Delay Interval Systems The Pid Parameter Three-dimensional Stability Region

To its good control effect, PID control technology has always been the dominant technology of actual industrial process control. Considering to that the system always need to meet some key performance of actual industrial process control, therefore, if we can get the stable region of PID controller parameter space which meet various performances, we can design the PID controller conveniently.In this paper, mainly for delay interval system, based on generalized Routh theorem, Hurwitz theorem, Hermite-Biehler theorem, Kharitonov theorem, they make it easy to analysis the stability of polynomials, and these theories is the basis of the study delay interval system. We study the problem in four steps:First, the interval plant can be divided into four Kharitonov sub-functions; Second, using the Hermite-Biehler theorem, we can calculate each sub-function corresponding system's stable region of proportional gain, also, the intersection of these stable regions can be obtained, actually, this intersection is the whole system's stable region of proportional gain. Third, using the anti-clockwise rule, on the basis of the fixed proportional gain, we can determine that each sub-function corresponding system's integral-differential gain of two-dimensional plane stable region, and then obtain the intersection of the two-dimensional stable regions, which namely the system's two-dimensional stable region. Forth, sweeping over the stable region of proportional gain, and then we can obtain the system's three-dimensional stable region. Finally, we can use this algorithm under the MATLAB environment, realize it by programming it, and validate the arithmetic. Because of the theorem of Kharitonov has limitations, two important extensions of the theorem for interval plant, two theorem is the edge theorem and the box theorem.In condition of the time-delay systems stability, with this interactive GUI interface, three-dimensional PID control parameters stability regions can be drawd. It provides a convenient method to adjust online and design based on performance in practice. And this software also allows users to research stability characteristics of integral and differential plane for a fixed proportional gain, which provides a convenient method to research stability characteristics in three-dimensional PID control parameters stability regions.