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Fuzzy Controller Design And Application For Nonlinear Systems Based On T-S Models

Posted on:2010-10-26Degree:DoctorType:Dissertation
Country:ChinaCandidate:J ChenFull Text:PDF
GTID:1118360278975150Subject:Control theory and control engineering
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With the rapid development of science technology, the problem of modeling, analyzing and designing for complex nonlinear systems is very hard to be solved by traditional control theory. Since the eighties of the twentieth century, fuzzy control technology has obtained great evolution in control theory and engineering practice becaue that it is easier to design controller, suitable for applying in many nonlinear control systems and has stronger robust characteristic. However, due to the essential nonlinearity of fuzzy control system, the stability analysis and performance design for fuzzy control system are still short of rigorous theory foundation. As a result, the systematic synthesis approach is difficult to be formed. In 1985, the Takagi-Sugeno (T-S) fuzzy model proposed by Takagi and Sugeno brings far-reaching impact for fuzzy control theory and its applications, and it also makes stability analysis of fuzzy control system to a new theoretical height. In particular, under the framework of parallel distributed compensation (PDC) scheme and linear matrix inequality (LMI) technique, an effective design methodology has been developed to study the stability analysis and controller design for nonlinear systems.The work of this dissertation mainly investigates nonlinear systems, including those systems subject to uncertainty, time delay and stochastic jumps. Based on the Lyapunov stability theory, some fuzzy control problems for a class of nonlinear systems are studied by applying the parallel distributed compensation scheme. The research contents relate to filter design, guaranteed cost control, regional pole assignment, non-fragile control, constraints control, robust performance analysis and robust stabilization and so on. All obtained results can be reduced to a feasible problem of linear matrix inequalities. Due to the interior-point algorithm, the solutions of LMIs are solved very easily.The main research works of this dissertation are as follows:(1) Under the assumptions that the statistical characteristic of the external disturbance and the measurement noise is unknown, a new design method of H_∞filter for continuous-time nonlinear system is provided. At first, the T-S fuzzy model is utilized to approximate the controlled plant. Then, by introducing an additional slack variable, a less conservative result is obtained, in which the Lyapunov matrix and system matrices are decoupled. Finally, a simulation example is verified the feasibility of the proposed method.(2) The approach of fuzzy guaranteed cost controller design is improved for a class of uncertain nonlinear systems from two aspects. In the first part, by using the idea of piecewise Lyapunov function, the existing condition of guaranteed cost control law which ensures the robust stability of systems is derived. The obtained results avoid the difficulty for seeking a common Lyapunov matrix, so it has less conservativeness. In the second part, based on the relaxed stability condition and reciprocal projection lemma, as well as combining with the response rate of system, the design approach of guaranteed cost control law with decay rateαis given, which guarantees that the closed-loop uncertain fuzzy system is robust asymptotic stability.(3) For a class of nonlinear systems in the presence of norm-bounded and time-varying parameter uncertainties, the problem of robust guaranteed cost control with disk pole constraints is investigated. By applying T-S fuzzy control approach and considering the dynamic performance of the closed-loop systems, the controller design method is given both for continuous-time and discrete-time case. The results show that the designed controller can make the system achieve better stable behavior, and obtain the satisfied transient performance at the same time.(4) The problem of robust performance analysis and synthesis for nonlinear time delay systems is discussed. Firstly, on the basis of the relaxed stability condition, the problem of robust H_∞guaranteed cost control is considered for a class of uncertain discrete-time nonlinear systems with bounded time delays in both state and control input. Secondly, in the presence of the additive controller gain perturbations, a design procedure of non-fragile LQ /H_∞controller is provided for discrete-time nonlinear systems. The designed controller can not only guarantee the delay-dependent stability of the closed-loop fuzzy system, but also make the system achieve a H_∞disturbance attenuation level. Finally, by constructing an appropriate type of fuzzy weighting-dependent Lyapunov functional and adopting the free-weighting matrix method, a new delay-dependent stability criterion is derived for nonlinear systems with interval time-varying delay. This criterion fully considers the time delay information with its lower bound and upper bound. Furthermore, the limit that the derivative of time-varying delay must be smaller than one is not required. Therefore, the obtained results are less conservative than the existing ones.(5) From the aspect of constraints control, H_∞control and robust control, the stability analysis and controller design are primarily discussed for nonlinear systems with Markovian jumping parameters by applying T-S fuzzy models. Based on the stochastic Lyapunov stability theory, the corresponding fuzzy controller design methods are given in the form of state feedback. Different from the generic state feedback controller, the controller gains designed here are all depend on the Markovian jump modes.Finally, the conclusion of this paper is given. Upon this conclusion, some further research work and existing issues will be pointed out.
Keywords/Search Tags:nonlinear systems, time delay, Markovian jumping parameters, Takagi-Sugeno (T-S) fuzzy model, filtering control, guaranteed cost control, disk pole constraints, non-fragile control, H_∞control, constraints control, robust control
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