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Linear system stability region of PID parameters

Author: LiBen
Tutor: FangBin
School: Nanjing University of Technology and Engineering
Course: Control Theory and Control Engineering
Keywords: PID control Parameter stability region Inverse Nyquist plot Hermite-Biehler theorem MATLAB GUI Stability margin
CLC: TP13
Type: Master's thesis
Year: 2009
Downloads: 254
Quote: 8
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Abstract


PID controller because of its simple structure , robustness , and wide range of use , and be able to get better control effect , widely used in industrial process control . The quality of all quality control are built on the stability of the system on the basis of concern based on other performance is meaningful , and therefore of great significance to the PID control parameters stable domain . Based on the inverse Nyquist curve , this paper presents a method to determine the linear system stability region of PID controller parameters . The basic idea is to determine the stability of the proportional gain range , and then obtained a fixed proportional gain Integral gain - the Differential Gain plane stable range , and then through the proportional gain in its stable range traversal ultimately determine the stability domain . Extremal point by the inverse Nyquist curve on the real part of the PID proportional gain first divided into several intervals ; draw two conditions using the generalized Hermite-Biehler theorem to determine the stability of the proportional gain based on the number of intersections of the longitudinal linear inverse Nyquist curve range; the proportional gain is fixed , by determining the sequence of I = { i 0 < / sub >, i 1 ..., i , l }, to give a group on the integral gain and differential gain linear inequalities, thereby determining the integral - derivative gain stability region of the plane ; given an integral - differential gain plane determine the stability domain of the \domain provides an effective method ; article also discussed the introduction of the concept of stability margin stability region of PID parameters determined on this basis . Finally, we use MATLAB GUI implementation of an interactive software provides a simple and practical tool for the study of the stability region of PID control parameters .

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