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

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 class 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, &thetas;-r manipulators and a two-link robot arm have been studied and will be given as illustrative examples in this thesis. (Abstract shortened by UMI.)...