Design Method of Gain Scheduling Model Predictive Controller for Multi-Working-Point Aquaculture

Abstract

The present invention relates to a design method of a gain-scheduled model predictive controller for multiple working points in aquaculture. By designing a basic MPC controller, multiple local linear sub-models with different working points are used to approximate the global non-linear dynamics. For each sub-model with different working points of the dissolved oxygen concentration in the recirculating aquaculture, sub-MPC controllers with different functions are designed. Combining the circadian rhythm of the linear sub-model under different working conditions of the dissolved oxygen in the recirculating aquaculture, a gain-scheduled signal is designed for the sub-MPC controller to adapt its stability and robustness. The sub-MPC controllers are switched through the gain-scheduled signal for overall scheduling control. The sub-MPC controllers are switched between each other to complete the design of the GSMPC controller. The performance of the GSMPC controller is evaluated using IAE, ISE, and IAC. Considering the control accuracy and the energy consumption generated by the control actions comprehensively for evaluation, its performance is confirmed, improving the control accuracy and reducing the energy consumption, and it can be effectively used for the long-term precise control of the dissolved oxygen level in aquaculture.

Description

Technical Field

[0001] The present invention relates to the technical field of aquaculture, and particularly relates to a design method for a gain-scheduling model predictive controller for multiple working points in aquaculture. Background Art

[0002] In the actual operation of a recirculating aquaculture system, the production environment is variable, with large time delays and many uncertain disturbances, which will bring uncertainty to system regulation. For the control method of dissolved oxygen, at home and abroad, aerators are mostly used to control the dissolved oxygen content in water, and sensors are used to detect the dissolved oxygen content in water. When this value is lower than the lower limit value, the aerator is turned on to increase the dissolved oxygen content in water; when this value is higher than the set upper limit, the aerator should be immediately turned off and stop working to effectively control the dissolved oxygen. In terms of specific methods, most oxygenation equipment still uses the traditional PID control method, but with the demand for control accuracy, intelligent control methods are constantly combined with the aquaculture industry.

[0003] Some research has proposed a differential evolution (DE) algorithm - an optimized radial basis function neural network PID controller. The proposed controller has two optimization parts: the first part uses an improved DE algorithm to solve the optimal initial parameters of PID; the second part uses the powerful learning ability of the RBF neural network to adjust the PID parameters online, which can not only eliminate overshoot but also improve the adaptive ability of the controller. Some research has proposed a single neuron adaptive PID controller based on fuzzy rule optimization to accurately control dissolved oxygen. In sewage treatment, some scholars have used the MPC (Model Predictive Control) algorithm to study the regulation of dissolved oxygen in the activated sludge model sewage treatment process. Verification on a benchmark simulation platform shows that compared with other control algorithms, the model predictive control algorithm has higher regulation efficiency and accuracy, and can adjust the dissolved oxygen in the sewage treatment oxygenation process to the optimal state. Due to the complexity and variability of actual production requirements, it is difficult for a single controller to achieve a satisfactory control effect in the actual aquatic environment. Summary of the Invention

[0004] Aiming at the deficiencies existing in the prior art, the purpose of the present invention is to provide a design method for a gain-scheduling model predictive controller for multiple working points in aquaculture.

[0005] To solve the above technical problems, the technical solution provided by the present invention is:

[0006] A design method for a gain-scheduling model predictive controller for multiple working points in aquaculture, comprising the following steps:

[0007] S1. Design a basic MPC controller, the MPC controller includes: a model predictive structure, a rolling optimization structure, and a feedforward-feedback control structure, and the design steps include:

[0008] S1.1 Establishment and discretization of the prediction model;

[0009] S1.2 Derivation of the prediction model to establish the system state matrix for a set period of time in the future;

[0010] S1.3 Design the objective function and optimize and solve the objective function to complete the design of the basic MPC controller;

[0011] S2. The prediction model includes several linear sub-models at different operating points; find the core cost function of the basic MPC controller in S1, and design sub-MPC controllers with four different functions of giving priority to control accuracy, two different ratios of balancing accuracy and energy consumption, and giving priority to controlling energy consumption for each linear sub-model in the dissolved oxygen concentration in recirculating aquaculture on the basic MPC controller; identify the linear sub-models under different working conditions by switching sub-MPC controllers; approximate the global non-linear dynamics using multiple local linear sub-models with different operating points;

[0012] S3. Combine the circadian rhythm of the linear sub-models under different operating conditions of the dissolved oxygen in recirculating aquaculture to design the gain scheduling signal for the sub-MPC controller in S2, adapt its stability and robustness, switch the sub-MPC controller through the gain scheduling signal, perform overall scheduling control, and optimize the switching of the Q and W weights in the objective function during the switching between sub-MPC controllers to complete the design of the GSMPC controller;

[0013] S4. Evaluate the performance of the GSMPC controller described in S3 using IAE, ISE, and IAC, and make an evaluation by comprehensively considering the control accuracy of the GSMPC controller and the energy consumption generated by the control actions to confirm the performance of the GSMPC controller.

[0014] Preferably, the S1 is specifically:

[0015] S1.1 Establishment and discretization of the prediction model

[0016] First, select the state vector: (2) Then establish the system state equation:

[0017]

[0018] Discretize the state equation using the forward Euler method:

[0019]

[0020] x(k + 1) = (I + TA)x(k) + TBu(k) (5)

[0021] Let Then there is:

[0022]

[0023] Wherein, x is the state vector of the system; The rate of change of the state vector; u is the input vector, including the external input of the system; A is the state matrix, representing the linear evolution of the system state variables; B is the input matrix, explaining the influence of the external input on the system state; D is the perturbation; T is the control period; x(k) is the state of the system at the k-th moment; u(k) is the control quantity of the system at the k-th moment;

[0024] S1.2 Prediction model derivation, establish the system state matrix for a set period of future time;

[0025] N p represents the prediction interval, N c represents the control interval, N p ≥N c , record the predicted system state p control periods in advance as:

[0026] X k =[x(k + 1|k) T x(k + 2|k) T … x(k + p|k) T T (7)

[0027] When predicting the future state of the dynamic system, the control quantity within the prediction interval is:

[0028] U k =[u(k|k) T u(k + 1|k) T … u(k + p - 1|k) T T (8)

[0029] Use the following formula to predict the system state for the next p control periods in sequence:

[0030]

[0031] Let Then

[0032] X k = Ψx(k)+ΘU k (10)

[0033] Wherein: X k , the system state; (k + 1|k), predict the state of the system at the (k + 1)-th moment based on the state at the k-th moment, and so on; U k , the control quantity and independent variable for the optimization problem to be solved, uk = 0 in the interval Nc ≤ k ≤ Np;​​

[0034] S1.3 Design the objective function and optimize and solve the objective function;

[0035] Define a series of reference values within the prediction interval Np:

[0036] R k = [r(k + 1) T r(k + 2) T … r(k + p) T T (11)

[0037] The objective function J is defined as the cumulative error between the predicted state vector and the reference value while observing the control variable constraints:

[0038]

[0039] The Q matrix adjusts the importance of the state error. The larger Q is, the faster the state converges. The W matrix adjusts the importance of the control input. When W is greater than Q, a smaller input is preferred;

[0040] Let E = Ψx(k) - R k , and substituting equation (8) into the above equation gives:

[0041] J = U k T (Θ T QΘ + W)U k + (2E T QΘ)U k + E T QE (13)

[0042] Let E T QE be a constant term, which does not affect the problem of "which value of U k makes the objective function J reach the minimum value", so it is omitted:

[0043]

[0044] The solution to the problem of solving the optimal control scheme by MPC is finally transformed into a QP problem:

[0045]

[0046] s.t. u min ≤ u(k + i|k) ≤ u max , = 0, 1, 2, …, p - 1 (16)

[0047] Δu min ≤ Δu(k + i|k) ≤ Δu max (17)​

[0048] Where: R k , set value; J, target solution function; Q, state error weight matrix; W, control input weight matrix, Q and W are diagonal matrices; u min , lower limit of control variable; u max , upper limit of control variable; Δu min , lower limit of control variable change rate; Δu max , upper limit of control variable change rate; u(k+i|k), control variable of k+i calculated at time k; Δu(k+i|k), control variable change of k+i calculated at time k;

[0049] Call the optimization solver in the MATLAB function to solve the constrained QP optimization problem, and extract the initial value of U k as the control variable for this control period.

[0050] Preferably,

[0051] The sub-MPC controller in S2 includes MPC1-MPC4;

[0052] The MPC1 controller quickly drives the state close to the set point without considering energy consumption;

[0053] The MPC2 controller drives the state close to the set value while considering energy consumption;

[0054] The MPC3 controller takes into account both state error and energy consumption;

[0055] The MPC4 controller minimizes energy consumption without considering state error.

[0056] Preferably,

[0057] The operating point in S3 specifically analyzes and designs the gain scheduling signal by comprehensively considering the dissolved oxygen concentration model and the diurnal rhythm requirements of fish.

[0058] Preferably, the design scheme of the gain scheduling signal is specifically as follows:

[0059] In the stage of 0-1.8 hours, the aerator enables the maximum aeration flow rate, that is, the upper limit of the control variable and the upper limit of the control variable change rate, and the dissolved oxygen concentration in the fish pond reaches the set target value at the fastest speed;

[0060] In the stage of 1.8-3 hours, there is a certain time delay in the change of the dissolved oxygen concentration in the fish pond relative to the control action of the controller. The MPC4 controller is used to prevent the dissolved oxygen peak from exceeding 5% of the set reference value, and the aeration rate is reduced as much as possible. Priority is given to minimizing energy consumption and controlling weights;

[0061] In the stages of 3 - 5 hours, 19.3 - 26.5 hours, 43.3 - 50.5 hours, and 67.3 - 70 hours, the respiratory oxygen consumption of the fish is relatively low at these working points, and the dissolved oxygen concentration is still rising when reaching the set value. Select the MPC3 controller with the same error weight and control weight; increase the control weight.

[0062] In the stage of 5 - 6 hours, use the MPC2 controller to increase the error weight of the controller to increase the dissolved oxygen concentration in the fish pond.

[0063] In the stages of 6 - 19.3 hours, 26.5 - 43.3 hours, and 50.5 - 67.3 hours, according to the circadian rhythm, the respiratory oxygen consumption of the fish starts to rise and gradually increases during these time periods. At these working points, use the MPC1 controller to increase the dissolved oxygen concentration in the fish pond at the fastest speed.

[0064] Preferably,

[0065] In S4, IAE, ISE, and IAC are used to evaluate the performance of the GSMPC controller. The specific equations are as follows:

[0066]

[0067] In the formula, e is the error, u is the control input, and T is the control period.

[0068] Preferably,

[0069] In S1, a linear model of the object, disturbance, and noise is used to estimate the state of the basic MPC controller and predict the future output of the controlled object. Based on the predicted output of the controlled object, the basic MPC controller solves the quadratic programming optimization problem of the optimal control quantity of the aerator in the dissolved oxygen concentration control to determine the control action.

[0070] The controlled object is the dissolved oxygen concentration in the recirculating aquaculture system, and its model is:

[0071]

[0072] In the formula, V is the volume of the water body in the fish pond; Q in is the influent flow rate; C is the dissolved oxygen concentration in the recirculating aquaculture fish pond; k1, k2, k3, and β are all constants obtained by fitting the measured data using Gaussian - Newton nonlinear regression analysis; Q is the aeration flow rate; t d is the delay time, T w is the current water temperature; K rear is the oxygen re - aeration coefficient on the water surface; M is the total mass of the fish; R m is the average daily oxygen consumption rate; A is the amplitude of the circadian rhythm model, f is the model frequency, φ is the model phase; P k is the temperature coefficient.

[0073] Preferably,

[0074] The sub-MPC controller can handle control problems under multiple constraints and give the optimal control quantity under these constraints;

[0075] The sub-MPC controller decomposes the optimization control problem with a long or even infinite time span into multiple optimization control problems with shorter or finite time spans to obtain the optimal solution.

[0076] A gain-scheduling model predictive controller system for aquaculture with multiple operating points adopts the design method of a gain-scheduling model predictive controller for aquaculture with multiple operating points described in any one of the above.

[0077] The above-mentioned gain-scheduling model predictive controller system for aquaculture with multiple operating points is applied to the precise tracking control of long-term dissolved oxygen in aquaculture.

[0078] The beneficial effects of the present invention are:

[0079] The present invention proposes a design method of a gain-scheduling model predictive controller for aquaculture with multiple operating points, which improves the control accuracy, reduces the energy consumption, and can be effectively used for the long-term precise control of the dissolved oxygen level in aquaculture. The GSMPC (Gain Scheduling Model Predictive Control) controller of the present invention has accumulated further experience for solving the actual needs of the recirculating aquaculture system. Description of the Drawings

[0080] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention, and do not constitute a limitation to the present invention. In the drawings:

[0081] Figure 1 It is a schematic diagram of the design of a gain-scheduling model predictive controller for recirculating aquaculture with multiple operating points of the present invention

[0082] Figure 2 It is a structural diagram of model predictive control

[0083] Figure 3 It is a structural diagram of GSMPC

[0084] Figure 4 It is a structural diagram of GSMPC for adjusting the weight of the gain-scheduling signal

[0085] Figure 5 It is a diagram of the weight of the gain-scheduling signal and the control result

[0086] Figure 6 It is a diagram of the control effect of the MPC controller and the GSMPC controller

[0087] Figure 7 Control error diagrams for the MPC controller and the GSMPC controller

[0088] Figure 8 Control input diagrams for the MPC controller and the GSMPC controller Specific implementation manners

[0089] The preferred examples of the present invention will be described below with reference to the accompanying drawings. It should be understood that the following embodiments are given only for the purpose of illustration and are not intended to limit the scope of the present invention. Those skilled in the art can make various modifications and substitutions to the present invention without departing from the purpose and spirit of the present invention.

[0090] As Figure 1 shown, the present invention provides a design method for a gain-scheduled model predictive controller for aquaculture with multiple operating points, including the following steps:

[0091] S1. Design a basic MPC controller. The MPC controller includes: a model predictive structure, a receding horizon optimization structure, and a feedforward-feedback control structure. The design steps include:

[0092] S1.1 Establish and discretize the prediction model;

[0093] S1.2 Derive the prediction model and establish the system state matrix for a set future period of time;

[0094] S1.3 Design the objective function and optimize and solve the objective function to complete the design of the basic MPC controller;

[0095] S2. The prediction model includes several linear submodels with different operating points; find the core cost function of the basic MPC controller in S1, and design sub-MPC controllers with four different functions of giving priority to control accuracy, balancing accuracy and energy consumption in two proportions, and giving priority to energy consumption for each linear submodel in the dissolved oxygen concentration in recirculating aquaculture on the basic MPC controller; identify the linear submodels under different working conditions by switching the sub-MPC controllers; approximate the global nonlinear dynamics with multiple local linear submodels with different operating points;

[0096] S3. Design a gain-scheduling signal for the sub-MPC controller in S2 in combination with the circadian rhythm of the linear submodels under different working conditions of the dissolved oxygen in recirculating aquaculture to adapt its stability and robustness. Switch the sub-MPC controllers through the gain-scheduling signal for overall scheduling control. When switching between sub-MPC controllers, optimize the switching of the Q and W weights in the objective function to complete the design of the GSMPC controller;

[0097] S4. Evaluate the performance of the GSMPC controller described in S3 using IAE, ISE, and IAC. Make an evaluation by comprehensively considering the control accuracy of the GSMPC controller and the energy consumption generated by the control actions, and confirm the performance of the GSMPC controller.

[0098] The controlled object of the present invention is the dissolved oxygen concentration in a recirculating aquaculture system The dynamic analysis model of dissolved oxygen based on circadian rhythm can be expressed as:

[0099]

[0100] In the formula, V is the volume of the water body in the aquaculture fishpond; Q in is the influent flow rate; C is the dissolved oxygen concentration in the recirculating aquaculture fishpond; k1, k2, k3, and β are all constants obtained by fitting the measured data using Gaussian - Newton nonlinear regression analysis; Q is the aeration flow rate; t d is the delay time, T w is the current water temperature; K rear is the re - oxygenation coefficient of the water surface; M is the total mass of the fish; R m is the average daily consumption rate of dissolved oxygen; A is the amplitude of the circadian rhythm model, f is the model frequency, φ is the model phase; P k is the temperature coefficient.

[0101] 1. Design of the basic MPC controller

[0102] As Figure 2 shown, it is the gain - scheduling model predictive control structure diagram of the present invention.

[0103] The MPC controller uses a linear model of the controlled object, disturbances, and noise to estimate the controller state and predict the future output of the object. Based on the predicted output of the controlled object, this controller solves a quadratic programming optimization problem to determine the control action. MPC can handle control problems under multiple constraints and give the optimal control quantity under these constraints. MPC has the ability of optimization and prediction, and is committed to decomposing the optimization control problem with a long or even infinite time span into multiple optimization control problems with shorter or finite time spans, while pursuing the optimal solution to a certain extent.

[0104] The MPC controller includes three components: a model prediction structure, a rolling optimization structure, and a feed - forward - feedback control structure.

[0105] The design method of the MPC controller is as follows:

[0106] 1.1 Establishment and discretization of the prediction model

[0107] First, select the state vector:

[0108]

[0109] Then establish the system state equation:

[0110]

[0111] Discretize the state equation using the forward Euler method:

[0112]

[0113] x(k + 1) = (I + TA)x(k) + TBu(k) (5)

[0114] Let Then we have:

[0115]

[0116] In the formula, x is the state vector of the system; The rate of change of the state vector; u is the input vector, including the external input of the system; A is the state matrix, representing the linear evolution of the system state variables; B is the input matrix, explaining the influence of the external input on the system state; D is the disturbance; T is the control period; x(k) is the state of the system at the k-th moment; u(k) is the control quantity of the system at the k-th moment.

[0117] 1.2 Prediction model derivation, establish the system state matrix for a period of time in the future

[0118] To predict the future system state, Np represents the prediction interval, Nc represents the control interval, Np ≥ Nc, and the predicted system state is recorded p control periods in advance as:

[0119] X k = [x(k + 1|k) T x(k + 2|k) T … x(k + p|k) T T (7)

[0120] When predicting the future state of a dynamic system, the control quantity within the prediction interval is:

[0121] U k = [u(k|k) T u(k + 1|k) T … u(k + p - 1|k) T T (8)

[0122] Predict the system state for the next p control periods in sequence using the following formula:

[0123] ​​

[0124] X k = Ψx(k) + ΘU k (10)

[0125] Where: X k , the system state; (k+1|k), the state of the system predicted based on the state at time k, and so on; U k , the control variable and independent variable for the optimization problem to be solved, Np represents the prediction horizon, Nc represents the control horizon, and in the interval Nc ≤ k ≤ Np, uk = 0.

[0126] The lower triangular matrix form in the above equation directly reflects the causal relationship of the system in time. Specifically, the input at time k+1 has no effect on the state at time k, and the input at time k+2 has no effect on the states at times k and k+1.

[0127] 1.3 Design the objective function and optimize and solve the objective function;

[0128] Define a series of reference values within the prediction horizon N p :

[0129] R k = [r(k+1) T r(k+2) T … r(k+p) T T (11)

[0130] The cost function is defined as the cumulative error between the predicted state vector and the reference value while observing the control variable constraints:

[0131]

[0132] Let E = Ψx(k) - R k , substituting Equation (8) into the above equation gives:

[0133] J = U k T (Θ T QΘ + W)U k + (2E T QΘ)U k + E T QE (13)

[0134] Let E T QE be a constant term, which does not affect the problem of "which value of U k makes J reach the minimum value", so it is omitted:

[0135] ​

[0136] In summary, the solution to the problem of solving the optimal control scheme by MPC is ultimately transformed into a QP problem:

[0137]

[0138] s.t. u min ≤ u(k + i|k) ≤ u max , i = 0, 1, 2, …, p - 1 (16)

[0139] Δu min ≤ Δu(k + i|k) ≤ Δu max (17)

[0140] where: R k , setpoint; J, objective solution function; Q, state error weight matrix; W, control input weight matrix, Q and W are diagonal matrices; u min , lower limit of control quantity; u max , upper limit of control quantity; Δu min , lower limit of control quantity change rate; Δu max , upper limit of control quantity change rate; u(k + i|k), control quantity of k + i calculated at time k; Δu(k + i|k), control quantity change of k + i calculated at time k.

[0141] H is an n×n symmetric matrix, which can also be called a Hessian matrix. The optimality of the function is related to the positive definiteness of the Hessian matrix. When the Hessian matrix is a positive definite matrix, that is, all eigenvalues of the matrix are greater than 0, this quadratic programming problem must have a unique global minimum; when the Hessian matrix is a positive semi - definite matrix, that is, all eigenvalues of the matrix are non - negative, this convex quadratic programming problem must have a global minimum; when the Hessian matrix is a non - positive definite matrix, that is, all eigenvalues of the matrix are less than 0, this convex quadratic programming problem has multiple local extreme points.

[0142] To solve the constrained QP optimization problem, the optimization solver in the MATLAB function can be directly called. The initial value of U k (solving multiple control quantities, but only using the first control quantity) is extracted as the control quantity for this control cycle.

[0143] The present invention designs a dedicated GSMPC controller for recirculating aquaculture, which is used to regulate the aerator in the recirculating aquaculture system to achieve precise control of the dissolved oxygen in the pond. The MPC control algorithm mentioned above will be used as the basis for controller design. The GSMPC controller designed by the present invention will design multiple sub - MPC controllers with different functions for different working points in recirculating aquaculture, and then design a gain - scheduling signal according to the model characteristics of the controlled object to overall - ly schedule these sub - MPC controllers to achieve better control effects.

[0144] 2. Design of Multi-Working-Point Multi-MPC Controller

[0145] Dissolved oxygen aeration is a dynamic non-linear process. The traditional MPC controller design is based on the linear model of a certain steady-state working point of the system, which cannot ensure good control effects of the system within the entire operating conditions range. In order to achieve precise control of the dissolved oxygen concentration, single-model predictive control cannot provide sufficient controller performance.

[0146] The gain-scheduling design method of the present invention makes full use of the advantage that the traditional MPC controller has good control effects near the steady-state working point. GSMPC focuses on using multiple local linear sub-models with different working points to approximate the global non-linear dynamics, and designs MPC controllers for each sub-model to meet its stability and robustness. By switching the controller, the linear models under different operating conditions can be identified, and the influence of prediction model mismatch can be reduced. The GSMPC structure is as Figure 3 shown. GSMPC is still a feedforward-feedback structure. Considering the system output feedback, working point and disturbance, the gain-scheduling signal is designed. The gain-scheduling signal is responsible for making decisions to switch to the sub-MPC controller that best meets the real-time control requirements, and conducts real-time control of the aerator.

[0147] The cost function of MPC obtained in the above 1.3 is as follows:

[0148]

[0149] The Q and W matrices are crucial when designing a demand-based controller, directly affecting the performance of the controller. The Q matrix adjusts the importance of the state error. The larger Q is, the faster the state converges. On the contrary, the W matrix adjusts the importance of the control input. When W is greater than Q, a smaller input is more preferred.

[0150] For the operating points in the RAS scheduling, four different MPC controllers (MPC1 - MPC4) are designed. Generally, only the first few time steps have a great influence on the prediction (because the first few time steps will be pulled towards the anti-trajectory and the subsequent time steps will remain stable), so choosing a larger control range will only increase the computational complexity. Therefore, follow the rule of thumb: control interval = 10% - 30% × prediction interval.

[0151] The parameter selections of MPC1 - MPC4 are shown in Table 1. The MPC1 controller is designed to quickly drive the state close to the set point without considering energy consumption; the MPC2 controller drives the state close to the set value considering energy consumption; the MPC3 controller design takes both state error and energy consumption into account; the MPC4 controller design minimizes energy consumption without considering the state error.

[0152] Table 1 Parameter Settings of the MPC Controller

[0153]

[0154] The main objective of the GSMPC controller designed in the present invention is to schedule the switching of the above-mentioned controller at an appropriate time to ensure the optimal growth of fish while minimizing energy consumption.

[0155] 3. Gain Scheduling Signal Design

[0156] The GSMPC structure that follows the gain scheduling signal for model switching can be expressed as Figure 4 shown. GSMPC involves switching between a set of predefined MPC controllers in a coordinated manner, which can be optimized as the switching of Q and W weights to accelerate the response speed and save controller resources. To implement GSMPC, first, an MPC must be designed for each operating point, as shown in Table 1, and then a scheduling signal must be created to switch between the controllers during operation.

[0157] A 70-hour control experiment was conducted, and the detailed design scheme of the operating point gain scheduling signal is as follows:

[0158] In the stage from 0 to 1.8 hours, this stage requires the dissolved oxygen concentration in the fish pond to reach the set target value at the fastest speed; in the stages from 6 to 19.3 hours, 26.5 to 43.3 hours, and 50.5 to 67.3 hours, according to the circadian rhythm, the respiratory oxygen consumption of fish starts to rise and gradually increases during these time periods. Within these operating points, the MPC1 controller can be used to increase the dissolved oxygen concentration in the fish pond at the fastest speed. There is a certain time delay in the change of the dissolved oxygen concentration in the fish pond relative to the control action of the controller. In the stage from 1.8 to 3 hours, in order to prevent excessive overshoot, the aeration rate should be reduced as much as possible, and at this time, energy consumption minimization (priority control weight) can be given priority. Therefore, the MPC4 controller can be used for this specific operating point. According to the circadian rhythm, the respiratory oxygen consumption of fish starts to increase in the stage from 5 to 6 hours, and the error weight of the controller needs to be increased to appropriately increase the dissolved oxygen concentration in the fish pond, and the MPC2 controller is used for this operating point. From 3 to 5 hours, 19.3 to 26.5 hours, 43.3 to 50.5 hours, and 67.3 to 70 hours, the respiratory oxygen consumption of fish is relatively low within these operating points, and when the dissolved oxygen concentration is still rising when the set value is reached, the control weight of the controller can be appropriately increased to reduce energy consumption. At this time, the MPC3 with the same error weight and control weight is selected.

[0159] Generally, the smaller the values of the integral absolute error (IAE) and the integral square error (ISE), the better the tracking accuracy of the controller. The integral absolute control (IAC) represents the integral of the absolute control input over a period of time and is used to evaluate the power consumption or activation intensity of the controller. The smaller the value of this index, the lower the energy consumption or activation intensity of the controller over a period of time, which is crucial for many long-term used devices.

[0160] The IAE, ISE, and IAC are used to evaluate the performance of the proposed controller. The specific equations are as follows:

[0161]

[0162] where e is the error, u is the control input, and T is the control period.

[0163] The present invention proposes a design method for a gain-scheduling model predictive controller for multi-operation points in recirculating aquaculture. The experimental site is the National Digital Fisheries Innovation Center of the College of Information and Electrical Engineering, China Agricultural University. The setpoint tracking results and dynamic weights of the GSMPC controller are as Figure 5 shown. The horizontal axis represents the specific experimental time, the left vertical axis represents the dissolved oxygen concentration, and the right vertical axis represents the weight value. The red curve represents the control effect of the GSMPC controller on the dissolved oxygen concentration, the black curve represents the target set reference value, the blue curve is the value of the error weight matrix Q, and the yellow curve is the value of the control weight matrix W. Figure 5 It shows that the gain-scheduling signal designed by the present invention can well call four sub-controllers with different functions, achieving the goal of improving control accuracy and reducing control energy consumption.

[0164] The separate control effects of the four MPCs designed in GSMPC are as Figure 6 shown. The blue curve represents the tracking result of the MPC1 controller. The MPC1 controller has the shortest rise time and the shortest peak time, but the largest overshoot and the smallest overall tracking error. The result meets the accuracy-priority design goal of MPC1: tracking the set target value at the fastest speed. The green curve represents the tracking result of the MPC2 controller. The control weight of the MPC2 controller is appropriately increased, and energy conservation begins to be considered, resulting in a slight decrease in performance, but the overshoot will decrease at this time. The red curve represents the tracking result of the MPC3 controller. The error weight and control weight of the MPC3 controller are the same. At this time, only the peak can reach the set target value, and energy consumption reduction is also considered. However, this will also lead to a greater decrease in performance. The gray curve represents the tracking result of the MPC4 controller. The control weight of the MPC4 controller is the highest, aiming to quickly reduce energy consumption and minimize the control output, but this will also cause the tracking error to reach the maximum.

[0165] The state errors of the MPC controller and the GSMP controller are as Figure 7As shown. The blue, green, orange, gray, and red curves represent the control errors of MPC1 - MPC4 and the GSMPC controller respectively. The control errors of all controllers also show a periodic fluctuation phenomenon along with the circadian rhythm of the model. From MPC1 to MPC4, as the error weight gradually decreases, the state error of the sub - controller gradually increases, and the error of MPC1 is the smallest. The control error of GSMPC is even smaller than that of MPC1, indicating that the error of GSMPC has been reduced and the accuracy has become higher.

[0166] The control inputs of the MPC controller and the GSMP controller are as Figure 8 shown. The blue, green, red, gray, and black curves represent the control inputs of MPC1 - MPC4 and the GSMPC controller respectively. The control inputs of all controllers also show a certain periodic fluctuation phenomenon along with the circadian rhythm of the model. Due to the switching between controllers, there are certain mutation phenomena in the control input of GSMPC, but all mutations are within the constraint range. From MPC1 to MPC4, the control input gradually decreases and the energy consumption gradually reduces, with the control input of MPC1 being the largest. The control input of GSMPC is less than that of MPC1, indicating that the energy consumption of GSMPC has been reduced.

[0167] According to the above results of dissolved oxygen set - point tracking control, calculate the control performance indicators such as IAE, ISE, and IAC of the GSMPC controller and the sub - MPC controllers. The results are shown in Table 2. From the table, we can see that IAE and ISE gradually increase from MPC1 to MPC4, indicating that the state error gradually increases from MPC1 to MPC4, with the error of MPC1 being the smallest. IAC gradually decreases from MPC1 to MPC4, indicating that from MPC1 to MPC4, the control input gradually decreases and the energy consumption gradually reduces, with the control input of MPC1 being the largest and the control amount of MPC4 being the smallest, almost zero, equivalent to turning off the aerator. MPC1 is the weight setting of the common MPC controller, and the goal of this weight setting is to achieve the best possible tracking effect. The designed GSMPC controller is compared with it.

[0168] Table 2 Control index values of the controller

[0169]

[0170] Compared with the MPC1 controller, the IAE of the GSMPC controller has decreased by 23.45%, the ISE has decreased by 11.25%, and the IAC has decreased by 11.28%. This means that the GSMPC controller reduces errors and also reduces energy consumption. The GSMPC controller has the best control performance, meets the requirements of accurate, fast, and stable dissolved oxygen control, reduces energy consumption, conforms to the circadian rhythm of fish, and can be used for long - term precise tracking control of dissolved oxygen in aquaculture.

[0171] The content not described in detail in this specification belongs to the prior art well-known to those skilled in the art.

[0172] Finally, it should be noted that the above are only preferred examples of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A design method for a gain-scheduled model predictive controller for aquaculture with multiple operating points, characterized in that: The steps include: S1. Design a basic MPC controller, the MPC controller comprising: a model prediction structure, a rolling optimization structure and a feedforward-feedback control structure, and the design steps include: S1.1 Establishment and discretization of prediction model; S1.2 Derivation of prediction model, establishing the system state matrix for a set period of time in the future; S1.3 Design the objective function, optimize and solve the objective function, and complete the design of the basic MPC controller; The objective function J is defined as the cumulative error between the predicted state vector and the reference value while complying with the control variable constraints: Among them, X k The predicted system state is recorded p control cycles in advance; U k When predicting the future state of a dynamic system, the control quantity within the prediction interval; R k is a series of reference values ​​defined within the prediction interval; The Q matrix adjusts the importance of the state error. The larger the Q, the faster the state converges. The W matrix adjusts the importance of the control input. When W is greater than Q, it prefers smaller inputs. S2. The prediction model includes several linear sub-models with different working points; find the core cost function of the basic MPC controller in S1, and design sub-MPC controllers with four different functions for each linear sub-model based on the basic MPC controller for dissolved oxygen concentration in recirculating aquaculture: control accuracy priority, two different proportions of balancing accuracy and energy consumption, and control energy consumption priority; identify the linear sub-models under different working conditions by switching the sub-MPC controllers; use multiple local linear sub-models with different working points to approximate global nonlinear dynamics; S3. Combined with the circadian rhythm of the linear sub-model under different working conditions of dissolved oxygen in recirculating aquaculture, a gain scheduling signal is designed for the sub-MPC controller of S2 to adapt to its stability and robustness. The sub-MPC controller is switched through the gain scheduling signal to perform overall scheduling control, and the switching between sub-MPC controllers is optimized as the switching of Q and W weights in the objective function to complete the design of the GSMPC controller. S4. Use IAE, ISE and IAC to evaluate the performance of the GSMPC controller described in S3, comprehensively consider the control accuracy of the GSMPC controller and the energy consumption generated by the control action to make an evaluation, and confirm the performance of the GSMPC controller.

2. The design method of a gain-scheduled model predictive controller for aquaculture with multiple operating points according to claim 1, characterized in that: The S1 is specifically: S1.1 Establishment and discretization of prediction model First choose the state vector: Then establish the system state equation: The forward Euler method is used to discretize the state equation: make Then we have: Where x is the state vector of the system; The rate of change of the state vector; u, the input vector, contains the external input of the system; A, the state matrix, represents the linear evolution of the system state variables; B, the input matrix, describes the impact of the external input on the system state; D, the disturbance; T, control period; x(k), the state of the system at the kth moment; u(k), the control amount of the system at the kth moment; S1.2 Derivation of prediction model, establishing the system state matrix for a set period of time in the future; N p represents the prediction interval, N c represents the control interval, N p ≥N c , record the predicted system state p control cycles in advance as: X k =[x(k+1∣k) T x(k+2∣k) T …x(k+p∣k) T ] T (7) When predicting the future state of a dynamic system, the control quantity within the prediction interval is: Use the following formula to predict the system state of the next p control cycles: make but X k =Ψx(k)+ΘU k (10) Where: X k , system state; (k+1|k), based on the state at time k, predict the state of the system at time k+1, and so on; U k , the control quantity and independent variable of the optimization problem to be solved are in the interval Nc≤k≤Np, uk=0; S1.3 Design the objective function and optimize the objective function; In the prediction interval N p A series of reference values ​​are defined: R k =[r(k+1) T r(k+2) T …r(k+p) T ] T (11) The objective function J is defined as the cumulative error between the predicted state vector and the reference value while respecting the control variable constraints: The Q matrix adjusts the importance of the state error. The larger the Q, the faster the state converges. The W matrix adjusts the importance of the control input. When W is greater than Q, it prefers smaller inputs. Let E = Ψx(k)-R k , Substituting formula (8) into the above formula, we get: make E T QE is a constant term and does not affect "U k The problem of "which value is the minimum value of the objective function J" is omitted: The solution of the MPC optimal control solution problem is finally transformed into a QP problem: s.t.u min ≤u(k+i|k)≤u max ,i=0,1,2,…,p-1 (16) Δu min ≤Δu(k+i|k)≤Δu max (17) Where: R k , set value; J, target solution function; Q, state error weight matrix; W, control input weight matrix, Q and W are diagonal matrices; u min , the lower limit of control quantity; u max , the upper limit of control quantity; Δu min , the lower limit of the control variable change rate; Δu max , the upper limit of the control variable change rate; u(k+i|k), the control amount of k+i is calculated at time k; Δu(k+i|k), the control change amount of k+i is calculated at time k; Call the optimization solver in the MATLAB function to solve the restricted QP optimization problem and obtain U k The initial value of is extracted as the control quantity of this control cycle.

3. The design method of a gain-scheduled model predictive controller for aquaculture with multiple operating points according to claim 1, characterized in that: The sub-MPC controllers in S2 include MPC1-MPC4; The MPC1 controller is a fast drive state approaching the set point without considering energy consumption; The MPC2 controller drives the state close to the set value while considering energy consumption; The MPC3 controller takes into account both state error and energy consumption; The MPC4 controller minimizes energy consumption without considering state errors.

4. The design method of a gain-scheduled model predictive controller for aquaculture with multiple operating points according to claim 1, characterized in that: The working point in S3 is specifically analyzed and designed by taking into account the dissolved oxygen concentration model and the circadian rhythm requirements of fish.

5. The design method of a gain-scheduled model predictive controller for aquaculture with multiple operating points according to claim 4, characterized in that: The gain scheduling signal design scheme is specifically as follows: During the 0-1.8 hour period, the aerator uses the maximum aeration flow, which is the upper limit of the control amount and the upper limit of the control amount change rate, and the dissolved oxygen concentration in the fish pond reaches the set target value at the fastest speed; In the 1.8-3 hour period, the change of dissolved oxygen concentration in the fish pond has a certain time delay relative to the control action of the controller. The MPC4 controller is used to prevent the dissolved oxygen peak from exceeding the set reference value by 5%, and the oxygenation rate is reduced as much as possible, giving priority to minimizing energy consumption and giving priority to control weight. In the stages of 3-5 hours, 19.3-26.5 hours, 43.3-50.5 hours, and 67.3-70 hours, the respiratory oxygen consumption of fish in these working points is low, and the dissolved oxygen concentration is still rising when the set value is reached. The MPC3 controller with the same error weight and control weight is selected; the control weight is increased; In the 5-6 hour stage, the MPC2 controller was used to increase the controller error weight to increase the dissolved oxygen concentration in the fish pond; During the 6-19.3 hour, 26.5-43.3 hour and 50.5-67.3 hour stages, the respiratory oxygen consumption of fish begins to rise and gradually increases in accordance with the circadian rhythm. Within these working points, the MPC1 controller is used to increase the dissolved oxygen concentration in the fish pond as quickly as possible.

6. The design method of a gain-scheduled model predictive controller for aquaculture with multiple operating points according to claim 1, characterized in that: In the S4, IAE, ISE and IAC are used to evaluate the performance of the GSMPC controller, and the specific equation is as follows: Where e is the error, u is the control input, and T is the control period.

7. The design method of a gain-scheduled model predictive controller for aquaculture with multiple operating points according to claim 1, characterized in that: In the S1, a linear model of the object, disturbance and noise is used to estimate the state of the basic MPC controller and predict the future output of the controlled object. The basic MPC controller solves the quadratic programming optimization problem of the optimal control quantity of the aerator in the dissolved oxygen concentration control to determine the control action based on the predicted output of the controlled object; The controlled object is the dissolved oxygen concentration in the circulating aquaculture system, and its model is: Where V is the volume of the fish pond; Q in is the water flow rate; C is the dissolved oxygen concentration in the circulating water aquaculture fish pond; k1, k2, k3, and β are all constants, which are obtained by fitting the measured data using Gauss-Newton nonlinear regression analysis; Q is the aeration flow rate; t d is the delay time, T w is the current water temperature; K rear is the water surface reoxygenation coefficient; M is the total mass of fish; R m is the average daily consumption rate of dissolved oxygen; A is the amplitude of the circadian rhythm model, f is the model frequency, φ is the model phase; P k is the temperature coefficient.

8. The design method of a gain-scheduled model predictive controller for aquaculture with multiple operating points according to claim 1, characterized in that: The sub-MPC controller can handle control problems under multiple constraints and give the optimal control quantity under these constraints; The sub-MPC controller decomposes an optimization control problem with a longer or even infinite time span into multiple optimization control problems with shorter or finite time spans to obtain the optimal solution.

9. A gain-scheduled model predictive controller system for aquaculture with multiple operating points, which adopts the design method of a gain-scheduled model predictive controller for aquaculture with multiple operating points as described in any one of claims 1 to 7.

10. Application of the gain-scheduled model predictive controller system for aquaculture with multiple operating points as described in claim 9 in precise tracking and control of long-term dissolved oxygen in aquaculture.

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