Pid Parameters Of The Linear System To Stabilize The Domain Study

PID controller is widely used in kinds of industry for its simple structure, strong robustness and good effect. The quality of all control systems is based on the stability of the controlled systems, on this basis, consider other performance is meaningful, therefore the study on the stability region of PID parameters is of great significance.Based on the inverse Nyquist curve, a method is presented to ascertain the stability region of PID parameters for the linear system. The basic idea is get the stabilizing range of Proportion gains firstly, determining the stabilizing region in the Integral-Differential plan and then griping the Proportion gains. Firstly , according to the extreme points of the real part on inverse Nyquist characteristics, the Proportion gains can be divided into several regions; applying the two conditions derived from Generalized Hermite-Biehler Theorem, the stabilizing range of Proportion gains can be obtained according to the number of points which are intersections of the inverse Nyquist curve and vertical line; for the fixed Proportion gains the stabilizing regions of Integral-Differential plan are defined by a set of linear inequality, which are fixed by the array I = {i₀, i₁,...,i_l}; and also a "counterclockwise" discipline is proposed to quickly get the stabilizing Integral-Differential plan; furthermore, the situations of setting stability margin are discussed in detail.Finally, a interactive software is proposed based on MATLAB GUI ,and it provides a simple and practical tool for the study of the PID parameters stability region...