A dynamic matrix dimensionality reduction method and device based on predictive control

Abstract

The present invention relates to the field of predictive control technology, and in particular to a dynamic matrix dimensionality reduction method and device based on predictive control, including: obtaining the associated control step number and the number of predicted time domain overlap points according to the model length of a multi-input multi-output system; adjusting the distribution information of the control time domain according to the model length and control step number of the step response model, and equivalently merging all step response models of the multi-input multi-output system; obtaining the optimal position of the predicted time domain overlap points according to the equivalently merged step response model and the number of predicted time domain overlap points, and a particle swarm differential evolution strategy; reducing the dimension of the dynamic matrix of the multi-input multi-output system according to the optimal position of the predicted time domain overlap points and the distribution information of the control time domain, and obtaining a low-dimensional dynamic matrix. Its beneficial effect is that it effectively reduces the calculation amount of predictive control while maximally ensuring the accuracy of the prediction after the prediction time domain interval calculation.

Description

Technical Field

[0001] The present invention relates to the technical field of predictive control, and in particular to a dynamic matrix dimensionality reduction method and device based on predictive control. Background Art

[0002] As an advanced control algorithm, model predictive control was born directly from the practical application of industrial process control, and has been continuously completed and matured in the process of close integration with industrial applications. Among them, DMC (dynamic matrix control) technology based on step response sequence is an important branch of model predictive control. Due to its simple implementation, ability to effectively handle multi-input and multi-output coupling, and strong control robustness, it has been widely used in chemical industry, petroleum and other fields.

[0003] Dynamic matrix control is based on the step response relationship between variables to achieve the prediction of future processes. Therefore, it is necessary to calculate the dynamic matrix of the controller as a whole to predict the future state of the device. As the scale of the controller increases, the number of controlled quantities and manipulated variables increases, and the dynamic response time increases, the scale and length of the dynamic matrix are also increasing, and the time consumed by the algorithm calculation also increases exponentially accordingly, so the calculation efficiency becomes lower. When dealing with large-scale multi-input and output devices, its calculation time is difficult to meet the minute-level control cycle requirements. Due to this limitation, engineers may need to manually disassemble the controller during implementation, which reduces the efficiency of engineering implementation.

[0004] The dimension of the dynamic matrix is ​​mainly determined by the length of the prediction time domain, the length of the control time domain and the number of variables. The common method for dealing with the problem of the amount of calculation of model predictive control is to select the number of prediction time domain points and reduce the length of the control time domain, thereby reducing the dimension of the matrix. However, although this method can reduce the amount of calculation, the selection of the prediction time domain coincidence point and the selection of the control time domain length will greatly affect the future prediction quality of the model and the controller effect, and increase the difficulty of controller parameter tuning. For example, for systems with faster processes, the first few steps of the prediction time domain and the control time domain should be selected to pursue fast response; for processes with slower dynamic performance, it is difficult to stably control the system by only considering the first few steps of the time domain, and the prediction coincidence points and the number of control steps are distributed more evenly. Therefore, it is difficult to set a universal method for process devices with different characteristics. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a dynamic matrix dimensionality reduction method and device based on predictive control, which solves the technical problems that the future prediction quality of the model and the controller effect are affected when sampling the number of prediction time domain points and reducing the control time domain length, and the technical problem that it is difficult to stably control the system when only considering the first few steps in the time domain for a system with slow dynamic performance.

[0007] (II) Technical solution

[0008] In order to achieve the above object, the main technical solutions adopted by the present invention include:

[0009] In a first aspect, an embodiment of the present invention provides a dynamic matrix dimensionality reduction method based on predictive control, the method is implemented based on a pre-built multi-input multi-output system, and the method includes:

[0010] S100, according to the model length of the step response model in the MIMO system, obtaining the number of control steps and the number of predicted time domain coincidence points associated with the model length of the step response model;

[0011] The MIMO system includes at least one step response model, and all the step response models have a uniform model length;

[0012] S200, adjusting the distribution information of the control time domain according to the model length and the number of control steps of the step response model, and equivalently merging all step response models of the multi-input multi-output system;

[0013] S300, obtaining the optimal position of the predicted time domain coincidence point according to the equivalent merged step response model and the number of predicted time domain coincidence points, and a preset particle swarm differential evolution strategy;

[0014] S400, according to the optimal position of the predicted time domain overlap point and the adjusted control time domain distribution information, the dynamic matrix of the MIMO system is reduced in dimension to obtain a low-dimensional dynamic matrix, so that the controller constructs an MPC problem based on the low-dimensional dynamic matrix to obtain a calculated control output.

[0015] Optionally, the S200 includes:

[0016] According to the model length and the number of control steps of the step response model, the distribution information of the control time domain is adjusted so that the number of control steps is evenly distributed in the first half of the model length of the step response model;

[0017] According to the model length of the step response model and the model characteristics of each step response model in the pre-set multi-input multi-output system, and the pre-set formula 1, all step response models of the multi-input multi-output system are equivalently merged; the model characteristics of each step response model include: the dynamic response relationship between the input quantity and the output quantity; the formula 1 is:

[0018] ;

[0019] Among them, G is the step response model after equivalent merging, W is the number of inputs of the MIMO system, Q is the number of outputs of the MIMO system, G ijThe dynamic response relationship between the input and output of the step response model corresponding to the i-th input and j-th output of the MIMO system;

[0020] The dynamic response relationship between the input and output of any step response model is:

[0021] G ij =[g ij1 ,…,g ijP ];

[0022] Among them, G ij is the dynamic response relationship between the input and output of the step response model corresponding to the ith input and jth output of the MIMO system. P represents the step response length, i.e., the model length. g ij1 ,…,g ijP are the responses of the MIMO system to the i-th output of the j-th input signal.

[0023] Optionally, the S300 includes:

[0024] S300-10, according to the number of predicted time domain coincidence points, randomly extract the predicted time domain coincidence point positions in the predicted time domain of the MIMO system, generate a parameter population, repeat a preset number of times until the number of parameter populations reaches a preset value, and the number of predicted time domain coincidence point positions in each parameter population is equal to the number of predicted time domain coincidence points; wherein any parameter population X i =[x1, x2, …, x N ], x1 is the first predicted time domain coincidence point position, x1, x2, ..., x N are the predicted time domain coincidence points in the parameter population, and N represents the number of predicted time domain coincidence points;

[0025] S300-20, according to the equivalent combined step response model, fitting a step response curve corresponding to the equivalent combined step response model;

[0026] According to the positions of all predicted time domain coincidence points in each parameter population, the step response curve corresponding to each parameter population is fitted;

[0027] S300-30. According to the step response curve corresponding to each parameter population and the step response curve corresponding to the equivalent merged step response model, the objective function value corresponding to each parameter population is obtained, and the parameter population corresponding to the minimum objective function value is taken as the optimal parameter population. The position of the predicted time domain coincidence point in the optimal parameter population is the optimal position of the predicted time domain coincidence point.

[0028] Optionally, the S300-30 includes:

[0029] According to the step response curve corresponding to each parameter population and the step response curve corresponding to the equivalently merged step response model, as well as the preset formula 2, the residual of the step response curve corresponding to each parameter population and the step response curve corresponding to the equivalently merged step response model is obtained, that is, the objective function value corresponding to each parameter population; the formula 2 is:

[0030] ;

[0031] Among them, g o is the step response curve value at the oth predicted time domain coincidence point of the step response curve corresponding to the equivalent merged step response model, x1, x2, ..., x N All are predicted time domain coincidence point positions, g x1 , g x2 , ..., g xN are the step response curve values ​​of each predicted time domain coincidence point in the parameter population, J is the residual of the step response curve corresponding to the parameter population and the step response curve corresponding to the equivalent merged step response model, that is, the objective function value; P represents the step response length

[0032] The parameter population corresponding to the minimum objective function value is taken as the optimal parameter population, and the position of the predicted time domain coincidence point in the optimal parameter population is the optimal position of the predicted time domain coincidence point.

[0033] Optionally, after S300-10 and before S300-20, the method further includes:

[0034] S300-11. Evolving each parameter population based on a preset evolution degree factor to obtain an evolved population corresponding to each parameter population;

[0035] S300-12, based on the preset random strategy and crossover factor, crossover and mutation are performed on each parameter population and the evolutionary population corresponding to the parameter population to obtain an updated population corresponding to each parameter population;

[0036] Then the S300-20 also includes:

[0037] According to the positions of all predicted time domain coincidence points in each updated population, the step response curve corresponding to each updated population is fitted;

[0038] The S300-30 includes:

[0039] According to the step response curves corresponding to each parameter population and each update population, as well as the step response curves corresponding to the equivalently merged step response model, the objective function values ​​corresponding to each parameter population and each update population are obtained, and the parameter population or update population corresponding to the minimum objective function value is taken as the optimal parameter population. The position of the predicted time domain coincidence point in the optimal parameter population is the optimal position of the predicted time domain coincidence point.

[0040] Optionally, the S300 further includes:

[0041] S300-40, repeat steps S300-10 to S300-30 up to the preset number of times, compare the objective function values ​​corresponding to all optimal parameter populations, and use the optimal parameter population with the smallest objective function value as the optimal parameter population finally used. The predicted time domain overlap point position in the optimal parameter population finally used is the optimal position of the predicted time domain overlap point.

[0042] Optionally, the S300-11 includes:

[0043] According to a preset evolution degree factor and a preset formula 3, each parameter population is evolved to obtain an evolution population corresponding to each parameter population; the number of the parameter population is greater than or equal to 2;

[0044] The formula three is:

[0045] ;

[0046] Among them, X a is the parameter population to be evolved, F is the evolution factor, and 0≤F≤2, X b and X c are two different parameter populations randomly selected from all parameter populations, X a * is the evolutionary population corresponding to the parameter population to be evolved.

[0047] Optionally, the S300-12 includes:

[0048] Based on the preset random strategy and crossover factor, and the preset formula 4, each parameter population and the evolutionary population corresponding to the parameter population are cross-mutated to obtain the update population corresponding to each parameter population; the formula 3 is:

[0049] ;

[0050] Among them, X a is the parameter population to be cross-mutated, X a * is the evolutionary population corresponding to the parameter population to be cross-mutated, is the update population corresponding to the parameter population to be cross-mutated.

[0051] Optionally, the S400 includes:

[0052] According to the optimal position of the predicted time domain overlap point and the adjusted control time domain distribution information, the dynamic matrix of the MIMO system is reduced in dimension, and the P*P dynamic matrix is ​​reduced in dimension to N*M to obtain a low-dimensional dynamic matrix, so that the controller constructs the MPC problem based on the low-dimensional dynamic matrix to obtain the calculated control output, where P is the model length of the step response model in the MIMO system, N represents the number of predicted time domain overlap points, and M is the number of control steps;

[0053] The dynamic matrix without dimensionality reduction is:

[0054] ;

[0055] a0,a1,...,a P-1 , a P-2 , ..., a P-M All are step response sequences;

[0056] The dynamic matrix after dimensionality reduction is:

[0057] ;

[0058] are all step response sequences after dimension reduction, c1,...,c M They are all control blocks, and the number is consistent with the number of control steps.

[0059] In a second aspect, an embodiment of the present invention provides a dynamic matrix dimensionality reduction device based on predictive control, comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the above-mentioned dynamic matrix dimensionality reduction method based on predictive control.

[0060] (III) Beneficial effects

[0061] The beneficial effects of the present invention are as follows: a dynamic matrix dimensionality reduction method based on predictive control of the present invention effectively reduces the amount of calculation of predictive control by designing the control time domain interval sampling points, that is, the distribution information of the control time domain and the optimal position of the prediction time domain overlap point, ensuring that large-scale state controllers can also meet the control cycle requirements of the minute level; and the use of the particle swarm differential evolution strategy maximizes the accuracy of the prediction after the prediction time domain interval calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a flow chart of a dynamic matrix dimensionality reduction method based on predictive control;

[0063] Figure 2 It is a flow chart of a dynamic matrix dimensionality reduction method based on predictive control;

[0064] Figure 3 Flowchart of differential evolution for optimizing control time domain. DETAILED DESCRIPTION

[0065] In order to better explain the present invention and facilitate understanding, the following term explanations are provided:

[0066] Predictive control: Model predictive control (MPC) is a special type of control in which the current control action is obtained at each sampling instant by solving a finite-time open-loop optimal control problem.

[0067] Dynamic Matrix Predictive Control Method: Dynamic Matrix Predictive Control, referred to as DMC, is an important typical representative algorithm of predictive control. It has basic characteristics such as predictive model, online rolling optimization and error feedback correction. Its uniqueness lies in the use of easy-to-measure object step response as a model. The algorithm is simple and robust, and is suitable for non-minimum phase systems with pure time delay and open-loop asymptotic stability. It has been proven to be a successful and effective control algorithm in process control in the chemical and petroleum sectors.

[0068] Step response sequence: refers to the zero-state response of the system after receiving a unit step function input. The so-called zero-state response means that the system is in the initial state before receiving the specified input, that is, it is guaranteed that the response change of the system is completely due to the specified input (here, the unit step input).

[0069] Prediction horizon: refers to the length of time or number of steps used in model predictive control to predict future outputs. In the prediction horizon, the MPC controller uses the system model to predict the future system behavior. This allows the controller to understand in advance how the system response will change at a certain time in the future, so that better control decisions can be made.

[0070] Control horizon: refers to the time length or number of steps of the control input actually applied during the optimization process. The length of the control horizon determines the number of steps for each control operation. A shorter control horizon can reduce the frequency of control strategy adjustments and save computing resources, but may not be able to fully respond to some emergencies, and will be more aggressive for processes with long process times.

[0071] The present invention will be described in detail below through specific implementation modes in conjunction with the accompanying drawings.

[0072] A dynamic matrix dimensionality reduction method based on predictive control proposed in an embodiment of the present invention effectively reduces the computational complexity of predictive control by designing the control time domain interval sampling points, i.e., the distribution information of the control time domain and the optimal position of the prediction time domain overlap point, thereby ensuring that large-scale state controllers can also meet the control cycle requirements of minutes; and the use of a particle swarm differential evolution strategy maximizes the accuracy of the prediction after the prediction time domain interval calculation.

[0073] In order to better understand the above technical solution, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a clearer and more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0074] Example 1

[0075] This embodiment provides a dynamic matrix dimensionality reduction method based on predictive control. The method is implemented based on a controller. The controller includes a pre-built multi-input multi-output system, and the multi-input multi-output system is a W-input Q-output system, where W and Q are both non-zero natural numbers.

[0076] like Figure 1 As shown, the method includes:

[0077] S100. According to a model length of a step response model in a MIMO system, the number of control steps and the number of predicted time-domain coincidence points associated with the model length of the step response model are obtained; the MIMO system includes at least one step response model, and all step response models have a uniform model length.

[0078] S200, adjusting the distribution information of the control time domain according to the model length and the number of control steps of the step response model, and equivalently merging all step response models of the multi-input multi-output system; specifically:

[0079] According to the model length and the number of control steps of the step response model, the distribution information of the control time domain is adjusted so that the number of control steps is evenly distributed in the first half of the model length of the step response model;

[0080] According to the model length of the step response model and the model characteristics of each step response model in the pre-set multi-input multi-output system, and the pre-set formula 1, all step response models of the multi-input multi-output system are equivalently merged; the model characteristics of each step response model include: the dynamic response relationship between the input quantity and the output quantity; the formula 1 is:

[0081] ;

[0082] Among them, G is the step response model after equivalent merging, W is the number of inputs of the MIMO system, Q is the number of outputs of the MIMO system, G ij The dynamic response relationship between the input and output of the step response model corresponding to the i-th input and j-th output of the MIMO system;

[0083] The dynamic response relationship between the input and output of any step response model is:

[0084] G ij =[g ij1 ,…,g ijP ];

[0085] Among them, G ij is the dynamic response relationship between the input and output of the step response model corresponding to the ith input and jth output of the MIMO system. P represents the step response length, i.e., the model length. g ij1 ,…,g ijP are the responses of the MIMO system to the i-th output of the j-th input signal.

[0086] S300, according to the equivalent merged step response model and the number of predicted time domain coincidence points, and the preset particle swarm differential evolution strategy, the optimal position of the predicted time domain coincidence point is obtained; specifically:

[0087] According to the number of predicted time domain coincidence points, the predicted time domain coincidence point positions are randomly selected in the predicted time domain of the MIMO system to generate a parameter population, and the preset number of times is repeated until the number of parameter populations reaches the preset value, and the number of predicted time domain coincidence point positions in each parameter population is equal to the number of predicted time domain coincidence points; wherein, any parameter population X i =[x1, x2, …, x N ], x1 is the first predicted time domain coincidence point position, x1, x2, ..., x N are the predicted time domain coincidence points in the parameter population, and N represents the number of predicted time domain coincidence points.

[0088] According to a preset evolution degree factor and a preset formula 3, each parameter population is evolved to obtain an evolution population corresponding to each parameter population; the number of the parameter population is greater than or equal to 2;

[0089] The formula three is:

[0090] ;

[0091] Among them, X a is the parameter population to be evolved, F is the evolution factor, and 0≤F≤2, X b and Xc are two different parameter populations randomly selected from all parameter populations, X a * is the evolutionary population corresponding to the parameter population to be evolved.

[0092] Based on the preset random strategy and crossover factor, and the preset formula 4, each parameter population and the evolutionary population corresponding to the parameter population are cross-mutated to obtain the update population corresponding to each parameter population; the formula 3 is:

[0093] ;

[0094] Among them, X a is the parameter population to be cross-mutated, X a * is the evolutionary population corresponding to the parameter population to be cross-mutated, is the update population corresponding to the parameter population to be cross-mutated.

[0095] According to the equivalent combined step response model, a step response curve corresponding to the equivalent combined step response model is fitted;

[0096] According to the positions of all predicted time domain coincidence points in each parameter population, the step response curve corresponding to each parameter population is fitted;

[0097] According to the positions of all predicted time-domain coincidence points in each updated population, the step response curve corresponding to each updated population is fitted.

[0098] According to the step response curve corresponding to each parameter population and each update population, the step response curve corresponding to the equivalently merged step response model and the preset formula 2, the objective function value corresponding to each parameter population and each update population is obtained (the objective function value is the residual of the step response curve corresponding to any parameter population or update population and the step response curve corresponding to the equivalently merged step response model), and the parameter population or update population corresponding to the minimum objective function value is used as the optimal parameter population, and the position of the predicted time domain coincidence point in the optimal parameter population is the optimal position of the predicted time domain coincidence point; the formula 2 is:

[0099] ;

[0100] Among them, g o is the step response curve value at the oth predicted time domain coincidence point of the step response curve corresponding to the equivalent merged step response model, x1, x2, ..., x N All are predicted time domain coincidence point positions, g x1 , g x2 , ..., g xNare the step response curve values ​​of each predicted time domain coincidence point in the parameter population or update population, J is the residual of the step response curve corresponding to the parameter population and the step response curve corresponding to the equivalent merged step response model, that is, the objective function value; P represents the step response length.

[0101] Repeat step S300 for a preset number of times, compare the objective function values ​​corresponding to all optimal parameter populations, and use the optimal parameter population with the smallest objective function value as the optimal parameter population finally used. The predicted time domain coincidence point position in the optimal parameter population finally used is the optimal position of the predicted time domain coincidence point.

[0102] S400, according to the optimal position of the predicted time domain overlap point and the adjusted control time domain distribution information, the dynamic matrix of the MIMO system is reduced in dimension to obtain a low-dimensional dynamic matrix, so that the controller constructs an MPC problem based on the low-dimensional dynamic matrix to obtain a calculated control output.

[0103] This embodiment provides a dynamic matrix dimensionality reduction method based on predictive control, which effectively reduces the calculation amount of predictive control by designing the control time domain interval sampling points, that is, the distribution information of the control time domain and the optimal position of the prediction time domain overlap point, ensuring that large-scale state controllers can also meet the control cycle requirements of minutes; and using the particle swarm differential evolution strategy, it maximizes the accuracy of the prediction after the prediction time domain interval calculation.

[0104] Example 2

[0105] The present embodiment provides a dynamic matrix dimensionality reduction method based on predictive control. First, a step response model relationship is obtained based on data identification or mechanism identification, and the number of control steps and their specific distribution in the controller control time domain are determined by expert rules; then the number of prediction time domain overlap points is determined based on the model length; then, a random optimization algorithm is constructed to adaptively calculate the optimal position of the prediction time domain overlap points by minimizing the residual; finally, before the controller is started or when the model time constant and time lag change, the above operation is used to use the dynamic matrix after dimensionality reduction in the subsequent model prediction problem construction and solution process, while ensuring the prediction accuracy, reducing the calculation time of the algorithm.

[0106] The specific process is as follows Figure 2 As shown, including:

[0107] Step 1: Given the number of control steps and the number of predicted coincidence points based on expert experience;

[0108] Based on the model length predetermined by the controller, as well as expert experience and user settings, the corresponding control steps M and the number of predicted time domain overlap points N are automatically given; expert experience and user settings can be reflected by setting a mapping strategy, which is used to give the recommended control steps and the number of predicted time domain overlap points for the model length based on the model length. The longer the step response model length, the more predicted control steps and predicted overlap points are selected. For example, if the model length is 30, the recommended control steps are 8 and the number of overlap points is 15; when the model length is 200, the recommended control steps are 19 and the number of overlap points is 26. The model length P can be obtained in advance through the identification software.

[0109] Step 2, setting the distribution of control steps in the control time domain;

[0110] To achieve smoother control, the control steps are evenly distributed in the first half of the model length. For example, if the model length is 32 and the control step number M is 8, the control step number distribution is [1, 3, 5, 7, 9, 11, 13, 15].

[0111] After completing the above steps 1 and 2, that is, completing the distribution optimization of the control time domain, it is necessary to set the overlap point of the prediction time domain.

[0112] Step 3, equivalently merge the step response models of the MIMO system;

[0113] Step one can determine the number of predicted time-domain overlap points that need to be calculated, and the specific locations can be distributed in the step response model of length P. In order to select the appropriate overlap point location, it is necessary to weigh the characteristics of all step response models in the multi-input multi-output system of all controllers, so all step response models need to be equivalently merged.

[0114] Taking a 2-input 1-output system as an example, the system consists of 2 step response models. The dynamic response relationship between the input and output of any step response model is:

[0115] G ij =[g ij1 ,…,g ijP ];

[0116] Among them, G ij is the dynamic response relationship between the input and output of the step response model corresponding to the ith input and jth output of the MIMO system. P represents the step response length, i.e., the model length. g ij1 ,…,g ijP They are the responses of the MIMO system to the i-th output of the j-th input signal. In order to integrate the characteristics of each model, it is necessary to merge multiple step response curves without gain, such as: .

[0117] Step 4: Based on the equivalent merged step response model, the particle swarm differential evolution strategy is used to solve the optimal position of the predicted time domain coincidence point;

[0118] like Figure 3 As shown, specifically including:

[0119] Based on the idea of ​​prediction time domain coincidence point, it is necessary to extract N steps from the prediction time domain of the model length of the step response model to make future predictions of the state of the controlled variable.

[0120] Therefore, the parameter to be optimized can be defined as X i =[x1, x2, …, x N ], x1 is the first predicted time domain coincidence point position, x1, x2, ..., x N are the predicted time domain coincidence points in the parameter population, and N represents the number of predicted time domain coincidence points. Execute the above steps 10 times and repeat the iterative learning times.

[0121] More specifically, define and randomly initialize 10 parameter populations X i , calculate the objective function value of each parameter population, , where g o is the step response curve value at the oth predicted time domain coincidence point of the step response curve corresponding to the equivalent merged step response model, x1, x2, ..., x N All are predicted time domain coincidence point positions, g x1 , g x2 , ..., g xN are the step response curve values ​​of each predicted time domain coincidence point in the parameter population or update population respectively, and J is the residual of the step response curve corresponding to the parameter population and the step response curve corresponding to the equivalent merged step response model, that is, the objective function value.

[0122] Then, each population is evolved, and the formula is: ; Among them, X a is the parameter population to be evolved, is the evolution degree factor, and 0≤F≤2, X b and X c are two different parameter populations randomly selected from all parameter populations, X a * is the evolution population corresponding to the parameter population to be evolved. Based on the preset random strategy and crossover factor, and the preset formula 4, each parameter population and the evolution population corresponding to the parameter population are cross-mutated to obtain the update population corresponding to each parameter population; the formula 3 is:

[0123] ;

[0124] Among them, X a is the parameter population to be cross-mutated, X a * is the evolutionary population corresponding to the parameter population to be cross-mutated, is the update population corresponding to the parameter population to be cross-mutated, C is the crossover factor, which is 0≤C≤1 and is used to control the intensity of the exchange. Calculate the objective function value of the update population; , g o is the step response curve value at the oth predicted time domain coincidence point of the step response curve corresponding to the equivalent merged step response model, x1, x2, ..., x N All are predicted time domain coincidence point positions, g x1 , g x2 , ..., g xN are the step response curve values ​​of each predicted time domain coincidence point in the parameter population or update population respectively, and J is the residual of the step response curve corresponding to the parameter population and the step response curve corresponding to the equivalent merged step response model, that is, the objective function value.

[0125] The parameter population or updated population corresponding to the minimum objective function value is taken as the optimal parameter population, and the position of the predicted time domain coincidence point in the optimal parameter population is the optimal position of the predicted time domain coincidence point.

[0126] Furthermore, multiple rounds of standard differential evolution algorithm repeat the above steps, and calculate the optimal position of the optimal predicted time domain coincidence point by optimizing and solving the principle of minimizing the objective function, that is, the optimal parameter population with the smallest objective function value is used as the optimal parameter population finally used, and the position of the predicted time domain coincidence point in the optimal parameter population finally used is the optimal position of the predicted time domain coincidence point.

[0127] Step 5: Reduce the dimension of the dynamic matrix based on the number of control steps and the optimal position of the predicted time domain overlap point;

[0128] According to the model predictive control principle, according to the DMC algorithm prediction model iteration formula, the dynamic matrix is ​​multiplied by the future action amount Predict the future state of the controlled variable. y(t) represents the state of the controlled variable at time t, generally representing the state at the current time. y(t+P|t) represents the predicted value at time t for the future P time later. ... It represents the predicted control quantity from the current moment to the future moment P, which is the value solved by the prediction control optimization. ai represents the step response curve value of the ith point.

[0129] ;

[0130] in, is a dynamic matrix used to mark the linear relationship between input and output, a0, a1, ..., a P-1 , a P-2 , ..., a P-M All are step response sequences.

[0131] As can be seen from the above formula, if dimensionality reduction is not performed, it is necessary to predict the state of the controlled variable in the future P steps, and at the same time, it is necessary to calculate and solve the action amount of P steps. At the same time, the dimension of the matrix will increase with the increase of the matrix dimension, and the computational burden is heavy.

[0132] Therefore, it is necessary to combine the control block points obtained in step 2 and the predicted overlap point strategy obtained in step 4. In the P-step controlled variable prediction state [y(t+1|t),y(t+2|t)...y(t+P|t)], we extract the overlap point position with the highest fit, perform row dimensionality reduction of the matrix, and reduce the predicted control quantity that needs to be calculated by the number of control steps.

[0133] ;

[0134] The above formula is a simplified iterative prediction model that combines the number of control steps, the distribution information of the adjusted control time domain, and the optimal position of the coincidence point in the prediction time domain. y(t+xi|t) represents the prediction of the future x at time t. i The predicted value after time, x i is the position of the coincident point obtained by the i-th solution, It represents the predicted action amount at the future time c1 that needs to be calculated. c1 represents the first control block point. There are M control block points in total, which are obtained from step 2, that is, the distribution information of the control time domain.

[0135] The prediction of the controlled variable from P steps is reduced to N steps by sampling. At the same time, the change of P steps is quantified and simplified to the number of control steps M by controlling the blocks. As the dimensions of the controlled variable and the input control variable are reduced, the dimension of the dynamic matrix is ​​also reduced.

[0136] Step 6: Use the dynamic matrix after dimensionality reduction to construct the MPC problem and solve it to obtain the computational control output.

[0137] The dynamic prediction matrix after dimensionality reduction obtained in step five is used to construct the optimization problem of model predictive control to predict the future position of the controlled quantity, and perform differential optimization with the expected target or expected control trajectory given by the user to obtain a set of optimal control quantities, and select the first step for controller control output.

[0138] This embodiment effectively reduces the amount of calculation of the predictive control algorithm by sampling points at intervals in the control time domain and the prediction time domain of the model predictive control; optimizes the strategy of prediction coincidence points by using a differential evolution algorithm based on the response sequence, thereby achieving adaptive optimization of prediction coincidence points, thereby reducing the amount of calculation while ensuring prediction accuracy and effectiveness.

[0139] Example 3

[0140] This embodiment provides a dynamic matrix dimensionality reduction device based on predictive control, including a memory, a processor and a computer program stored in the memory, and the processor executes the computer program to implement the dynamic matrix dimensionality reduction method based on predictive control described in Example 1 or Example 2.

[0141] In the description of the present invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0142] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0143] In the present invention, unless otherwise clearly specified and limited, when a first feature is “on” or “below” a second feature, it may be that the first and second features are in direct contact, or that the first and second features are in indirect contact through an intermediate medium. Moreover, when a first feature is “above”, “above” or “above” a second feature, it may be that the first feature is directly above or obliquely above the second feature, or it may simply mean that the first feature is higher in level than the second feature. When a first feature is “below”, “below” or “below” a second feature, it may be that the first feature is directly below or obliquely below the second feature, or it may simply mean that the first feature is lower in level than the second feature.

[0144] In the description of this specification, the description of the terms "one embodiment", "some embodiments", "embodiment", "example", "specific example" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are contradictory.

[0145] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may alter, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A dynamic matrix dimensionality reduction method based on predictive control, the method is implemented based on a pre-built multi-input multi-output system, characterized in that: The method comprises: S100, according to the model length of the step response model in the MIMO system, obtaining the number of control steps and the number of predicted time domain coincidence points associated with the model length of the step response model; The MIMO system includes at least one step response model, and all the step response models have a uniform model length; S200, adjusting the distribution information of the control time domain according to the model length and the control step number of the step response model, so that the control step number is evenly distributed in the first half of the model length of the step response model; and, according to the model length of the step response model and the model characteristics of each step response model in the multi-input multi-output system set in advance, equivalently merging all step response models of the multi-input multi-output system; S300, randomly extracting the positions of the predicted time domain coincidence points in the predicted time domain of the MIMO system according to the number of predicted time domain coincidence points, generating a parameter population, and repeating the process for a preset number of times; According to the equivalent combined step response model, a step response curve corresponding to the equivalent combined step response model is fitted; According to the positions of all predicted time domain coincidence points in each parameter population, the step response curve corresponding to each parameter population is fitted; According to the step response curve corresponding to each parameter population and the step response curve corresponding to the equivalent merged step response model, the objective function value corresponding to each parameter population is obtained, and the position of the predicted time domain coincidence point in the parameter population corresponding to the minimum objective function value is the optimal position of the predicted time domain coincidence point; S400, according to the optimal position of the predicted time domain overlap point and the adjusted control time domain distribution information, the dynamic matrix of the MIMO system is reduced in dimension, and the P*P dynamic matrix is ​​reduced in dimension to N*M to obtain a low-dimensional dynamic matrix, so that the controller constructs an MPC problem based on the low-dimensional dynamic matrix to obtain a calculated control output, wherein P is the model length of the step response model in the MIMO system, N represents the number of predicted time domain overlap points, and M is the number of control steps; The dynamic matrix without dimensionality reduction is: ； a0,a1,...,a P-1 , a P-2 , ..., a P-M All are step response sequences; The dynamic matrix after dimensionality reduction is: ； are all step response sequences after dimension reduction, c1,...,c M They are all control blocks, and the number is consistent with the number of control steps.

2. The dynamic matrix dimensionality reduction method based on predictive control according to claim 1, characterized in that: The S200 includes: According to the model length and the number of control steps of the step response model, the distribution information of the control time domain is adjusted so that the number of control steps is evenly distributed in the first half of the model length of the step response model; According to the model length of the step response model and the model characteristics of each step response model in the pre-set multi-input multi-output system, and the pre-set formula 1, all step response models of the multi-input multi-output system are equivalently merged; the model characteristics of each step response model include: the dynamic response relationship between the input quantity and the output quantity; the formula 1 is: ； Among them, G is the step response model after equivalent merging, W is the number of inputs of the MIMO system, Q is the number of outputs of the MIMO system, G ij The dynamic response relationship between the input and output of the step response model corresponding to the i-th input and j-th output of the MIMO system; The dynamic response relationship between the input and output of any step response model is: G ij =[g ij1 ,…,g ijP ]; Among them, G ij is the dynamic response relationship between the input and output of the step response model corresponding to the ith input and jth output of the MIMO system. P represents the step response length, i.e., the model length. g ij1 ,…,g ijP are the responses of the MIMO system to the i-th output of the j-th input signal.

3. The dynamic matrix dimensionality reduction method based on predictive control according to claim 1, characterized in that: The S300 includes: S300-10, according to the number of predicted time domain coincidence points, randomly extract the predicted time domain coincidence point positions in the predicted time domain of the MIMO system, generate a parameter population, repeat a preset number of times until the number of parameter populations reaches a preset value, and the number of predicted time domain coincidence point positions in each parameter population is equal to the number of predicted time domain coincidence points; wherein any parameter population X i =[x1, x2, …, x N ], x1 is the first predicted time domain coincidence point position, x1, x2, ..., x N are the predicted time domain coincidence points in the parameter population, and N represents the number of predicted time domain coincidence points; S300-20, according to the equivalent combined step response model, fitting a step response curve corresponding to the equivalent combined step response model; According to the positions of all predicted time domain coincidence points in each parameter population, the step response curve corresponding to each parameter population is fitted; S300-30. According to the step response curve corresponding to each parameter population and the step response curve corresponding to the equivalent merged step response model, the objective function value corresponding to each parameter population is obtained, and the parameter population corresponding to the minimum objective function value is taken as the optimal parameter population. The position of the predicted time domain coincidence point in the optimal parameter population is the optimal position of the predicted time domain coincidence point.

4. The dynamic matrix dimensionality reduction method based on predictive control according to claim 3, characterized in that: The S300-30 includes: According to the step response curve corresponding to each parameter population and the step response curve corresponding to the equivalently merged step response model, as well as the preset formula 2, the residual of the step response curve corresponding to each parameter population and the step response curve corresponding to the equivalently merged step response model is obtained, that is, the objective function value corresponding to each parameter population; the formula 2 is: ； Among them, g o is the step response curve value at the oth predicted time domain coincidence point of the step response curve corresponding to the equivalent merged step response model, x1, x2, ..., x N All are predicted time domain coincidence point positions, g x1 , g x2 , ..., g xN are the step response curve values ​​of each predicted time domain coincidence point in the parameter population, J is the residual between the step response curve corresponding to the parameter population and the step response curve corresponding to the equivalent merged step response model, that is, the objective function value; P represents the step response length; The parameter population corresponding to the minimum objective function value is taken as the optimal parameter population, and the position of the predicted time domain coincidence point in the optimal parameter population is the optimal position of the predicted time domain coincidence point.

5. The dynamic matrix dimensionality reduction method based on predictive control according to claim 3, characterized in that: After S300-10 and before S300-20, the following further includes: S300-11. Evolving each parameter population based on a preset evolution degree factor to obtain an evolved population corresponding to each parameter population; S300-12, based on the preset random strategy and crossover factor, crossover and mutation are performed on each parameter population and the evolutionary population corresponding to the parameter population to obtain an updated population corresponding to each parameter population; Then the S300-20 also includes: According to the positions of all predicted time domain coincidence points in each updated population, the step response curve corresponding to each updated population is fitted; The S300-30 includes: According to the step response curves corresponding to each parameter population and each update population, as well as the step response curves corresponding to the equivalently merged step response model, the objective function values ​​corresponding to each parameter population and each update population are obtained, and the parameter population or update population corresponding to the minimum objective function value is taken as the optimal parameter population. The position of the predicted time domain coincidence point in the optimal parameter population is the optimal position of the predicted time domain coincidence point.

6. The dynamic matrix dimensionality reduction method based on predictive control according to claim 5, characterized in that: The S300 further includes: S300-40, repeat steps S300-10 to S300-30 up to the preset number of times, compare the objective function values ​​corresponding to all optimal parameter populations, and use the optimal parameter population with the smallest objective function value as the optimal parameter population finally used. The predicted time domain overlap point position in the optimal parameter population finally used is the optimal position of the predicted time domain overlap point.

7. The dynamic matrix dimensionality reduction method based on predictive control according to claim 5, characterized in that: The S300-11 includes: According to a preset evolution degree factor and a preset formula 3, each parameter population is evolved to obtain an evolution population corresponding to each parameter population; the number of the parameter population is greater than or equal to 2; The formula three is: ； Among them, X a is the parameter population to be evolved, F is the evolution factor, and 0≤F≤2, X b and X c are two different parameter populations randomly selected from all parameter populations, is the evolutionary population corresponding to the parameter population to be evolved.

8. The dynamic matrix dimensionality reduction method based on predictive control according to claim 5, characterized in that: The S300-12 includes: Based on the preset random strategy and crossover factor, and the preset formula 4, each parameter population and the evolutionary population corresponding to the parameter population are cross-mutated to obtain the update population corresponding to each parameter population; the formula 4 is: ； Among them, X a is the parameter population to be cross-mutated, is the evolutionary population corresponding to the parameter population to be cross-mutated, is the update population corresponding to the parameter population to be cross-mutated.

9. A dynamic matrix dimensionality reduction device based on predictive control, comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the dynamic matrix dimensionality reduction method based on predictive control as described in any one of claims 1 to 8.

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