Method and system for navigating a production process

Abstract

A method (1000) for navigation through one or more sequences of operating conditions referring to process variables including manipulated variables (MVs) and controlled variables (CVs) of a production process, the method includes: determining for the sequence(s) of operating conditions connecting tracks, each connecting track providing a connection between two consecutive operating conditions of the sequence(s) of operating conditions. Based on at least one dead-time between the MVs and the CVs, at least one lead-time for the MVs with respect to the CVs is determined. Based on a planned start time of at least one CV and the at least one lead-time for the MVs, a navigation start time for navigation through the one or more sequences of operating conditions of the production is determined. At the navigation start time, navigation through the sequence(s) is started by executing the MVs in accordance with the at least one lead-time. At each sampling time after the navigation start time and until a last operating condition of the sequence(s) of the operating conditions is reached, the following processes are repeated: calculating, using a process response model of the production process, MVs for the navigation so that the process variables are expected to stay on the connecting tracks; and executing the calculated manipulated variables.

Description

[0001] Method and system for navigating a production process

[0002] The present disclosure relates to navigating a production process for producing a specified product, in particular to navigate through operating conditions of the production process such as an industrial production process, a corresponding computer program product and / or a computer-readable medium, and a corresponding system, in particular a corresponding control system.

[0003] Technical background:

[0004] Considering the control of an industrial process, a production line can be viewed as a process with multiple output variables that are affected by multiple input variables. There are typically multiple input variables that are important to a process of producing products with various properties, along with multiple output variables such as the physical or chemical qualities of the products. For example, a paper machine may involve input variables such as different refined fibers, chemical additions, dyes, water, steam, electricity, various flows, pressures, temperatures, and speed settings to produce paper sheet with different output variables such as paper sheet’s areal weight, moisture contents, sheet thickness, strength, color, and other properties. The relationships between the input variables and output variables of the process are complex. The output variables from a manufacturing process are also known as controlled variables (CVs) and the input variables are also called manipulated variables (MVs).

[0005] During a steady-state operation, a control system compares the process output variables (CVs) with their corresponding targets and generates the control actions for the process input variables (MVs) so that the controlled variables will follow their corresponding targets closely.

[0006] In particular, advanced process control, such as multi-variable model-based predictive control (MPC), has been applied to gain better product quality. Generally, MPC uses process models to predict the future movements of CVs based on past MV moves and planned MV moves. However, for multivariable complex processes, open-loop or steady-state feedback control approaches may not provide satisfactory control, in particular during production changes. Usually, a production line is capable for producing a range of products that meet various specifications. To produce products with various specifications, both process input and output variables would need to be operated at different conditions.Even for highly experienced production personnel it is often a major challenge to find the right settings for the input and output variables for producing products that meet various product quality specifications and also achieve production goals, such as maximizing production throughput or minimizing lost time, material, chemical, and energy usage among operating condition changes.

[0007] There are techniques that focus on identifying the mode of transition changes or the root causes of bad changes for better informing production personnel so that the production personnel may monitor production changes or correct identified root-cause issues. There are also techniques that utilize the historical data of production changes to extract the better change records as a reference for setting up and managing the similar changes in a new change plan. Furthermore, other techniques may try to find a better trajectory in between the current and the future product target to minimize the time needed for process change so as to reduce the potential lost time and wasted resources. However, none of these techniques addresses the need that require a production process to navigate through complex sequences of operating conditions at defined time intervals in order to make desired product specifications.

[0008] Summary of the invention

[0009] In view of the above, and for other reasons, there is a need for the present invention. Thus, according to the independent claims, respective typically computer-implemented methods, and a (control) system for performing said methods as well as respective computer program products and computer-readable media are provided.

[0010] According to an aspect of a typically computer-implemented method for navigation through one or more sequences of operating conditions of a production process in order to produce a specified product, the one or more sequences of operating conditions comprising nominal values and bounds for process variables of the production process, the process variables (PVs) including manipulated variables (MVs) and controlled variables (CVs), the method includes determining for the one or more sequences of operating conditions connecting tracks. Each connecting track provides a connection between two consecutive operating conditions of one of the one or more sequences of operating conditions. Based on at least one dead-time between the manipulated variables and the controlled variables, at least one lead-time for the manipulated variables with respect to the controlled variables is determined. Based on the at least one lead-time for at least one manipulated variable and a planned start time of at least onecontrolled variable, a navigation start time for navigation through the one or more sequences of operating conditions of the production process is determined. At the navigation start time, navigation through the one or more sequences of operating conditions of the production process is started by executing the manipulated variables in accordance with the at least one lead-time. Thereafter (after starting navigation and after the navigation start time, respectively), at each sampling time of typically a plurality of sampling times, calculating, using a process response model of the production process, manipulated variables for the navigation through the one or more sequences of operating conditions of the production process so that the process variables are expected to stay on the connecting tracks, and executing the calculated manipulated variables to navigate (further) through the one or more sequences of operating conditions are repeated until a last operating condition of the one or more sequences of the operating conditions is reached. At or after completion of the last operating condition the navigation (through the one or more sequences of operating conditions) can be terminated.

[0011] The relation between MVs and CVs that characterizes the cause-effect connection between the input and output variables may be described by a process response model. To generalize the characterization of the process, the combination of MVs and CVs called process PVs can be considered. This is because the condition of the process is often determined by the settings of the PVs.

[0012] Accordingly, the process response model can be a function to determine the controlled variables based on the manipulated variables.

[0013] Alternatively, the process response model is a function to determine the controlled variables based on the manipulated variables and disturbance variables (DVs) of the production process.

[0014] Like MVs and CVs, DVs can be measurable or at least predictable.

[0015] Similar as MVs, DVs can influence the CVs.

[0016] However, different to MVs, DVs are considered not controllable or adjustable. Nevertheless, DVs may influence the CVs and, thus, may have to be taken into account.

[0017] For example, a DV may refer to an uncontrollable quality of an input material of the production process such as a raw material or a fuel. As such a DV may refer to composition of the raw material or a combustibility of the fuel. Other exemplary DVs are ambient temperature and ambient moisture that may e.g. be important for producing sheet paper.Preferably, the process response model characterizes a dynamic behavior of the production process.

[0018] The process response model may in particular be a function that characterize a dynamic behavior of the production process.

[0019] The dynamic process response model includes and / or is based on at least one of: transfer functions in the Laplace domain, in particular a matrix of transfer functions in the Laplace domain, a regression model, historical data from the industrial process, and / or a trained model.

[0020] Typically, the trained model is trained by machine learning using historical data, in particular historical data of MVs (and optionally DVs) and CVs of the production process.

[0021] The dynamic process response model is typically a multiple-input and multiple-output process response model.

[0022] Further, the dynamic process response model typically takes into account deadtimes between the MVs and the CVs (and optionally any deadtimes between the DVs and the CVs.

[0023] Generally, the dynamic process response model can be based or even include any computational model of the production process such as transfer function(s) for mapping the MVs (and optionally the DVs) onto the CVs, in particular discrete transfer function(s) or a transfer matrix for mapping the MVs (and optionally the DVs) onto the CVs.

[0024] Due to using the process response model, process variables are expected to stay on their desired connecting tracks.

[0025] In the following, the connecting tracks are also referred to as navigation tracks or tracks for short.

[0026] Due to executing the manipulated variables in accordance with the at least one lead-time (ahead of the planned start time(s) of the controlled variable(s) in accordance with the dead-time(s)), the navigation through the sequence(s) of operating conditions can (is, under normal production conditions, at least expected to) be completed as planned.

[0027] This is not only important for synchronizing production processes but is often critical for producing a product to the desired quality and avoiding the waste that can result from terminating the navigation early or late. For example, in paper manufacturing, terminating thenavigation early can result in paper quality (such as weight, moisture, etc.) not reaching the desired specifications, and hence producing unsellable off-spec paper. On the other hand, terminating the navigation late would lead to the unnecessary over production of a particular quality of paper, so as increasing operational costs.

[0028] The navigation may in particular be terminated close to or even at the planned navigation end time.

[0029] Automatically controlling the navigation through sequence(s) of operating conditions as explained herein usually (provided that no unforeseen problems such as machine defects occur) ensures terminating in time. This has so far mostly been achieved empirically.

[0030] Navigation through sequence(s) of operating conditions, as explained herein, may also be considered as performing the navigation with manipulated variables which are time-shifted with respect to the controlled variables in accordance with the lead-time(s) and / or the dead-time(s) between the manipulated variables and the controlled variables.

[0031] Typically, the planned start time of the respective controlled variable is a time at which a change of the controlled variable should start.

[0032] Further, the planned start time preferably is determined as a clock time of a controller for navigation through the operating condition(s).

[0033] The sequence(s) of operating conditions preferably include a plurality of operating conditions, in particular at least 2, more particular at least 3-5 or even at least 6-10 operating conditions.

[0034] Typically, each operating condition of the one or more sequences of operating conditions includes a nominal value, bounds, in particular an upper bound and a lower bound, and a corresponding time information for (at least) one of the process variables of the production process.

[0035] An operating condition may also include a nominal value, bounds, and a (common) time information for more than one of the process variables, for example for two or three process variables.

[0036] The time information is typically different to the clock time of the controller. The time information may in particular refer to a design time (or timeline).Each operating condition of the one or more sequences of operating conditions may be defined by a nominal value, an upper bound and a lower bound for one or more of the process variables of the production process, and a time information for each nominal value and each operating condition, respectively, in particular a corresponding time difference with respect to a first of the operating condition or a respective time difference between two consecutive operating conditions.

[0037] Preferably, each of the operating conditions of manipulated variables includes, for one (or more) of the manipulated variables, a nominal value (for the respective manipulated variable), an upper bound (for the respective manipulated variable) and a lower bound (for the respective manipulated variable).

[0038] Further, each of the operating conditions of the controlled variables typically includes a nominal value, an upper bound and a lower bound for one of the controlled variables.

[0039] In particular, an operating condition may include a nominal value, an upper bound, a lower bound and a time information for one process variable.

[0040] As used herein, the terms of manipulated variable(s), controlled variable(s) and / or process variable(s) can refer to scalar value, vector quantities or arrays with plurality of scalar quantities (values).

[0041] The terms manipulated variable or controlled variable may refer to a scalar quantity (value) for a single input and single output production process. In this embodiment, the nominal values and the bounds are scalar values. The term process variable which consists of manipulated variable and / or controlled variable, hence a process variable could be either a scalar quantity or a vector quantity or an array for a single input and single output production process.

[0042] However, for a multiple inputs and multiple outputs production process, the terms of manipulated variable(s), controlled variable(s) and / or process variable(s) are typically vector quantities or arrays with plurality of scalar quantities (values).

[0043] In further embodiments, one or more of the MVs and / or CVs may have scalar values for their nominal values and bounds, while the nominal values and bounds for the remaining MVs and / or CVs are vector quantities or arrays.The connecting tracks are typically determined for at least one sequence of operating conditions of controlled variables and at least one sequence of operating conditions of manipulated variables one or more sequences of operating conditions, in particular one sequence of operating conditions of CVs and one sequence of operating conditions of MVs.

[0044] Each connecting track may include one of, preferably several or even all of: a nominal line connecting the nominal values of two consecutive operating conditions (of one PV), a lower boundary line connecting the lower bounds of two consecutive operating conditions (of one PV), and an upper boundary line connecting the upper bounds of the consecutive operating conditions (of one PV).

[0045] The connecting line may include or even be a straight line or a curve line such as cubic spline. The connecting tracks for a process variable may form a band connecting the bounds and the nominal values of the operating conditions of the PV.

[0046] Prior to determining the connecting tracks, the one or more sequences of operating conditions are typically specified.

[0047] In particular, the sequence(s) of operating conditions may be specified by a user, in particular an operator of the production process.

[0048] The user may in particular specify a sequence of operating conditions of the CVs and a sequence of operating conditions of the MVs.

[0049] Likewise, the user may specify the planned start time of at least one controlled variable, typically planned start times of all controlled variables.

[0050] Alternatively, the planned start time may be determined by a separate control system.

[0051] In addition, the user may be provided with a guidance for specifying the sequence(s) of operating conditions.

[0052] Alternatively or in addition, the one or more sequences of operating conditions and / or the planned start time are received prior to determining the connecting track, in particular from a separate control system.

[0053] Prior to starting navigation (prior to the navigation start time), the method typically further includes at least one of, typically at least several or even all of:make the manipulated variables lead the corresponding controlled variables in accordance with the at least one calculated lead-time,

[0054] determine all deadtimes between the manipulated variables and the controlled variables;

[0055] determine, based on the at least one deadtime, in particular all non-vanishing deadtimes, a respective lead-time for the manipulated variables with respect to the controlled variables,

[0056] make each of the manipulated variables lead the corresponding controlled variables in accordance with the respective calculated lead-times, and

[0057] update the one or more sequences of operating conditions of process variables in accordance with the at least one lead-time, preferably in accordance with all calculated lead-times.

[0058] In particular, the navigation start time can be determined from the earliest lead-time among all manipulated variables.

[0059] More particular, the navigation start time may be as an earliest start-time of the manipulated variables.

[0060] Alternatively, the navigation start time may be determined as a medium start-time of the manipulated variables, or a start-time of a specified pair of a manipulated variable and a controlled variable, for example a pair of manipulated variable and controlled variable, which has a high or even the highest priority.

[0061] The lead-time of a manipulated variable with respect to a plurality of controlled variables can be a longest, a medium, a weighted-average, or a specific lead-time among the lead-times with respect to the plurality of controlled variables.

[0062] Accordingly, the navigation start time can be one of an earliest, a medium, a weighted-average, or a specific start-time among the start times with respect to the plurality of manipulated variables.

[0063] Updating the one or more sequences of operating conditions can include at least one of, preferably both of:transferring the at least one sequence of operating conditions of the CVs and the at least one sequence of operating conditions of the MVs into a production timeline so that the manipulating operating conditions lead the corresponding control operating conditions variables in accordance with the at least one lead-time, preferably in accordance with all nonvanishing deadtimes, and

[0064] forming a combined sequence of the operating conditions.

[0065] Preferably, the combined sequence of the operating conditions includes all operating conditions of MVs and CVs in chronological order.

[0066] Accordingly, forming combined sequence of the operating conditions facilitate the navigation.

[0067] The updated one or more sequences of operating conditions, in particular the combined sequence of the operating conditions is used for at least one of, preferably all of:

[0068] starting the navigation,

[0069] calculating the manipulated variables for the navigation, and

[0070] executing the calculated manipulated variables.

[0071] Executing the calculated manipulated variables typically includes sending the calculated manipulated variables to actuators of a machine or production facility for producing the specified product.

[0072] In addition, at every sampling time, the calculated manipulated variables are adjusted or updated based on one of, preferably all of: measured controlled variables, future tracks of the PVs, constraints of the PVs, and weighting priorities of the PVs according to a model predictive control scheme.

[0073] The updated manipulated variables are calculated for the navigation through a remaining part of the one or more sequences of operating conditions of the production process.

[0074] The calculated manipulated variables can in particular be updated by: optimizing a cost function determined from the future tracks of the process variables, future actions of the manipulated variables, predicted future controlled variables, and / or priority weightings for process variables.Typically, the future process variables are predicted for a prediction time horizon and the future actions of the manipulated variables are predicted for a control time horizon shorter than the prediction time horizon.

[0075] In particular, the predicted future controlled variables can be calculated based on or using the past history of the manipulated variables, the future actions of the manipulated variables, updated process variable feedbacks, and the process response model for the prediction time horizon for the controlled variables.

[0076] According to an embodiment, calculating the manipulated variables using a process response model includes at least one of, preferably all of:

[0077] designing and / or selecting a quadratic cost function of differences between the predicted future process variables and the nominal process variables and differences between consecutive manipulated variables with respective priority weightings over the respective prediction time horizon or control time horizon of the process variables,

[0078] deriving constraints of process variables from the future tracks of process variables over the respective prediction time horizon or control time horizon of the process variables,

[0079] performing constrained optimization of the (designed and / or selected) cost function by deriving current and future control actions over the control time horizon while keeping all process variables at least substantially satisfying the derived constraints over the respective prediction time horizon or control time horizon of the process variables,

[0080] adjusting the priority weightings and iterating the constrained optimization to keep process variables at least substantially staying on track for the process variables.

[0081] For the constrained optimization, the nominal values of the tracks are used as the references for all process variables.

[0082] Alternatively or in addition, the upper and lower bounds of the tracks are used as the constraints for the constrained optimization.

[0083] The calculated manipulated variables for the respective sampling time (or interval) are calculated such that the PVs stay on their connecting track, follow the nominal value, stay near a bound, or anywhere between the bounds as specified by the weighting priorities.According to an aspect of a control system for navigation through a sequence of operating conditions of a production process, the control system includes one or more computing units and / or one or more controller(s) (each providing at least one computing unit) configured to perform any of the methods and / or processes as explained herein.

[0084] The controller can be an internal model controller or model predictive controller.

[0085] The system may also include a distributed control system.

[0086] The production process can be a continuous or a batch production process.

[0087] Preferably, the production process is an industrial production process.

[0088] The production process can e.g. be a papermaking process, pulp-making process, or chemical product process.

[0089] Furthermore, the production process may include a product specification transition process.

[0090] According to an aspect of a computer program product or typically non-volatile computer-readable medium, the computer program product and the computer-readable medium, respectively, includes instructions which, when executed by one or more computing units, in particular a computing unit of a controller, cause the computing unit(s) to carry out any of the methods and / or processes as described herein.

[0091] The methods, devices and systems described herein also allow in particular address moving from producing one specification of product to the next. During this phase of operation, the production process could otherwise become unstable, interrupted, and producing large amount of off-spec production. It is crucial important that the production process efficiently navigate through a sequence of operating conditions until it reach the final operating condition for producing the desired product.

[0092] The described technique typically includes specifying connecting tracks for a sequence of operating conditions of both MVs and CVs, determining the lead-time for MV and the start time of the navigation task, starting the navigation calculation at start time and repeating the navigation calculation at every sampling time with latest process variables, adjusting manipulated variables as the navigation progress, keeping process variables staying on their tracks between operating conditions until the entire sequence of operating conditions for the set of process variables are completed.Further advantages, features, aspects and details that can be combined with embodiments described herein are evident from the dependent claims, the description and the drawings.

[0093] Brief description of the Figures:

[0094] The details will be described in the following with reference to the figures, wherein

[0095] Fig. 1 is a flow chart of a method for navigation through one or more sequences of operating conditions of a production process in order to produce a specified product according to embodiments.

[0096] Fig. 2A is a schematic view of a process response model of the production process that can be used for the method for navigation shown in Fig. 1 according to an embodiment.

[0097] Fig. 2B is a schematic view of a production system for producing a specified product including a control system for controlling a production process according to an embodiment.

[0098] Fig. 3 A to 4C illustrate determining connecting tracks according to embodiments.

[0099] Fig. 5 A and 5B illustrate determining one or more lead-times for the manipulated variables with respect to the controlled variables according to embodiments.

[0100] Fig. 6 illustrates a step response of a stable transfer function according to an embodiment.

[0101] Fig. 7 illustrates predicting of process output that can be used in a cost function for calculating manipulated variables for the navigation through the one or more sequences of operating conditions according to an embodiment.

[0102] Fig. 8 illustrates navigation through one or more sequences of operating conditions of a production process in order to produce a specified product according to an embodiment.

[0103] Detailed description of the Figures and of embodiments:

[0104] Reference will now be made in detail to the various embodiments, one or more examples of which are illustrated in each figure. Each example is provided by way of explanation and is not meant as a limitation. For example, features illustrated or described as part of one embodimentcan be used on or in conjunction with any other embodiment to yield yet a further embodiment. It is intended that the present disclosure includes such modifications and variations.

[0105] Within the following description of the drawings, the same reference numbers refer to the same or to similar components. Generally, only the differences with respect to the individual embodiments are described. Unless specified otherwise, the description of a part or aspect in one embodiment applies to a corresponding part or aspect in another embodiment as well.

[0106] In the given embodiments, a papermaking process is used as an example for illustrating the general aspects described above. The described method and system can be equally applicable for other types of production processes, in particular industrial production processes.

[0107] Referring to Fig. 1, an exemplary computer-implemented method 1000 for navigation through operating conditions of a production process is explained.

[0108] In a block 1100, connecting tracks are determined from (and for) one or more sequences of operating conditions OCXof process variables (PVs) of the production process, in particular one or more sequences of the operating conditions of manipulated variables (MVs) and one or more sequences of the operating conditions of controlled variables (CVs) of the production process.

[0109] In one embodiment, there is one sequence of operating conditions for each (relevant) PVs.

[0110] As indicated by block 1010, the sequence(s) of operating conditions OCXare typically predetermined, in particular specified by an operator for the production process.

[0111] The sequences of operating conditions include nominal values and bounds for the process variables of the production process.

[0112] Each operating condition may be given by a nominal value, an upper bound and a lower bound for at least one of the process variables of the production process and a time information.

[0113] In a block 1100, typically after receiving the sequence(s) of OCs, the connecting tracks can be calculated based on the sequence(s) of operating conditions OCXalone.

[0114] In one embodiment, for each PV, the nominal values of consecutive operating conditions OCX, OCx+1of the respective PV are connected, the upper bounds of the consecutive operating conditions of the respective PV are connected, and the lower bounds of the consecutiveoperating conditions of the respective PV are connected, for example by respective lines. This is described in detail below with reference to Figures 3 A to 4C.

[0115] In a subsequent block 1200 of method 1000, desired lead-time(s) of the manipulated variables from the controlled variables are determined.

[0116] Typically, a plurality of lead-times is determined in block 1200.

[0117] In particular, the lead-time(s) of the manipulated variables are calculated based on dead-time(s) between the manipulated variables and the controlled variables. This is described in detail below with reference to Fig. 2A.

[0118] Furthermore, based on a planned start time tyiof at least one controlled variable, in particular an earliest CV, and the lead-time(s), a navigation start time tstartfor navigation through the sequences of operating conditions of the production is also determined in block 1200 of method 1000.

[0119] The planned start time tyiof the at least one controlled variable, typically planned start times of all controlled variables CVs are typically planned (specified) in advance (in the planning phase) and may be received, as indicated by the dashed-dotted arrow between blocks 1020 and 1200.

[0120] As indicated by the time axis tp, the navigation start time tstartcan in particular refer to a production timeline and / or be determined as a clock time of a controller performing the navigation.

[0121] In a subsequent block 1300 of method 1000, navigation through the sequence(s) of operating conditions of the production process is started.

[0122] Note that prior to starting navigation, a single combined sequence of the operating conditions, in which the OCs are sorted according to their chronological order, may be formed.

[0123] Starting navigation can be achieved by executing the earliest manipulated variable(s) of the sequence(s) of operating conditions, in particular by sending the earliest manipulated variable(s) to actuators of the production process and the production system, respectively.

[0124] Thereafter, navigation can be performed iteratively until a last operating condition OCx endof the sequence(s) of the operating conditions OCX, e.g. the last operating condition of the combined sequence is completed, in particular at the end time tend.At this time or thereafter, the navigation is terminated in block 1600.

[0125] Referring to Fig. 2A, a process response model RM that can be used for the method 1000 shown in Fig. 1 is explained. From process control perspective, an industrial production process or line can be treated as a process where multiple inputs (w) feed into the process and multiple outputs (y) come out from the process, as indicated by the arrows in Fig. 2A.

[0126] The input variables can be either manipulated variables (MVs) and / or disturbance variables (DVs).

[0127] For the simplicity of illustration, the present description focuses on the manipulated variables as the input variables to the process. The output variables are known as “controlled variables” (CVs). The input and output variables can be related to each other as

[0128] y(t) = ^(u(t),t) (1)

[0129] where t is time, u(f) and y(f) are input (MV) and output (CV) variables respectively. The function g is known as “process response model” which characterizes the cause-effect relation between the input and output variables. In general, process response model may include timevarying nonlinear functions that characterize the process dynamic behavior.

[0130] For the illustration purpose, the linear and time-invariant process response models are described in detail. A linear and time-invariant process response model that associates the input and output variables are often expressed as a transfer function G(s) in the Laplace transformed.s-domain as:

[0131] y(s) = G(s)u(s) (2)

[0132] where y(s) and u(s) are the Laplace transformation of input and output variables and G(s) is the Laplace transformation of g function that represents the dynamic response model of a process. For a single input and single output process (SISO), the transfer function is often formulated as:

[0133] G(s) = ^-ds(3)

[0134] where N(s) and (s) are numerator polynomial and denominator polynomial respectively and d represents the deadtime delay of the output y with respect to the input u. As an example, a first-order with dead-time delay process is expressed as:

[0135] G

[0136]

[0137] O) = ■^rd’’su)where kp, rp, and dpare process response gain, time constant, and dead-time respectively. For a multiple inputs and multiple outputs (MIMO) process, the function that associates multiple MVs and multiple CVs is a matrix that connects the MV vector and CV vector as:

[0138] >10)’ 'Ui(s)'

[0139] y2(s) _ pVijGOe-di7.sl u2(s)

[0140] yO) = = G(s)u(s) (5)

[0141] nxm

[0142]

[0143] .yn(5). -Um (s). where5) and u(s) are vectors of CVs and MVs respectively, n and m are the sizes of j’ and u vectors respectively.

[0144] G(s) is a nxm matrix of transfer functions, i and j are indices in y and u vectors respectively. dy is the dead-time delay of the / -th output^, with respect to the / -th input

[0145]

[0146] The process response model may also be expressed using discrete transfer function as:

[0147] 'yi(z)' 'u^zy

[0148] y2(z) = fe£lz-h; u2(z)

[0149] y(z) = l = G(z)u(z)

[0150] LDi,(z)JJ nxm

[0151]

[0152] .yn(z). Mm GO.

[0153] where z = eTsSis a discrete variable and T5is the sampling interval.

[0154] ly is the deadtime delay of the z-th output^, with respect to the / -th input in the number of sampling intervals, ly is usually rounded up to an integer number.

[0155] The operation of a process to produce a specified product is often determined by certain settings of MVs and CVs. The combination of MVs and CVs is called “process variables (PVs)”:

[0156] p

[0157]

[0158] w = <’)

[0159] For a production process to produce a product with certain specifications, the process will have to be operated under a set of input and output parameters. In other word, a proper set of process variables are often used to specify an operating condition. An operating condition (OC) is specified with a set of nominal values ( / X) and their upper (py and lower bounds pL) for a process variable p. While a production process produces different specifications of products, the process is operated at different operating condition.

[0160] Fig. 2B illustrates a corresponding production line (production system) 500 for producing the specified product including a control system 550 for controlling the production process of producing a specified product.Control system 550 is configured to control the navigation through the sequence(s) of operating condition as described herein, in particular to perform method 1000 explained above with respect to Fig. 1.

[0161] For this purpose, production system 500 has actuators 580 for adjusting the production process in accordance with control signals which are received from control system 550 for the manipulated variables, and sensors 530 for measuring feedback data of the running production process referring to the process variables (process variables feedback, FB).

[0162] Control system 550 may be implemented by a single controller or several controllers and a distributed control system, respectively.

[0163] As shown in Fig. 2B, control system 550 is typically functionally connected with a separate control system 560 for receiving the (specified) sequence(s) of OCs and the planned start time tyf with respect to the production time line.

[0164] As already explained above, when a production line (system) is scheduled to change its product specification, the process and control system 550, respectively, often needs to navigate through a sequence of operating conditions.

[0165] Table 1 and Fig. 3 A show an exemplary sequence of operating conditions specified for a process variable p (one manipulated variable Uj of m MVs in the exemplary embodiment), e.g. in block 1010 of method 1000.

[0166] Exampleofasequenceoperatingconditions(OC)of MV(Uj, j=1,2,...,m)

[0167]

[0168] Operating

[0169] Condition (uOCf) limeft3) Nominal (UN) Lower Bound (uj Upper Bound (UH) uOC10.00 50 45 55 uOC27.00 53 43 59 uOC313.00 55 43 65 uOC430.00 55 43 65

[0170]

[0171] uOC539.00 52 45 60 Table 1. Exemplary sequence of operating conditions uOCafor MVs

[0172] In this example, each operating condition OCawith a=l, 2,..., 5 is defined by a nominal value an upper bound UjHaand a lower bounds M, / ", for the process variables Uj at a respective time (time information).

[0173] Fig. 3B and Fig. 3C illustrate connecting tracks uTf-a+1that can be formed (in block 1100 of method 1000) between consecutive operating conditions uOCa, uOCa+1of MV Uj.For this purpose, a respective line may be determined between consecutive (pairs of) nominal values ujNa, ujNa+1of MV u, (nominal lines of MV w7), between consecutive (pairs of) upper bounds UjHa, u]Pf+1of MV Uj (upper boundary lines of MV w7), and between consecutive (pairs of) lower bounds

[0174]

[0175] UjLa+1of MV Uj (lower boundary lines of MV w7).

[0176] For sake of clarity, in Fig. 3B, reference signs uJN3’4, ujr1-4, and ujL3’4are only provided for the respective lines of the connecting track uT}34between operating conditions uOC3, uOC4.

[0177] Typically, the entirety of the connecting tracks uTf-a+1forms a band connecting the bounds and the nominal values of the respective manipulated variable («,).

[0178] The connection lines can be straight lines, as shown in Fig. 3 A, or smooth lines like cubic spline lines, as shown in Fig. 3B.

[0179] Likewise, respective connecting tracks are also formed for an exemplary sequence of seven operating condition yOCbof controlled variables^, of the process according to table 2 (and Fig.

[0180] 4A) which are to be controlled by the manipulated variables Uj of Fig. 3 A and table 1, respectively.

[0181] Bcampleof asequenceof operatingconditions (OCs) of CV(y„ i=1,2 n)

[0182]

[0183] Operating

[0184] Condition (yOC5) ■fimeC5) Nominal (YN) Lower Bound (yj Upper Bound (YH) yOC10.00 200 185 205 yOC23.00 210 190 215 yOC38.00 215 195 230 yOC415.00 218 200 255 yOC521.00 230 215 265 yOC627.00 240 235 280

[0185]

[0186] yOC737.00 275 270 285

[0187] Table 2. Exemplary sequence of operating conditions yOCbfor CVs

[0188] As shown in Fig. 4B and 4C, connecting tracks yTtb’b+1(with b=l, 2, 7) for the CVs can also be formed by straight nominal lines yiNb-b+1between consecutive pairs of nominal values yiNb, yiNb+1, straight upper boundary lines yiHb,b+1between consecutive pairs of upper bounds yiHb, yiHb+1, and straight lower boundary lines yiLb’b+1between consecutive pairs of lower bounds yiLb, yiLb+1(Fig- 4B) or respective smooth lines (Fig. 4C).Note that different process variables typically have a different number of operating conditions referring to the PV.

[0189] Preferably, the tracks are determined for all process variables to be taken into account by the process model.

[0190] To successfully navigate through the operating conditions and stay on the tracks, the present control technique takes into account of the process dynamics in its calculation. More specifically, the dead-time delays of the process responses are coordinated between CVs and MVs. In order to start the navigation of a CV at a planned time, a lead-time for the first operating condition of the MV is set to lead from the first operating condition of the CV by the lead-time of the process responses, as shown in Fig 5B for table 3, which is also shown in Fig. 5A.

[0191] Exampleof asequenceof operatingconditions(OC) of FVon timeline (pkIk=1,2 n+m)

[0192]

[0193] Operating

[0194] Condition (pOC0) Clocktime(tp) Nominal (PN) Lower Bound (pj Upper Bound (PH) pOC'=uOC' 9:47:00 AM 50 45 55 pOC2=uOC29:54:00 AM 53 43 59 pOC3=uOC310:00:00 AM 55 43 65 pOC -yOC110:00:00 AM 200 185 205 pOCL’=yOC 10:03:00 AM 210 190 215 pOC6=yOC310:08:00 AM 215 195 230 pOC7=yOC410:15:00 AM 218 200 255 pOC8=uOC410:17:00 AM 55 43 65 pOC9=uOC510:26:00 AM 52 45 60 pOC10=yOC510:21:00 AM 230 215 265 pOC11=yOC610:27:00 AM 240 235 280

[0195]

[0196] pOC12=yOC710:37:00 AM 275 270 285

[0197] Table 3. Exemplary ordered combined sequence of operating conditions pOCcfor PVs.

[0198] The shown combined sequence of the operating conditions pOCcis formed for the sequence of operating conditions yOCbof CVs according to table 2 and the corresponding sequence of operating conditions uOCaof MVs according to table 1. Both sequences operating conditions uOCa, yOCbmay be determined by an operator in advance, typically in a different timeline, in particular a design timeline.

[0199] At the planned navigation start time, navigation through the combined sequence of the operating conditions pOCccan be started and performed until last operating condition pOC12(c=l, 2,..., c-end, c-end=12) is reached (completed).In the exemplary embodiment, the combined sequence of the operating conditions pOCcis formed by transferring the sequence of operating conditions yOCband the sequence of operating conditions uOCainto a production timeline tpreferring to a controller clock time so that the manipulating operating conditions uOCalead the control operating conditions yOCbin accordance with the lead-times Ly (which are calculated based on pairs of dead-times dy between the manipulated variables Uj and the controlled variables j’,)- For a MIMO system, the lead-time for a MV is determined from its dead-times to each CV and each CV’s first operating condition. Usually, the longest lead-time is considered. However, other schemes like the medium lead-time or the lead-time of a critical pair may also be considered. The critical pair is defined as the pair of MV and CV that has the higher priority than other pairs from an application perspective. For example, stock flow to sheet basis weight or steam pressure to sheet moisture content are usually considered as the critical pairs for a papermaking process.

[0200] The operating conditions, the tracks, and the lead-times of MVs are determined before the navigation task is actually executed. The actual (navigation) start time / start of the navigation task is also determined in advance. The navigation start time / start is to be set to a time earlier than or at the earliest among the lead-times of all MVs. When the clock time (real-time clock) tpreaches the navigation start time Zstart, the navigation calculation and execution is performed and iterated at every subsequent sampling time. The end time tendis set to a time after the completion of the last operating conditions of all process variables including both MVs and CVs.

[0201] The navigation calculation of the present technique is based on a model -based predictive control methodology. The model-based predictive control methodology may be formulated in a number of different approaches. For simplicity purpose but not limited, the Dynamic Matrix Control (DMC) expression is illustrated in this application.

[0202] According to an embodiment, the navigation calculation and execution mainly consist but is not limited to the following tasks.

[0203] 1. The control system uses the history of the process variables that includes MVs, DVs and CVs and the process response model to predict the future CVs for a prediction horizon that is phstep in the future. The predicted future CVs also include the prediction from the potential future MV actions over a specified control horizon ch.2. The control system minimizes a cost function that is determined from the future process variable tracks, the future MV’s actions, the predicted future CVs, and the priority weightings for process variables. An example of the cost function will be shown in the later section.

[0204] 3. The minimization of the cost function takes into account of the constraints of process variables. The constraints on MVs are handled through the constrained optimization techniques such as a quadratic programming (QP). The minimization of the defined cost function produces a set of control actions to MVs for the specified control horizon.

[0205] 4. The control system applies the most current MV control actions from the above calculation to MVs at the current sample time.

[0206] The above navigation calculation and execution is repeated as the time progress to the next sampling time. The iteration of the navigation calculation and execution is carried out repeatedly until the last operating condition among all process variables is reached and completed.

[0207] This navigation calculation is explained in more details in the following sections.

[0208] Prediction:

[0209] The prediction uses the discrete process response model and process input and output variables to forecast the future process outputs. For prediction calculation, a process response model can be expressed in its unit step response coefficients as shown in Fig. 6.

[0210] By using the unit step response coefficients sk, the predicted process output at the -th step in the future is calculated as:

[0211] y

[0212]

[0213] (t + ip) = Sk=i SfcAu(t + ip— k) + sNu(t + ip— IV) (8)

[0214] where

[0215] skfor k = 1, 2, 3, … N are unit step response coefficients between a process output y(i) and a process input u(f). N is the number of steps to the steady-state of the response. Au is the change of u(f) between two consecutive sampling time

[0216] For the present navigation technique, the control actions used for predicting the future process outputs uses both the past control actions and the future control actions within the future control horizon as shown in Fig 7 illustrating predicting of process output that can be used in a costfunction for calculating manipulated variables for the navigation through the one or more sequences of operating conditions.

[0217] The prediction calculation uses all control actions including MVs measurable disturbances DVs, other measurable feedforward input actions, and the current measurements of CVs to determine the predicted CV values.

[0218] Cost function:

[0219] The future control actions used for the CV prediction are unknown before the optimization calculation. The future control actions appear in a cost function are unknown variables to be resolved through the optimization of the cost function. The cost function is often formulated as:

[0220] J = ∑pi=1

[0221] ||y(t + ip) - yw(t + ip)||^ + > / ?ol|u(t + jp) -uN(t + jp)\\2R

[0222] iP=l ^—‘jp=0

[0223]

[0224] (9)

[0225] where the symbol ||x||2C= xTCx is a quadratic weighted norm of a vector x with the weighting matrix C.

[0226] W is a diagonal weighting matrix that specifies the relative weightings among controlled variables in the output vector y(t). R is a diagonal weighting matrix that specifies the relative weightings among manipulated variables in the input vector u(t). Q is a diagonal weighting matrix that specifies the relative weightings among the changes of the manipulated variables. The parameter p0is a priority weighting between MV and CV. The parameter Pi is a weighting on the rate of MV changes.

[0227]

[0228] y(t + ip) is the predicted CV at the zp-th step in the future relative to the current sampling time. yN(t + ip) is the nominal CV along the CV track at the ip-th step in the future relative to the current sampling time.

[0229] u(t + jp) is the control action at the jp-th step in the future counting from the current sampling time.

[0230] uN(t + jp) is the nominal MV along the CV track at the jp-th step in the future counting from the current sampling time.

[0231] Δu(t + jp) = u(t + jp) — u(t + jp—1) is the change of u(t) at the jp-th step in the future counting from the current sampling time.phand chare prediction horizon and control horizon respectively. Prediction horizon is set equal to or longer than the sum of control horizon, dead-time delay of the process, and the settling time of process dynamic responses.

[0232] Constraints:

[0233] Aside from setting up the cost function as specified above, the track boundaries are used as the constraints for all process variables as:

[0234]

[0235] uL(t + jp) ≤ u(t + jp) ≤ uH(t + jp) for jp= 0 to ch- 1 (10)

[0236] yL(t + ip) < y(t + ip) < yH(t + ip) for ip= 1 to ph(11)

[0237] where uL, uH, yLand yHare determined from the upper and lower bounds of the specified tracks respectively.

[0238] Additionally, MVs may also have constraint on their rate of change as:

[0239] |

[0240]

[0241] Δu(t + jp) | ≤ Δumaxfor jp= 0 to ch— 1 (12)

[0242] When the specified cost function J is minimized, both CVs and MVs are maintained substantially staying on the operating tracks. Constrained optimization algorithms explicitly keep MVs staying within the track. If a CV does not stay within the track, then its priority weighting needs to be increased for tightening the deviation of that CV. The adjustment of weightings in W matrix allows user to make the trade-off between MVs and CVs.

[0243] Nominal values of navigation tracks:

[0244] The nominal values of an operating condition may have multiple options (see US Patent No. 11,644,814, which is incorporated by reference herein in its entirety).

[0245] The nominal value of a process variable can be set at a specific value between the upper and lower bounds of the operating conditions, at a value near upper or lower bounds, or at any value between the bounds. For the last option, the mid-point between the upper and lower bounds is designated as its nominal value. The nominal values along the track between two consecutive operating conditions are set to be a line to connect the nominal values of the consecutive operating conditions. The connecting line may be a straight line or a smooth line such as a line derived from cubic spline technique.

[0246] The trace of nominal values is a function of time mark. The examples of the nominal traces (traces of nominal values) are shown as dashed lines in Figs. 3B, 3C, 4B, 4C, and 5B. The nominal traces of MVs and CVs are discretized for the cost function formulation. Thediscretized nominal traces appear in the cost function as yN(t + ip) and uN(t + jp) respectively. The nominal traces extend into the future as the guiding references for the process variables to navigate through their operating conditions.

[0247] Navigation progression:

[0248] At each sampling time, the control actions for the entire control horizon are derived from the constrained optimization calculation that minimizes the specified cost function. After the optimization calculation, the control system applies only the most current control actions to the manipulated variables.

[0249] The control system repeats the optimization calculation and execution at every sampling time until the very last operating condition of all process variables is reached. After this point, the navigation task is completed and terminated. At the end of navigation, the process may be switched back to regular closed-loop control operation or the specified product is discharged. During the navigation period, some process variables may exceed the range that are specified in their tracks. For example, the track specification may be too tight for the optimization to reach a feasible solution. It is crucial for the control system that implements the present navigation technique to verify the feasibility of the calculated control actions. Prevention of exceeding the specified limits is needed. In the meantime, alarm messages for alerting production personnel are also needed. The online real-time adjustment to navigation tracks to improve the control feasibility is allowable for practical applications of the present navigation technique.

[0250] Example of the present technique and system:

[0251] Table 4 is an example of a multiple-input and multiple-output process response model.

[0252] Nominal = 2600 Nominal = 2.85 Nominal = 2.7 Nominal = 280 Test Model

[0253] N01 (STOlj IN02 (PR02) IN03 (PR01I INtM (MSOl) Gain = 0.0422 Gain = -0.395 Nominal = 143 CVOl(DWOl) Delay =:120 s No Model No Model Delay =:30s Time Const = 35s Time Const = 30s Gain =0.002 Gain = -1.9 Gain = 0.028 Nominal = 1.15 CV02 (MT02) Delay = 120s Delay = 70s No Model Delay = 20s Time Const = 35s Time Const = 35s Time Const =:30s Gain = 0.009 Gain = -1.9 Gain = -4.0 Gain = 0.09 Nominal - 6 CV03 (MT01) Delay = 120 s Delay - 70s Delay - 60s Delay - 10s Time Const = 35s Time Const = 35 s Time Const = 90s Time Const = 30s Gain = 1 Nominal = 280 CV04 (5P02) No Modei No Model No Model Delay - Os

[0254]

[0255] Time Const = 10s Table 4 Example of a multiple-input and multiple-output processWith this response model, the dead-time(s) between CV and MV variables are used for determining the lead-time between CVs and MVs (tracks).

[0256] Based thereon, the control actions in MVs can lead the changes of CVs through the navigation tracks set for CVs.

[0257] Figure 8 illustrates navigation result of one MV-CV pair of the actual process inputs and output measurements (thick solid lines) that passing through the specified operating conditions and staying on the navigation tracks. The (shaded) time period between tstartand tendis the execution of the navigation progression. The actual process outputs (CVs, see the upper part of Fig. 8) and process inputs (MVs, see the lower part of Fig. 8) stay on their defined tracks (thin solid bounds and dashed nominal lines) closely.

[0258] According to an embodiment, which can be combined with other embodiments described herein, a method for navigating through a sequence of operating conditions referring to process variables of a production process for producing a product, the process variables including manipulated variables (MVs) and controlled variables (CVs), the method includes specifying, for the sequence of operating conditions, connecting tracks between consecutive operating conditions, determining lead-time(s) for MVs and a start time of the navigation, starting the navigation calculation at the start time and repeating: navigation calculation at every sampling time with latest process variables, adjusting manipulated variables as the navigation progress, and keeping process variables at least substantially staying on their connecting tracks until the entire sequence of operating conditions is completed.

[0259] According to an embodiment, which can be combined with other embodiments described herein, a method for navigation through one or more sequences of operating conditions of a production process in order to produce a specified product, the one or more sequences of operating conditions referring to process variables of the production process, the process variables comprising manipulated variables and controlled variables, the method includes: determining for the one or more sequences of operating conditions connecting tracks, each connecting track providing a connection between two consecutive operating conditions of one of the one or more sequences of operating conditions. Preferably, each operating condition includes a nominal value and bounds for one (or more) process variable of the production process, in particular the nominal value, an upper bound and a lower bound for the respective process variable, and time information for the operating condition. Preferably, each connecting track refers to one process variable. Based on at least one dead-time between the manipulated variables and the controlledvariables, at least one lead-time for the manipulated variables with respect to the controlled variables is determined. Based on a planned start time of at least one controlled variable and the at least one lead-time for the manipulated variables, a navigation start time for navigation through the one or more sequences of operating conditions of the production is determined. At the navigation start time, navigation through the one or more sequences of operating conditions of the production process is started by executing the manipulated variables in accordance with the at least one lead-time. At each sampling time after the navigation start time and until a last operating condition of the one or more sequences of the operating conditions is reached, the following processes are repeated: calculating, using a process response model of the production process, manipulated variables for the navigation through the one or more sequences of operating conditions of the production process so that the process variables are expected to at least substantially stay on their connecting tracks; and executing the calculated manipulated variables to navigate through the one or more sequences of operating conditions. At or after completion of the last operating condition, the navigation can be terminated.

[0260] The methods explained herein allows the production process to navigate through the sequences of operating conditions, while stay on track between consecutive operating conditions, and to finish the navigation at the desired end time.

[0261] By navigating through the required operating conditions and staying on the specified tracks, a production process may operate smoothly and efficiently to produce the specified products with less potential waste.

[0262] Further, the described control technique and system provides flexibility for navigating through the operating conditions while at least substantially staying on the tracks and achieving economic criteria as additional objectives.

[0263] Further, the described control technique and system allows production personnel to plan ahead of the actual start time of the navigation task and lead control actions to MVs for on time changes of process outputs (CVs) as production schedule is planned.

[0264] Accordingly, the manufacturing and / or processing of products such as paper or pulp products is improved.

[0265] This disclosure is however not limited to use with systems for (continuous) manufacturing or processing paper and / or pulp products, but can be applied to a wide range of industrial processesincluding continuous and batch operations. It can e.g. also be used with systems that produce or process other items or materials (continuously or batch-wise), such as plastic, textiles, metal foil or sheets, or other or additional materials.

[0266] A number of embodiments and examples have been described. Nevertheless, it is understood that various modifications may be made without departing from the scope of the invention, which is defined by the claims that follow.Reference signs and abbreviations:

[0267] FB feedback

[0268] MV manipulated variable (input to process)

[0269] CV controlled variable (output from process)

[0270] PV process variable

[0271] DV disturbance variable (input to process)

[0272] RM process response model

[0273] uj(t) j-th manipulated variable, j=1,2,…,m

[0274] yi(t) i-th controlled variable, i=1,2,…,n

[0275] pk(t) k-th process variable, k=1,2,…,n+m

[0276] djj dead-time between i-th CV and j-th MV

[0277] Ly lead-time between i-th CV and j-th MV

[0278] tpproduction time line

[0279] tyiplanned start time of yion production time line

[0280] tstartnavigation start time on production time line

[0281] tendnavigation end time on production time line

[0282] OCXx-th operating condition

[0283] OCx-endlast operating condition

[0284] uOCaa-th operating conditions for MVs

[0285] yOCbb-th operating conditions for CVs

[0286] pOCcc-th operating conditions for PVs

[0287] ujNanominal of the a-th operating condition of the manipulated variable ujyiNbnominal of the Z>-th operating condition of the controlled variable ytPkNcnominal of the c-th operating condition of the process variable pk ujHaupper bound of the a-th operating condition of the manipulated variable ujujLalower bound of the a-th operating condition of the manipulated variable ujyiHbupper bound of the b-th operating condition of the controlled variable yiyiLblower bound of the b-th operating condition of the controlled variable yipkHcupper bound of the c-th operating condition of the process variable pkPkLclower bound of the c-th operating condition of the process variable pk ujNa,a+1sectional nominal track between a and a+1 operating conditions of uju]Ha’a+1sectional upper bound track between a and a+1 operating conditions of udujLa’a+1sectional lower bound track between a and a+1 operating conditions of u, yiNb,b+1sectional nominal track between b and b+1 operating conditions of yiyiHb,b+1sectional upper bound track between b and b+1 operating conditions of yiytLb’b+1sectional lower bound track between b and b+1 operating conditions of

[0288]

[0289] chcontrol horizon

[0290] Ph prediction horizon

[0291] 500 system for navigation

[0292] 530 sensors

[0293] 550 control system, e.g. a controller

[0294] 560 separate control system

[0295] 580 actuators

[0296] >999 method, method steps

Claims

Claims:

1. A method (1000) for navigation through one or more sequences of operating conditions of a production process in order to produce a specified product, the one or more sequences of operating conditions (OCx) comprising nominal values (ujNa, yiNb, pkNc") and bounds (ujHa, ujLa, ylHb, ylLb, pkHc, pkLc) for process variables (pk) of the production process, the process variables (p) comprising manipulated variables (u) and controlled variables (y), the method comprising:• determining (1100) for the one or more sequences of operating conditions (OCX) connecting tracks (w7W°’a+7, UjHa-a+1, Uj] ’a+yiNb’b+1,yiHb-b+1,yiLb-b+1each connecting track providing a connection between two consecutive operating conditions (OCX, OCx+1) of one of the one or more sequences of operating conditions (OCX);• determining (1200):based on at least one dead-time (dij) between the manipulated variables (uj) and the controlled variables (yi), at least one lead-time (Lij) for the manipulated variables (uj) with respect to the controlled variables (yi); and based on a planned start time (tyi) of at least one controlled variable (yi) and the at least one lead-time (Lij) for the manipulated variables (uj), a navigation start time (tstart) for navigation through the one or more sequences of operating conditions of the production process;• at the navigation start time (tstart), starting (1300) navigation through the one or more sequences of operating conditions of the production process by executing the manipulated variables (w) in accordance with the at least one lead-time; • repeating, at each sampling time (Ts) after the navigation start time (tstart): calculating (1400), using a process response model (RM) of the production process, manipulated variables (w) for the navigation through the one or more sequences of operating conditions of the production process so that the process variables (p) are expected to stay on the connecting tracks; and executing (1500) the calculated manipulated variables (u) to navigate through the one or more sequences of operating conditions until a last operating condition (OCx-end) of the one or more sequences of the operating conditions (OCx) is reached; and • terminating (1600) the navigation at or after completion of the last operating condition (OCx)).

2. The method of claim 1, wherein the process response model (RM) characterizes a dynamic behavior of the production process, wherein the process response model (RM) is a function to determine the controlled variables (y) based on the manipulated variables (w), wherein the process response model (RM) is a function to determine the controlled variables (y) based on the manipulated variables (w) and disturbance variables (DVs) of the production process, wherein the process response model (RM) is a function that characterize a dynamic behavior of the production process, and / or wherein the dynamic process response model (RM) comprises and / or is based on at least one of: transfer functions in the Laplace domain, in particular a matrix of transfer functions in the Laplace domain, a regression model, historical data from the industrial process, and / or a trained model, the trained model typically being trained by machine learning using the historical data.

3. The method of any preceding claim, wherein each operating condition (pOCc) of the one or more sequences of operating conditions (pOCc) is defined by a nominal value (PkNc, an upper bound and a lower bound pkLc, PkH ) for at least one of the process variables pk) of the production process and a time information ( ) for each nominal value (p>kNcin particular a corresponding time difference with respect to the first operating condition or the time difference between two consecutive operating conditions.

4. The method of any preceding claim, wherein each of the operating conditions (uOCa) of manipulated variables (MV) comprises a nominal value, an upper bound and a lower bound for one of the manipulated variables («,), and / or wherein each of the operating conditions (yOCb) of controlled variables (CV) comprises a nominal value, an upper bound and a lower bound for one of the controlled variables (y;).

5. The method of any preceding claim, wherein the one or more sequences of operating conditions (uOCa, yOCb) comprises at least one sequence of operating conditions of the controlled variables (CV) and at least one sequence of operating conditions of the manipulated variables (MV), and / or wherein each of the sequences of operatingconditions (uOCa, yOCb)comprises a plurality of operating conditions, preferably a plurality of operating conditions including the corresponding time information.

6. The method of any preceding claim, wherein each connecting track comprises at least one of, preferably all of: a nominal line connecting the nominal values of the two consecutive operating conditions, a lower boundary line connecting the lower bounds of the two consecutive operating conditions, and an upper boundary line connecting the upper bounds of the two consecutive operating conditions, wherein the connecting line is a straight line or a curve line such as cubic spline, and / or wherein the connecting tracks for the process variables (PV) form a respective band connecting the bounds and the nominal values of the operating conditions of the process variable (pk).

7. The method of any preceding claim, prior to the navigation start time (tstart) further comprising at least one of, typically at least several or even all of:• make the manipulated variables (uj) lead the corresponding controlled variables (y,) in accordance with the at least one calculated lead-time;• determine (1200) all deadtimes between the manipulated variables (u) and the controlled variables (y);• determine, based on the at least one deadtime (dij), in particular all nonvanishing deadtimes (dij), a respective lead-time (Lij) for the manipulated variables (uj) with respect to the controlled variables (yi);• make each of the manipulated variables (uj) lead the corresponding controlled variables (yi) in accordance with the respective lead-time; and• update the one or more sequences of operating conditions of process variables in accordance with the at least one lead-time.

8. The method of claims 5 and 7, wherein updating the one or more sequences of operating conditions comprises at least one of, preferably both of:• transferring the at least one sequence of operating conditions of the controlled variables (yOCb) and the at least one sequence of operating conditions of the manipulated variables (uOCa) into a production timeline (tp) so that the manipulating operating conditions (uOCa) lead the corresponding control operating conditions (yOCb) in accordance with the at least one lead-time, preferably in accordance with all non-vanishing deadtimes (t^); and • forming a combined sequence of the operating conditions (pOCc).

9. The method of claim 7 or 8, further comprising using the updated one or more sequences of operating conditions, in particular the combined sequence of the operating conditions for at least one of, preferably all of: starting (1300) the navigation, calculating (1400) the manipulated variables (u) for the navigation, and executing (1500) the calculated manipulated variables (u).

10. The method of any preceding claim, wherein the navigation start time is determined from the earliest lead-time among all manipulated variables, wherein the lead-time of a manipulated variable (uj) with respect to a plurality of controlled variables is a longest, a medium, a weighted-average, or a specific lead-time among the lead-times with respect to the plurality of controlled variables, and / or wherein the navigation start time is one of an earliest, a medium, a weighted-average, or a specific start-time among the start times with respect to the plurality of manipulated variables.

11. The method of any preceding claim, wherein executing (1500) comprises:sending the calculated manipulated variables (u) to actuators (580).

12. The method of any of the preceding claims, wherein at every sampling time, the calculated manipulated variables are updated based on updated process variables feedback (FB), future tracks of the process variables, constraints of the process variables, and weighting priorities of the process variables according to a model predictive control scheme.

13. The method of claim 12, wherein the calculated manipulated variables are updated by optimizing a cost function determined from the future tracks of the process variables, future actions of the manipulated variables, predicted future controlled variables, and / or priority weightings for process variables, wherein the future process variables are predicted for a prediction time horizon (ph) and the future actions of the manipulated variables are derived for a control time horizon (ch) shorter than the prediction time horizon, wherein the updated manipulated variables (u) are calculated for the navigation through a remaining part of the one or more sequences of operating conditions of the production process.

14. The method of claim 13, wherein the predicted future controlled variables are calculated from the past history of the manipulated variables, the future actions of manipulated variables, updated process variable feedbacks (FB), and the process response model for the prediction time horizon (ph) for the controlled variables.

15. The method of any preceding claim, wherein calculating (1400) comprises at least one of, preferably all of:• designing a quadratic cost function of differences between the predicted future process variables and the nominal process variables and differences between consecutive manipulated variables with respective priority weightings over the respective prediction time horizon (ph) or control time horizon (ch) of the process variables;• deriving constraints of process variables from the future tracks of process variables over the respective prediction time horizon (ph) or control time horizon (ch) of the process variables;• performing constrained optimization of the designed cost function by deriving current and future control actions over the control time horizon (ch) while keeping all process variables at least substantially satisfying the derived constraints over the respective prediction time horizon (ph) or control time horizon (ch) of the process variables; and• adjusting the priority weightings and iterating the constrained optimization to keep process variables at least substantially staying on track for the process variables.

16. The method of claim 15, wherein the nominal values of the tracks are used as the references for all process variables for the constrained optimization, and / or wherein the upper and lower bounds of the tracks are used as the constraints for the constrained optimization.

17. The method of any preceding claim, wherein the calculated manipulated variables (u) for the respective sampling time / interval are calculated such that the process variables stay on their connecting track, follow the nominal value, stay near a bound, or anywhere between the bounds as specified by the weighting priorities.

18. The method of any preceding claim, wherein the production process is an industrial production process, wherein the production process is a continuous or a batch production process, wherein the production process comprises a product specification transition process, wherein the production process is a papermaking process, pulpmaking process, chemical product process.

19. The method of any preceding claim, further comprising at least one of:• performing the method by a control system (550) such as a controller;• specifying (1010) the one or more sequences of operating conditions (OCX);• providing guidance to a user in specifying (1010) the one or more sequences of operating conditions (OCX);• receiving the one or more sequences of operating conditions (OCX), in particular as one or more sequences of operating conditions (OCX) from a separate control system (560) functionally connected with the control system (550);• specifying (1020) the planned start time (tyi) of the of at least one controlled variable (yi), typically planned start times of all controlled variables (CVs); and • receiving the planned start time (tyi), in particular from the separate control system.

20. A control system (550) for navigation through one or more sequences of operating conditions (OCX) of a production process, the control system comprising a one or more computing units configured to perform the method of any of the preceding claims.

21. The control system of claim 20, wherein the one or more computing units are provided by a controller, wherein the controller is an internal model controller or model-based predictive controller, wherein the control system is a part of or functionally connected to a production system (500) for the production process of a specified product, the production system (500) comprising actuators (580) for adjusting the production process in accordance with control signals received from the controller for the manipulated variables, and sensors (530) for measuring data of the production process, which refer to process variables feedback, wherein the control system is a distributed control system, and / or wherein the industrial process is a continuous process or a batch process.

22. A computer program product and / or a computer-readable medium comprising instructions which, when executed by one or more computing units, in particular a computing unit of a controller, cause the computing unit to carry out the method of any of the claims 1 to 19.

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