Linear Pid Controller, Three-dimensional Stability Of Space Research

PID (Proportional, Integral, Differential) controller is widely used in kinds of industry for its simple structure, strong robustness and easiness to implement. During a long period, PID control plays a major role in the control technologies.The stability of the closed-loop system is the basic requirement. In a sense, the biggest difficulty in designing wonderful PID controller is to obtain the stability region of PID parameters accurately. Based on above problems, the main research ideals and results obtained in this paper are as followings:Firstly, the paper determine the whole stabilizing region of PID controller for a linear system through determining the stabilizing region in the Integral-differential plane for a fixed Proportion coefficient and then griding. Based on the existing results, a method to determining the stabilizing scope of the Proportion coefficient using the inverse Nyquist plot is proposed: getting some regions of the Proportion coefficient according to the points at which the inverse Nyquist curve intersects the real axis, applying the two conditions derived from Generalized Hermite-Biehler Theorem, then we get the stabilizing regions according to the number of points at which the inverse Nyquist curve intersects the negative frequency characteristic plot of PID. Then a method to determining the stabilizing region in the Integral-differential plane for a fixed Proportion coefficient is provided: through getting the stability boundary locus from the transfer function of the plant and determining the number of unstable poles of every region, we obtain the stabilizing regions.At last, an algorithm to plot the 3D stability region in parameters-space of PID controller for a given linear high-step system in MATLAB is realized. Results in this paper will offer convenience for tuning of PID controller parameter and will lead to research of stabilizing parameter region of PID controller for system with time-delay.