PID controllers have been widely used for industrial processes but 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 systems that cannot be precisely described by mathematical model formulation and 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 nonlinear fuzzy PID controllers with variable parameters.
At first, the fuzzy PID controller with fixed parameters is derived from the design procedure of the conventional fuzzy linguistic controller. The resulting controller is a discrete-time fuzzy version of the conventional PID controller, which has the same structure with proportional, derivative and integral parts but has nonconstant gains. However, all the gains of fuzzy PID controller are nonlinear function of the input signals at every sampling time. The resultant fuzzy PID controller has a simple structure of the conventional PID controller but posses its self-tuning control capability. In order to increase the applicability of the fuzzy PID controller using low-level microprocessors, a simplified fuzzy PID controller is introduced.
At second, a fuzzy PID controller with variable parameters, named variable parameter fuzzy PID controller, is suggested to improve the shortage of the fuzzy PID controller with fixed parameters. The fuzzy PID control action cannot be operated accurately when the scaled inputs are greater than the normalization parameter of the fuzzy input sets in case of the fuzzy PID controller with fixed parameters. If design parameters are adjusted by comparing magnitude among the inputs of the fuzzy controller at every sampling time, the partitions of all the scaled fuzzy inputs converge within regions confined by the normalization parameter and the resultant fuzzy PID controller with variable parameters can always accomplish PID control action precisely regardless of the input magnitude variation.
At last, several simulations for various systems including a linear time-invariant system and a nonlinear two-tank level control system are executed in order to verify that the suggested fuzzy PID controller is superior to other fuzzy PID controllers already discussed by comparing control performances among them.