CN-116627026-B - Adaptive PI type nonlinear control method, device and medium suitable for MIMO system

Abstract

The application provides a self-adaptive PI type nonlinear control method, equipment and medium suitable for a MIMO system, wherein the method comprises the steps of establishing a state equation of the MIMO system; establishing an MIMO system error equation according to the MIMO system state equation, designing a system error function S according to the MIMO system error equation, establishing a performance index function J z according to the system error function S, selecting a Lyapunov function V 1 , designing a system controller u d , and proving the stability of the MIMO system controlled by the system controller u d by utilizing the Lyapunov function V 1 . The method solves the problem that the whole running process cannot be effectively observed through the performance index function, solves the problem that the parameter of the PID control method is difficult to select by designing the controller to limit the square matrix and the non-square matrix of the MIMO system, and solves the problem that the PID control method in the MIMO system cannot process the non-linear item.

Inventors

• WANG JIANHUI
• WU YUSHEN
• ZHANG YUANQING
• LI YONGHUA
• WU WENQIANG
• HUANG WENQI
• KONG WEITING

Assignees

• 广州大学

Dates

Publication Date

20260505

Application Date

20230614

Claims (6)

1. 1. An adaptive PI nonlinear control method suitable for a MIMO system, comprising: s1, establishing a state equation of the MIMO system; s2, establishing an MIMO system error equation according to the MIMO system state equation; S3, designing a system error function S according to an MIMO system error equation; s4, establishing a performance index function according to the system error function S ; S5, selecting Lyapunov function ; S6, designing a self-adaptive PI type nonlinear control method, wherein the control method comprises the step of designing a system controller The self-adaptive algorithm parameters in the controller are combined with the radial neural network to realize automatic updating; S7, utilizing Lyapunov function Proving through a system controller Stability of the MIMO system being controlled; Wherein, a system controller is designed By introducing the matrix, the controller can adapt to the situation that the system matrix is a square matrix and also adapt to the situation that the system matrix is a non-square matrix; the S1 specifically comprises the following steps: the state equation for the MIMO system is as follows: equation 1; Wherein, the , , Is a matrix of system control inputs, , Is the output matrix of the system and, , Is a matrix of the system control gains, Is an uncertainty disturbance unknown to the system; Input matrix And (3) redesigning: equation 2; , , Is a controller In the middle of the design-able part, , Is a controller Is not defined by the number of the non-deterministic portions, ; The state equation of the MIMO system is rewritten as: equation 3; The step S2 specifically comprises the following steps: Setting error Obtaining a system error equation: equation 4; Wherein, the Representing system set uncertainty; the step S3 specifically comprises the following steps: designing new system error matrix based on system error equation : Equation 5; Wherein, the Is given a normal number, take This results in a polynomial Is a helvetz polynomial; Definition of a System generalized error function matrix in the form of PI , Equation 6; Wherein, the Is a constant which can be designed to be a function of the design, , Is the error matrix defined in equation 5; The step S4 specifically comprises the following steps: designing a performance index function based on an MIMO system error equation ; Equation 7; Wherein, the ; Is a constant which can be designed to be a function of the design, ; Is a matrix of weight constants that are selected, ; Is an identity matrix of the unit cell, ; Selected as a Helviz polynomial in equation 5, performance index function Expressed as: Equation 8; From the definition of z and s, it is possible to: equation 9.
2. 2. The method according to claim 1, wherein S5 specifically comprises: selecting lyapunov function The following are provided: Equation 10; In the formula, ; For a pair of And (5) deriving to obtain: equation 11; Substitution into The method can obtain: equation 12; Wherein, the Further can obtain , wherein, , , Is an uncertainty function synthesized in a centralized way, so that an RBFNN neural network function is adopted for approximation, and the method can be used for obtaining: Equation 13; Wherein the method comprises the steps of Is an input to the neural network and, ; Is an ideal weight; Is a known basis function; is a reconstruction error and satisfies , Is a constant that is not known in the art, Equation 14; Wherein, the , , Equation 15.
3. 3. The method according to claim 1, wherein S6 specifically comprises: For system matrix MIMO system with square matrix and design controller As follows, in the form of PI: Equation 16; Wherein, the And Is two parameters that can be designed; And Is the two parameters updated by the adaptive algorithm to be And (3) with 、 And (3) with The relationships are as follows: 、 wherein Is a constant which can be designed to be a function of the design, Substitution reduction, can obtain: equation 17; For system matrix The MIMO system is a non-square matrix, and on the basis of the square matrix system, the design controller is as follows: Equation 18; by combining parameters In combination with radial basis function neural networks such that the parameter parameters The online automatic updating is realized, and only one parameter needs to be updated in the running process of the system.
4. 4. A method according to claim 3, wherein the method further comprises: Will be The value is set as shown in the following formula, so that the system can stably operate in the action center of the controller; Equation 19.
5. 5. An electronic device, comprising: processor, and A memory arranged to store computer executable instructions which when executed cause the processor to perform the steps of the adaptive PI nonlinear control method in accordance with any one of claims 1-4 for a MIMO system.
6. 6. A storage medium storing computer executable instructions which when executed implement the steps of the adaptive PI nonlinear control method in accordance with any one of claims 1-4 for a MIMO system.

Description

Adaptive PI type nonlinear control method, device and medium suitable for MIMO system Technical Field The present document relates to the field of adaptive control technologies, and in particular, to an adaptive PI nonlinear control method, apparatus, and medium suitable for a MIMO system. Background In industrial process control, a control system for controlling proportional, integral and differential of errors generated by comparing information acquired by real-time data of a controlled object with a given value is called PID for short, and PID control has special significance due to simple structure and visual concept and is widely applied in practice. The traditional PID control method at present is to input the deviation into the proportional-integral-differential regulation link again after the output value is compared with the ideal value, and finally, the system output is enabled to be continuously approximate to the ideal set value through continuous feedback regulation. However, in this method, the PID parameters are usually determined by using a trial-and-error optimization method, and the parameter selection method has a long time and is difficult to select the optimal parameters, so that the control system cannot adapt to the system variation. Based on the traditional PID control, the PID control is combined with modern control methods such as fuzzy control, neural network control and the like, so that the parameter self-tuning of the PID controller can be realized. For example, BP neural network, mamdani fuzzy neural network, RBF neural network and the like are applied to the design of the PID control system, and the difference value between the output value of the control system and the ideal value is infinitely approximate to zero through multiple autonomous learning training of the neural network. However, the essence is a linear control method, and when nonlinear terms in an actual system are considered, an error feedback mode is adopted, and then P, I parameters are adjusted, so that a control system is designed. The error feedback form of the difference between the actual value and the expected value has poor processing effects on nonlinear terms, unknown interference terms and the like, and the accuracy and adaptability of the system are reduced. The nonlinear PID is improved by introducing nonlinear factors based on the traditional PID, and the error feedback is not simply obtained from the error of the output value and the expected value, but is the error after nonlinear change, so that the processing capacity of the system on the nonlinear factors is improved. However, the design process adopted by the design process is the conventional PID design process, and the design process of the nonlinear system is not combined, so that the robustness and the adaptability performance of the system are not ideal when the complex nonlinear system is processed. At present, for a multi-input multi-output (multiple input multiple output, MIMO) system with nonlinearity and modeling uncertainty, students have made great progress in control method research, and various advanced control methods are proposed. The MIMO system has the characteristics of strong nonlinearity, multiple coupling, uncertain system modeling and the like, and has great difficulty and challenge on how to control the stability of the MIMO system. The existing MIMO system control method is only used for researching the situation that the system matrix is a square matrix, the system matrix is not a square matrix, and meanwhile, the existing MIMO system control method is generally a design method of a nonlinear system, and is difficult to apply to an actual system. Therefore, a control method suitable for a MIMO system is needed to solve the problem that the existing control method for the MIMO system cannot effectively observe the whole operation process, solve the problem that the matrix of the MIMO system is limited to the square matrix and the non-square matrix, solve the problem that the parameters of the PID control method are difficult to select, and solve the problem that the PID control method in the MIMO system cannot process the non-linear term. Disclosure of Invention The invention provides a self-adaptive PI type nonlinear control method, equipment and medium suitable for a MIMO system, and aims to solve the problems. The embodiment of the invention provides a self-adaptive PI type nonlinear control method suitable for a MIMO system, which comprises the following steps: s1, establishing a state equation of the MIMO system; s2, establishing an MIMO system error equation according to the MIMO system state equation; S3, designing a system error function S according to an MIMO system error equation; S4, establishing a performance index function J z according to the system error function S; S5, selecting a Lyapunov function V 1; S6, designing a self-adaptive PI type nonlinear control method, wherein the control method compris