Research On Design For Sampled-Data Control System Based On Jump System Approach

With the rapid development of micro-electronics and digital computer technol-ogy, sampled-data control approach has been applied widely in practical industrialsystems. When the design performance requirement is high, it is better to design digi-tal controller based on the continuous performance index. Then sampled-data controlsystem is a typical hybrid system including continuous-time and discrete-time sig-nals. The control design problems of sampled-data control systems with parametricuncertainties including robust guaranteed cost control, robust H_∞control and reced-ing horizon control are investigated in this dissertation based on jump system modeland linear matrix inequality (LMI) technique. Moreover, some numerical simulationexamples are provided to demonstrate the effectiveness of proposed methods.Firstly, the sampled-data control system with parametric uncertainties is trans-formed into an equivalent jump linear system. Based on the jump system model, sta-bility conditions and H_∞performance conditions are analyzed, and these conditionsare the bases of further researches.Secondly, based on the piecewise continuous Lyapunov function (PCLF) andconstant Lyapunov function (CLF), the problems of robust guaranteed cost control forparametric uncertain sampled-data control systems are investigated by using the jumpsystem model and linear matrix inequality technique. Via the PCLF approach, state-feedback and output-feedback robust guaranteed cost controller are designed. Thesufficient condition of existence of the robust guaranteed cost controller is given interms of iterative LMIs, and the parameter matrices of the controller can be obtainedby the feasible solution of LMIs. When PCLF is simplified to CLF, the problem of theoutput-feedback guaranteed cost control is investigated based on CLF approach, andthe sufficient condition of existence of controller is transformed to the feasibility prob-lem of LMIs. Furthermore, it is shown that the parameter matrices of the controllercan be constructed by a feasible solution of LMIs. Simulation example illustrates theeffectiveness of the proposed methods.Thirdly, the problems of output feedback H_∞control for time-varying norm-bounded parametric uncertain sampled-data systems are investigated. According tothe structure of Lyapunov function, controller design methods are presented based on PCLF and CLF. In the PCLF method, via constructing piecewise continuous Lya-punov matrix by using the convex combination of two constant matrices, the onlineiterative algorithm for the dynamic output feedback H_∞controller designing is pro-posed, and the criterion condition of existence of the controller and the parametriza-tion of controller is also given. The obtained controller can satisfy the desired H_∞performance under admissible parameter uncertainties. By considering CLF as a spe-cial case of PCLF, two methods are proposed for designing the output feedback ro-bust H_∞controller, which converts the existence condition of admissible controllerinto the feasibility of convex problems subject to LMIs, and controller parameters canbe constructed by a feasible solution. Based on this, the controller design problemwith closed-loop H_∞performance constraints is also solved. Simulation examplesillustrate the effectiveness of the proposed methods.Lastly, considering the control and output constraints in practical engineer-ing systems, receding horizon control (RHC) problems of the parametric uncertainsampled-data system are investigated. Under the LMI optimization framework, RHCcontrol online algorithm under the quadratic performance index is proposed. The ex-istence condition and parameterized formulation of the predictive controller are givenin terms of LMI. The algorithm can consider uncertainties in real-time. Comparedwith the results of the LQR control method, simulation example illustrates the ef-fective of the proposed approach. The online algorithm of the H_∞receding horizonoptimization design for the norm-bounded parametric uncertain system is proposed.The optimal state-feedback H_∞controllers are obtained and these controller can pro-vide a performance tradeoff with respect to output constraints, i.e., the control strategyoffers the capability of relaxing the performance level automatically in order to obeyoutput constraints in the case of a larger disturbance. When the disturbance is restoredto a usual situation, this control strategy can also improve the performance of systemautomatically.