Research On Control Configuration And Parameters Of Multivariable Systems Based On Frequency Domain Method

During the design phase of chemical processes,the conventional decentralized PID controller design for multivariable systems consists of two steps,which are the control loop configuration and then the control parameter design.The traditional design method for control loop configuration is generally based on the time domain analysis,so the influence of dynamic characteristics is not fully considered.Besides,the traditional control parameter design method is lack of considering the influence of the uncertainty caused by the switchovers between open-loop and closed-loop of other control loops.For these reasons,this paper proposes the design method of decentralized PID control for multivariable systems based on frequency domain analysis to solve the problem of control loop configuration and control parameter design of decentralized PID controllers for multivariable systems.First,the control loop configuration or input-output variable pairing of decentralized PID control for multivariable systems is implemented.The concept of Relative Gain Array(RGA)is promoted to frequency domain and the dynamic RGA in frequency domain is put forward.The dynamic RGA in frequency domain can deal with the control loop configuration of multivariable systems containing time delay process,integral process and unstable process which steady-state RGA cannot dispose.Because the dynamic RGA in frequency domain is plural matrix and not comparable in size,the interaction measurement index matrix and the unit circle diagram in complex plane are proposed to reflect the distance between the relative gain in frequency domain and)0,1(j point in complex plane.Meanwhile,the RGA value is used to transform the plural form of dynamic RGA in frequency domain into a real number,and through minimizing the RGA value the optimal control loop configuration can be found.In the end,the control loop configuration under closed-loop control system is analyzed.Second,when some control loops are pre-established,the control loop configuration problem for other input-output variables is solved.The multivariable system is divided into the free sub-system and the definitive sub-system,and the interaction analysis is implemented when the definitive control loops are open-loop or closed-loop ideal control.The dynamic RGA in frequency domain of the free sub-system is presented,for which the unit circle diagram in complex plane is used for control loop configuration of the free sub-system,and the RGA value is used to confirm if the optimal control loop configuration is found.Third,the paper put forward the control parameter design method of decentralized controllers for multivariable systems based on stability margin.For the single variable system,the PI control parameters under different stability margins are determined according to the relationship between the magnitude margin,phase margin and PI control parameters.For the multivariable system,the magnitude margin and the phase margin are used as stability constraints,the influence of other control loops being open-loop or closed-loop ideal control is also considered,the feasible region of PI control parameters can be found.Finally,the proper PI control parameters of each loop for multivariable system are obtained through the optimization in frequency domain.