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The delay systems PID parameters dimensional stability region of

Author: ShiJiangWei
Tutor: FangBin
School: Nanjing University of Technology and Engineering
Course: Control Theory and Control Engineering
Keywords: Convex polygon intersection The inverse Nyquist plot Hermite - Biehler theorem Counterclockwise law Stability margin MATLAB GUI
CLC: TP13
Type: Master's thesis
Year: 2010
Downloads: 103
Quote: 3
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Abstract

PID controller because of its simple structure, control ability, widely used in various industrial control field; recent years to determine the the PID parameter three-dimensional stability region become a hot spot; delay phenomenon prevalent in the real system, resulting in a wide range of engineering background for Linear Systems. However, due to the complex industrial process itself and its mechanism, the approximate method of low-level time-delay systems are often not precise enough, only the high-order time-delay systems is available a more accurate description of the actual industrial process. Therefore, to study the three-dimensional stability region under the control of any order delay system PID has a very important theoretical significance and application value. Any order delay system, using the inverse Nyquist curve, determine the PID controller proportional gain stable range; based on generalized Hermite.Biehler theorem in the plane of integral and differential gain, the stable region boundary straight line, with Time Delay The two stability criterion inference proposed a \The simulation example shows the effectiveness of the algorithm. Delay systems PID control loop stability based on the introduction of further frequency domain stability margin: amplitude margin and phase margin. The proportional gain amplitude margin and phase margin into a complex domain: Pjγ / h, in the plurality of gain range, certain step the delayed object is equivalent to a set of equivalent frequency characteristics were determined which corresponds to the PID parameter plane stable region, the use of convex polygon intersection, intersected by twenty-two, ultimately determine whether a given amplitude, phase angle PID parameters under the constraint plane stable region. By traversing the proportional gain stability within the scope of all values, which gives a method for determining the amplitude of the phase angle margin constraints delay systems PID parameters dimensional stability domain algorithm. The simulation example shows the effectiveness of the algorithm. Finally, the theory using MATLAB GUI with an interactive software, the software can be given any order delay object and the amplitude and phase margin constraints, quickly draw a three-dimensional stability region of PID parameter set. The software is implemented as a delayed object PID parameter tuning and designed to provide a convenient means. While users can also use the software in the case of a given proportion of the gain stability characteristics in the study of integral and differential gain on the plane, to facilitate research in the a stable PID parameters set different PID control system performance parameters.

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