New design, stability analysis and applications of auto-tuned fuzzy PID controllers

Conventional proportional-integral-derivative (PID) controllers are used extensively in industry, due to their effectiveness in controlling simple linear systems, ease of design, and inexpensive cost. However, they are not as effective in handling nonlinear systems, higher order systems, time-delayed systems, or systems that do not have precise mathematical models. For these systems, fuzzy logic controllers have demonstrated their advantages. In this dissertation, the conventional PID controller and the fuzzy logic design methodology are combined to develop a new type of controller---the fuzzy PID controller. The design principle, tracking performance, applications to robotics and stability analysis of the fuzzy PID controllers are presented. In addition, methods for tuning the fuzzy PID controller are presented. Computer simulations and results from some practical robotic experiments are presented to demonstrate the superiority, and wider control capability, of the fuzzy controllers over their conventional counterparts. The fuzzy PID controllers preserve the simple linear structure of the conventional PID controllers, but possess self-tuning control capabilities due to their nonconstant control gains. A multivariable fuzzy control system based on the fuzzy PID controllers is also designed and used to control a two-link flexible-joint robot arm. Neural networks and a heuristic model-free approach are used as two approaches in determining the fuzzy PID controller gains. Analytical bounded-input bounded-output stability analyses using the small gain theorem, and graphical and Liapunov analyses for asymptotic stability of the fuzzy PID controllers and the multivariable closed-loop fuzzy control system, respectively, are carried out and presented. The two-link flexible-joint robot arm system is used as a typical example for the asymptotic stability analysis. Thus, this dissertation completes an entire project of developing new types of fuzzy PID controllers, from design, performance and stability analyses, to computer simulations and laboratory experiments with comparisons, and demonstrates the advantages of the new controllers over their conventional analogues in many practical control systems.