Analysis And Control For T Fuzzy Singular System With Timedelay  Posted on:20160616  Degree:Doctor  Type:Dissertation  Country:China  Candidate:C S Han  Full Text:PDF  GTID:1108330479978688  Subject:Control theory and control engineering  Abstract/Summary:  PDF Full Text Request  TakagiSugeno(TS) fuzzy singular models can approximate any nonlinear singular system in any small error, and fuzzy controller via parallel distributed compensation strategy is also approximation of a global controller, which can make use of fruitful results on linear singular system control field to solve complex nonlinear singular systems possible. The research of TS fuzzy singular systems has been received much attention. Some results of theory and application have been made, but there is still much room and open problem for improvement. A further study should be made to obtain more effective conditions for admissability analysis and controller designing with less conservatism. Based on TS fuzzy singular model with timedelay and stochastic disturbance, and by use of Lyapunov theory, this thesis aims to propose novel ideal and techniques on the analysis and synthesis and explore its potentials of nonlinear singular systems. Moreover, some of the obtained theoretical results will be applied to fuzzy singular control for the complex nonlinear stotch yoke mechanism. The main work and original theoretical contributions of this thesis are summarized as follows:The problems of admissibility analysis for TS fuzzy singular with interval timevarying delay systems are investigated. By taking into account the structure of timevarying delay, by employing an appropriate LyapunovKrasovskii functional, by applying and free weighting matrices and Jensenâ€™s inequality, two novel conditions are proposed by combining fuzzy basis dependent methods with delay partitioning method and the reciprocally convex approach. All obtained conditions are in terms of LMI and it can be can be extended to the general form that the lower bound of time delay is zero. Compared with existing methods, it shows that the results obtained in this chapter with more freedom and further less conservativeness.The problems of dissipativity analysis and controller design for TS fuzzy singular with constant timedelay are studiedã€‚ Obtained results are extended to the analysis and synthesis problems for passivity and Hâˆž performance. By employing delay partitioning method and slack matrices technique, a novel condition is given to make the system be admissible and strict (Q,R,S)Î± dissipative. All obtained conditions are dependent on timedelay and dissipativity index Î±. Furthermore, delay dependent condition for the existence of the problem of stabilization, and effective designed processing for desired controller are given. Meanwhile, conditions on analysis and corresponding design methods of desired controllers for passivity and Hâˆž performance are given in the form of extended corollary. Numerical examples are given to show the effectiveness and the less conservatism of the presented methods.The problems of admissibility analysis, passivity analysis and passification for TS fuzzy singular with timedelay and stochastic disturbance are concerned with. Firstly, based on an appropriate LyapunovKrasovskii and Ito formula and combined free weighting matrix technique with novel inequality method, the sufficient condition is given in the form of strict LMI, which shows the system is stochastically admissible and passive. As an extension, the case of nonlinear density function meeting Lipschitz condition is addressed. Furthermore, delaydependent criterion for the solvability for the problem of state feedback controllers and effective design methods for the desired statefeedback controller are presented by two different procedures. Among them, cone complementarity linearization method is used to solve nonconvex constraints during controller design process, and given the corresponding algorithm. Simulation examples demonstrate the effectiveness of the theory obtained in this section.The problems of sliding mode control for TS fuzzy singular with parameters uncertainty and nonlinear disturbance are discussed. Firstly, the proof of a key lemma is given. A sliding mode surface of integration type is specified related with derivative matrix and fuzzy basis. Then, we construct an appropriate LyapunovKrasovskii function by using of delay partitioning methods and deserve sufficient condition that make the nominal of sliding mode system to be admissible by employing lemma and free weighting matrices technique. And, the uncertain case of sliding mode system is considered. Next, sliding mode law is designed to meet the performance constraints. When some parameters cannot be measured, adaptive sliding mode law is also given. The simulation results show that the system is able to reach the designed sliding surface in finite time and meets the desired performance requirements, which verifies the validity of the obtained results in this chapter.The problems of robust admissibility and nonfragile guaranteed cost control are addressed for uncertainty TS fuzzy singular timedelay system with controller gain perturbations. A cost function is given associated with the system state and input. An appropri ate LyapunovKrasovskii function is constructed by taking account into an upper bound of timedelay. Under a unified framework, sufficient condition is proposed with additive and multiplicative disturbances, which meets the performance requirements. Two type of controllers are designed for different controller gain perturbations that makes the closedloop systems meet the constrained quadratic functions. Least upper bound of cost function is obtained through optimization technique. Meanwhile, to be compared with the previous results, an admissible condition is obtained in the form of corollary. Finally, simulation examples are given to validate the effectiveness and superiority of the obtained results.Some part of theoretical results are used to control a scotch yoke mechanism system. The fuzzy modeling process of a scotch yoke mechanism is given, which is represented as a 8rulesâ€™TS fuzzy singular model. According to the technique in fuzzybasisdependent of TS fuzzy singular systems in Chapter 2, a fuzzy state feedback controller is designed guaranteeing the scotch yoke system to be operated safely. Based on the actual physical parameters, the simulation results of the scotch yoke system system show the effectiveness of the proposed fuzzy state feedback controller. The obtained results of this chapter is the extension of the fuzzy controller design based on the TS fuzzy singular system and provide a fuzzy control design example for scotch yoke mechanism system to practical engineersâ€™s reference as well.
 Keywords/Search Tags:  TS fuzzy singular model, timedelay, admissibility, dissipativity, passivity, nonfragile control, sliding mode control  PDF Full Text Request  Related items 
 
