Robust Pid Controller Stable Parameter Domain

There is often some uncertain outside factors such as interference and noise and so on in the practical control systems. And there is also some uncertain internal factors on parameter perturbation in the systems because of aged equipment or abnormity. If the system is more sensitive, these uncertainties can bring about instability easily or even collapse, causing losses so that. So that it is very important that the system has strong robustness, namely insensitivity。Based on the above two points, the contents of this paper is about study the stability region of the parameters of robust PID controller for linear system. The study in this paper is about range of three parameters of robust PID controller that is Kp, Ki and Kd can make system stability and strong robustness in the three-dimensional space. This work and research results are as follows:Firstly, the study of this paper is three-dimensional stability region of the PID controller. I use the analytical method or graphical method to determine the stability region of KP.Linear programming of real-imaginary part decompositions based on the theorem of Hermite-Biehler is used to determine the two-dimensional Ki-Kd stability spatial domain. Through process of gridding Kp,determine three-dimensional stable region of Kp-Ki-Kd.Secondly, although PID controller with robustness, but not the strong robustness, based on research of PID controller,this paper study robust PID controller. In order to improve the robustness of the system, and based on three function of the sensitivity function, complementary sensitivity function and input sensitivity function constituting Mixed sensitivity function, algorithm of H∞is used in this paper. By deriving plural coefficients Equation of the controller parameters with stability region of the Hurwitz,we can determine stability region of Ki-Kd.Through process of gridding Kp,determine three-dimensional robust stability region of Kp-Ki-Kd.This paper provides a theoretical basis for tuning PID parameters of linear system, and will lead to research of stabilizing parameter region of PID controller for system with discrete-time systems or non-linear systems.