Studies on the stability and robustness of uncertain nonlinear systems based on fuzzy logic approach

Pao Yue-kong Library Electronic Theses Database

Studies on the stability and robustness of uncertain nonlinear systems based on fuzzy logic approach

 

Author: Lam, Hak-keung
Title: Studies on the stability and robustness of uncertain nonlinear systems based on fuzzy logic approach
Degree: Ph.D.
Year: 2000
Subject: Nonlinear systems.
Fuzzy systems.
Hong Kong Polytechnic University -- Dissertations.
Department: Dept. of Electronic and Information Engineering
Pages: xxviii, 241 leaves : ill. ; 31 cm.
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b1540309
URI: http://theses.lib.polyu.edu.hk/handle/200/689
Abstract: In this thesis, the stability and robustness analyses of uncertain multivariable nonlinear control systems based on fuzzy logic approaches are presented. A system that comprises a TSK fuzzy plant model and a fuzzy controller connected in closed-loop is first considered. The TSK fuzzy plant model represents an uncertain multivariable nonlinear system as a weighted sum of a number of sub-systems. Similarly, the fuzzy controller is a weighted sum of a number of sub-controllers. Difficulties have been found on analysing and designing this class of nonlinear systems using the conventional control theories. This is because the interactions of the plant among the sub-control systems, which are related to the nonlinearities, have to be considered. Moreover, the parameter uncertainties of the nonlinear plants make the analysis more difficult to be carried out, especially when the ranges of the parameter uncertainties are large and the values of the uncertain parameters are unknown. In view of the aforementioned difficulties, different methods of solving the control problem of multivariable nonlinear plants are proposed in this thesis. The work can be divided into three parts: (a) to develop ways of conducting stability and robustness analyses on uncertain fuzzy control systems, (b) to develop methods of controlling nonlinear plants subject to small or large parameter uncertainties, (c) to develop systematic design methodologies of robust or adaptive controllers with guaranteed closed-loop stability. As a result, the stability and robustness conditions of fuzzy control systems subject to small parameter uncertainties have been determined. Based on the analysis results, two approaches that are capable of controlling nonlinear systems subject to large parameter uncertainties are derived. This classs of nonlinear plants cannot be controlled satisfactorily by simple robust fuzzy controllers. To probe further, in order to tackle nonlinear plants subject to unknown parameters within given ranges, a switching controller is also proposed. The design is based on a proposed switching plant model developed from the TSK fuzzy plant model. To test the obtained results and the developed methods, applications on mass-spring-damper systems, inverted pendulum systems, two-inverted pendulum systems, ball-and-beam systems, switching DC-DC power converters, 8-r manipulators and a two-link robot arm have been studied and will be given as illustrative examples in this thesis. The achievements can be summarized as follows. (a) Stability and robustness of fuzzy control systems about a given operating point have been analyzed. It is termed as the small parameter uncertainty (SPU) approach. The stability and robustness conditions are obtained which can aid the design of a small parameter uncertainty (SPU) fuzzy controller for multivariable nonlinear systems subject to small parameter uncertainties within given ranges (b) A method of designing the gains of a proposed nonlinear controller that is based on the TSK fuzzy plant model has been developed. The number of matrix inequalities involved is reduce to p+1 instead of p(p+1)/2 as stated in [Wang 96], where p is the number of rules of the TSK fuzzy plant model. (c) To tackle multivariable nonlinear systems subject to large parameter uncertainties within given ranges, two controllers, namely a fuzzy scheduler and a multiple-grid-point(MGP) fuzzy controller have been realized based on the analysis results of the SPU approach. Both controllers have a number of SPU fuzzy controllers embedded inside, and the control signal is obtained based on these SPU fuzzy controllers's outputs. The design is based on an augmented TSK fuzzy plant model which is formed by the original TSK fuzzy plant model and a fuzzy uncertainty regenerator. Both controllers are effectively adaptive controllers. The fuzzy scheduler changes its parameters as the membership function values change with the uncertain plant parameters. The MGP fuzzy controller contains many SPU fuzzy controllers. During the operation, uncertain plant parameters's values are changing, the most suiable SPU fuzzy controller will be selected to control the plant. In both cases, the closed-loop system stability has been proven. Both approaches have their individual advantages. For a given nonlinear plant, the number of SPU fuzzy controllers that have to be designed under the fuzzy scheduler approach is fixed, and usually less than that of the MGP approach. However, the computational demand on deriving the control signal through the fuzzy scheduler approach is higher than that through the MGP approach. The fuzzy scheduler approach and the MGP approach are complementary to each other. (d) To tackle nonlinear systems subject to unknown parameters within given ranges, a switching controller has been proposed. Asystematic design methodology has been developed to obtain a stable and robust switching controller based on a proposed switching plant model, which is developed from the TSK fuzzy plant model. For some nonlinear plants, the closed-loop systems can be reduced to linear systems. The system state responses will then not be affected by the unknown parameters.

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