Sparse Design Of Multivariable Centralized Control System

The rapid development of industrial technology has led to the development of control system.High dimensional multivariable control systems gradually replace single variable control systems with poor control performance.However,there are interactions among variables in high-dimensional multivariable control systems,that is,the coupling effect of control quality exists in multivariable systems.This is a core problem that can not be ignored in the design of controller.Based on the peculiarities of high-dimensional multivariable control system,how to use the appropriate control theory to establish the optimal control structure and set the optimal controller parameters is the core problem of modern process control.Firstly,in the frequency domain,based on the Nyquist and inverse Nyquist stability criteria,with the help of the Gershgorin band criterion and diagonal dominance definition,the positive and inverse Nyquist array design methods are deduced.The proper pre-compensation array in frequency domain is found to achieve the diagonal dominance.Then a suitable dynamic controller and a feedback gain matrix are designed to achieve centralized control of multivariable systems.Secondly,the concepts of simple degree and decoupling degree are proposed to measure the design difficulty and decoupling performance of control systems respectively in order to make the pre-compensation array is as sparse as possible under the condition that the diagonal dominance is not greatly reduced.According to the element with the minimum zero gap in the pre-compensation array,which element should be made zero can be determined.During the calculation,the corresponding elements of the pre-compensation array are set to zero by the conversion matrix,and the iterative calculation is carried out.After per iteration,the performance index involving simple degree and decoupling degree of the pre-compensation array is investigated.When the performance index begins to decline,the iteration will be stopped and the sparse pre-compensation array is obtained.Finally,on the basis of the designed decentralized conventional PID control system,in order to weaken the coupling degree of the multivariable system,the concept of the open loop relative gain matrix is introduced to match the multivariable system auxiliary controller.According to the feed-forward control principle of the control system,the parameters of the controller are adjusted to realize the design of the auxiliary controller parameters.This method also reduces the coupling degree of the system and improves the control quality of the multivariable system.