Robust Fuzzy Digital PID Controller Design: A Contribution for Advanced Studies in Control and Automation

Robust Fuzzy Digital PID Controller Design: A Contribution for Advanced Studies in Control and Automation

Danúbia Soares Pires (Federal Institute of Education, Science and Technology, Brazil) and Ginalber Luiz de Oliveira Serra (Federal Institute of Education, Science and Technology, Brazil)
DOI: 10.4018/978-1-5225-1759-7.ch007
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Abstract

A robust fuzzy digital PID control methodology based on gain and phase margins specifications is proposed. A mathematical formulation based on gain and phase margins specifications, the Takagi-Sugeno fuzzy model of the process to be controlled, the structure of the digital PID controller, and the time delay uncertain system are developed. A multiobjective genetic strategy is defined to tune the fuzzy digital PID controller parameters, so the gain and phase margins specified to the fuzzy control system are found. An analysis of necessary and sufficient conditions for fuzzy digital PID controller design with robust stability, with the proposal of the two theorems, is presented. Experimental results show the efficiency of the proposed methodology in this chapter, applying a platform control in real time of a thermic process through tracking the reference and the gain and phase margins keeping closed the specified ones.
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Background

New methodologies have been developed to ensure high performance in control systems. Reaching this objective in front of uncertainties is not a trivial task, and still constitutes a challenge in the control theory. Especially, the robust control theory has received great interest from scientific community to develop controllers to deal with complex dynamics such as nonlinearities, uncertainties, time delay, among others, and guarantee robust control design (Mueller, 2011).

Nowadays, the interest for strategies to model and control of complex process has been motivated by the following factors (Serra, 2012):

  • Development of efficient identification methods and greater applicability of computational resources;

  • Improvement of softwares and hardwares technologies, making it possible to incorporate complex models in the control systems design.

The robust control theory has grown remarkably in recent years, gaining ground even in the industrial environment where it is a valuable tool for analysis and dynamic systems design (Wu et al., 2010). Due to its practical applicability, the control theory is used in solving engineering problems and it has been applied in several areas where practical requirements of performance are relevant (Zhong, 2006; Serra, 2012).

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