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PID Controller Design of Linear Systems with Time Delay Based on Parametric Space and GUI Simulation
Author: ZhouPeiDong
Tutor: YuLi；OuLinLin
School: Zhejiang University of Technology
Course: System Analysis and Integration
Keywords: time delay PID controller stability region performance criterion fractionalorder graphical user interface (GUI)
CLC: TP273
Type: Master's thesis
Year: 2011
Downloads: 85
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Abstract
PID control is one of the earliest developed control strategies. It is widely used in industrial process due to the structural simplicity, lower order, easy implement and robust performance. The time delay existed in the industrial control systems may degrade the system performance and even cause the systems instability. However, most of the present PID controller design methods of time delay systems utilize the rational approximation of the time delay, or is only applicable to the firstorder or secondorder models with time delay. Moreover, by using these methods, it is difficult to synthesize the desired performance criteria, such as fast speed, accuracy and robustness in the controller design so as not to satisfy multiple performance criteria flexibly. When the systems need to satisfy multiple performance criteria, PID control parameters have to be tuned again. Therefore, it is significant to explore the PID design method that can flexibly synthesize the different performance criteria for the industrial process with time delay.For arbitraryorder linear continuoustime, discretetime and fractionalorder systems with time delay, the parametric space design methods of continuous, digital and fractionalorder PID controllers are proposed by using the extended HermiteBiehler theorem, Tchebychev representation, satisfactory control theory, 3D method and singular frequencies method. Main contributions of the thesis are given as follows:1. For arbitraryorder linear continuoustime systems with time delay, a parametric design method of the H∞PID controller is presented. Firstly, the design problem to the PID controller satisfying H∞performance is converted to simultaneous stabilization problem of the complex quasipolynomial; then, an algorithm to calculate PID control parameters which can guarantee the complex quasipolynomial stable is obtained in terms of the extended HermiteBiehler theorem; based on the above algorithm, the set of the PID control parameters is provided both to meet the H∞norm requirement and to ensure the stability of the system. By gridding the control parameters in the resultant set, the set of the PID parameters satisfying other performance criteria can be obtained (e.g. overshoot, settling time and phase margin).? 2. For arbitraryorder linear discretetime systems with time delay, we use the Tchebyshev representation and satisfactory control theory to study the digital PID controller satisfying multiple performance criteria. The design idea of this method is first to present the set of the control parameters which stabilize the closedloop control system by adopting Tchebyshev representation and roots distribution conditions, and then to determine the corresponding parameters set satisfying each performance criterion on the basis of the resultant stabilizing set of the control parameters. Thus, by using satisfactory control theory, it is easily known that the parameter values located in the intersection of these sets must be the ones which can simultaneously satisfy multiple performance criteria. Moreover, in order to obtain the characterization of the digital PID control parameters set which satisfy H∞performance clearly, the set of the digital H∞PID controller is determined by calculating the boundaries in the control parameter space and examining which side of each boundary has less unstable poles. The parameter values in such set can not only guarantee the stability of the closedloop system, but also satisfy the corresponding H∞performance. It shows that there exists a set of the digital PID controller parameters satisfying the given H∞performance, but not one group of control values.3. For fractionalorder linear continuoustime systems with time delay, the stability region of fractionalorder PID parameters is studied. Firstly, the values of k p,? and ? are fixed; next, for both the two case that ? ? ?? 2 and ? ? ?? 2, the stable boundaries which contains real root boundary (RRB), complex root boundary (CRB) and infinite root boundary (IRB) are determined by using 3D method and singular frequencies method, respectively; finally the stability region of fractionalorder PID controller is obtained by examining which side of each boundary has less unstable poles.4. In order to avoid the repetitive and complicated computing, the graphical user interface (GUI) simulation software is developed based on the proposed design methods of PID controller. By using the GUI simulation software, the parameters set of PID controller can be quickly derived and displayed, and thus, it can help the users to select the control parameters satisfying the desired performance criteria intuitively and accurately.

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