PID controllers have been widely used for industrial processes due to its simplicity and effectiveness. They provide high sensitivity and stability of the overall feedback control system and reduce overshoot and steady-state error. It has been well known that PID controllers can be effectively used for 1st and 2nd-order linear systems, but they can suffer from problems on higher-order and nonlinear systems.
On the other hand, fuzzy controllers in general are suitable for many nontraditionally modeled industrial processes such as linguistically controlled devices and systems that cannot be precisely described by mathematical formulation, have significant unmodeled effects and uncertainties.
There are several types of control systems that adopt a fuzzy logic controller as an essential system component. The majority of applications during the past two decades belong to the class of fuzzy PID controllers.
This thesis describes the design principle, tracking performance, and stability analysis of a nonlinear fuzzy PID controller with fixed parameters and a nonlinear fuzzy PID controller with variable parameters.
Firstly, the fuzzy PID controller with fixed parameters is derived from the design procedure of fuzzy control. The resulting controller is a discrete-time fuzzy version of the conventional PID controller, which has the same linear structure in proportional, derivative and integral parts but has nonconstant gains, all the gains of fuzzy PID controller are nonlinear function of the input signals. The new fuzzy PID controller has a simple structure of the conventional PID controller but posses its self-tuning control capability. To increase the applicability of the fuzzy PID controller to digital computer, a simplified fuzzy PID controller is introduced. After a detailed stability analysis using ‘small gain theorem’, from which a simple and practical sufficient condition for the bounded-input/bounded-output stability of the overall feedback control system is derived.
Secondly, the fuzzy PID controller with variable parameters is proposed to improve the fuzzy PID controller with fixed parameters. The fuzzy PID control action is not used at all or cannot be operated accurately when the input is much greater than or much smaller than the reference input decided at design procedure. If parameters are adjusted by comparing magnitude among the inputs of fuzzy controller at each sampling time, the partitions of all the fuzzy input converge within variable normalization parameters and the resultant fuzzy PID controller with variable parameters can always be applied precisely regardless of the magnitude of inputs.
Finally several computer simulations are executed to confirm the effectiveness of the fuzzy PID controller with variable parameters. To verify the performance of nonlinear control, the position control of the hydraulic system is simulated for fuzzy PID controller. The outputs of the suggested control system are compared with those of the conventional linear PID controller and the fuzzy PID controller with fixed parameters.