Fuzzy PID control through optimization: A new method for PID control

Jingwei Xu, Marquette University

Abstract

Proportional, Integral, and Differential (PID) control plays the important role in industry. Despite decades of research in developing new control methods, the PID controller is still widely used, due to its simplicity and effectiveness. For a system with predictable and low-order dynamic behavior, PID control works well. However, PID control is far from perfect. It is already known that the performance of the PID controller is not satisfactory in time-varying and nonlinear systems. The design of the PID parameters is rather ad-hoc, so it is difficult to achieve optimal performance. Therefore, the objective of this study into find a new PID design or tuning method suitable for some systems where PID control currently does not work well. This dissertation proposes a novel method (called PID design through numerical optimization) for the design of adaptive fuzzy PID controllers to achieve optimal control performance. By applying numerical optimization, the fuzzy PID design problem is transferred to a numerical optimization problem. First, a fuzzy parameter tuner is built to generate initial PID parameters, including positions and shapes of fuzzy membership functions and scaling factors. Then the gradient-based Sequential Quadratic Programming (SQP) algorithm is employed to minimize the cost function by adjusting the parameters. Unlike conventional PID design, this method is capable of reaching the desired control performance, such as minimum overshoot. Another unique feature is that the optimized adaptive PID controller is applicable to a wide variety of time-varying and nonlinear systems. The proposed method is applied to DC motor and induction motor control problems, and the experimental results are presented to demonstrate its effectiveness and performance. Brief overviews of the related fields of PID control, fuzzy control, optimal control, optimization, and previous work in fuzzy PID are included, followed by the detailed description of the proposed method. An exploratory study of PID control and evaluation of the method's computational complexity are included.

Recommended Citation

Jingwei Xu, "Fuzzy PID control through optimization: A new method for PID control" (January 1, 2006). Dissertations (1962 - 2010) Access via Proquest Digital Dissertations. Paper AAI3231315.
http://epublications.marquette.edu/dissertations/AAI3231315

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