or PID controller, and / or (ii) said volume and said viable cell density, optionally wherein said one or more manipulated variables include said permeate flow rate, said effluent flow rate, and said feed flow rate.

14. The method according to any one of the preceding claims, further comprising one or more of the following: obtaining a measurement of one or more of said controlled variables or a variable from which one or more of said controlled variables can be derived, repeating the control method at one or more time points during operation of the bioprocess to determine corresponding values ​​of the one or more manipulated variables, repeating the control method at regular intervals during operation of the bioprocess to determine corresponding values ​​of the one or more manipulated variables, receiving a set of measurements of one or more of the controlled variables or variables from which one or more of the controlled variables can be derived, and determining a value of the manipulated variable using the one or more controller loops and the measurements, optionally wherein, repeating the determining step each time a new set of measurements is received, providing a set of values ​​of the manipulated variables determined by the one or more control loops to a user, a user interface, a computer, or an actuator, providing a signal to a control unit, said signal being used to control one or more effectors to set the value of said one or more manipulated variables according to the value determined by said one or more control loops, Optionally, values ​​of one or more parameters of the controller are received from a computer device, a data store, or a user via a user interface, wherein the parameters include parameters selected from the following: one or more predetermined targets for one or more controlled variables (e.g., set points for the one or more controlled variables; one or more of the predetermined targets may be variable during the course of the bioprocess, i.e., a different set point may be provided for each of a plurality of time points in the bioprocess), one or more parameters of the bioprocess (e.g., parameters related to the physical configuration of the bioprocess, the physical constraints of the bioprocess, the characteristics of the cell culture, temperature, etc.), one or more parameters of a dynamic model of the bioprocess (e.g., coefficients, initial values, etc.), a one or more predetermined thresholds of one or more controlled variables (e.g., a low threshold / high threshold below which a penalty is included in the objective function), selection of one or more controlled variables, selection of one or more manipulated variables, values ​​of one or more parameters of the control objective (e.g., values ​​of weights applied to any term of the control objective), and selection of a state observer model (e.g., a Kalman filter, a moving range estimator, a specific cost function of the moving range estimator, a dynamic model of the biological process to be used by the state observer, one or more parameters of the state observer, such as a gain of a Kalman filter, etc.), a time period for integration of the dynamic model of the biological process, and an iteration frequency of the control method, Predictions of values ​​of one or more states of the biological process are provided to a computing device, a data store, or a user via a user interface, the predictions being determined by integration of the dynamic model of the biological process.

15. A system for controlling a biological process, the system comprising: at least one processor; as well as at least one non-transitory computer-readable medium containing instructions which, when executed by the at least one processor, cause the at least one processor to perform the method according to any one of the preceding claims; Optionally, the system further comprises one or more of the following items operably connected to the processor: User interface; one or more biomass sensors; one or more metabolite sensors; one or more volume / level sensors; Distributed control units; and One or more effector devices, optionally, wherein the one or more effector devices are operable to set the value of one or more manipulated variables.

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