SYNTHESIS, TUNING AND STABILITY ANALYSIS OF FUZZY PID CONTROL SYSTEMS

Abstract

Fuzzy logic control is a kind of knowledge based control strategy that can be used to systematically and efficiently incorporate linguistic fuzzy information from human experts. On the other hand, it also provides nonlinear control functions that can improve the performance of closed-loop systems, The purpose of this dissertation is to explore the methods of structural design, parameter tuning and stability analysis of fuzzy PIO controllers. A fuzzy logic controller usually consists of an inference engine, a rule base and certain data bases. Changes of any parts may lead to the changes of control system structure. In the dissertation, the nonlinearities introduced by different fuzzy in­ ference methods are investigated. A parallel combination of PI and PD type fuzzy controller, is used to achieve PID control actions which consequently overcomes the difficulties to build up a 3-D rule base. In the dissertation, a simplest 2 x 2 fuzzy rule base structure is used since it has the advantages of retaining all the proper­ ties of fuzzy PI/PID controller, possible for theoretical analysis and possessing the highest nonlinearity. After determining the structure of a fuzzy controller, its parameters should be properly tuned so that certain closed-loop system requirements can be satisfied. To get rid of the time-consuming procedure of trial and error, this dissertation explored the idea of establishing a linkup of the tuning methods between fuzzy control and the widely used conventional PID control. Some tuning algorithms, based on approximated models of a plant and closed-loop system performance requirements, to the parameters of a fuzzy PI controller are derived. To improve system performance, a nonlinear self-tuning formula and a hierarchical structure of fuzzy controller are also developed. Furthermore, a tuning formula is introduced to determine the parameters of the fuzzy PID controller with the parallel structure. Another important issue for the analysis and evaluation of fuzzy controllers is stability. In the dissertation, the concept of local stability based on gain/phase margins is discussed in the design of fuzzy PI/PIO controllers. Extended circle criterion is used to design the parameters of a global stable fuzzy PI control system. Furthermore, small gain theorem is used as well to analyze the BIBO stability of the fuzzy PID control system by incorporating the nonlinear nature of both plant and fuzzy PI/PID controllers. Although conventional adaptive control methods are very successful in dealing with system uncertainties and time-variant elements, they have certain limitations such as applicable only to those with known structures. In the dissertation, a multiple model based adaptive control system is discussed. A higher level adaptation mechanism is constructed to supervise the system performance and select an optimal controller for the closed-loop system. Moreover, a fuzzy modification and a fuzzy PID backup with on-line parameter adaptation abilities are used to improve the system performance. Simulations and experiments are conducted and they show superior performance and suitability of the structure and tuning formulas of the proposed fuzzy PI/PID control systems. Simulations are also carried out to validate the combined adaptive and fuzzy control strategy.