Research Of Sampled-data Control For Singular System And Its Application To Ship Dynamic Positioning System

With the rapid development of digital signal technology,sampled-data system has been widely applied to modern industrial processes.The outstanding feature of the systems is that both discrete-time and continuous-time signals exist in one system,which is difficult to be analyzed and designed.However,the existing sampled-data control theory research is aimed at state-space systems,but few for singular systems.Compared to the state-space system,the singular system has more extensive form which can be easier to describe the practical systems,and most of the research results for the singular system can be extended to the state-space system.Therefore,it is both theoretical significance and application value to analyze sampled-data control theory for singular system.Based on the unified framework of sampled-data control,by using the input delay approach and improved Lyapunov-Krasovskii function method etc.,this paper studies the admissible conditions and controller design methods for the linear and nonlinear singular system,and the research object includes delay systems,neutral systems,uncertain systems,fuzzy systems etc.Then,the obtained theory and method are extended to deal with the sampled-data control problem for the ship dynamic positioning system which has more practical engineering applications.The main contents of this paper are given as follows:Firstly,the robust H? sampled-data control problem for linear singular systems is studied.At First,by using input delay approach,the linear singular sampled-data system is transformed into singular system with time-varying delays.By constructing a delay-dependent Lyapunov function,combining with reciprocal convex combination method,sufficient conditions are derived to guarantee the system to be admissible with a prescribed H? performance level.Then,the H? sampled-data control problem for singular neutral systems based on mixed feedback is studied.Through the state and integral feedback control law and the input delay approach,the singular sampled-data system is transformed to the singular neutral system with time-varying delays.By constructing a new Lyapunov function,combining the Wirtinger integral inequality with the delay decomposition method,sufficient conditions are derived to ensure the system to be admissible with a prescribed H? performance index,and the design methods of robust H? sampled-data controller is present.Secondly,the sampled-data control problem of a class of uncertain linear singular system with constant delay is studied.In order to make full use of the information available of the actual sampled-data model,a delay-dependent Lyapunov functional is constructed,which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals.Then the exponentially admissible conditions and design methods of sampled-data controller for norminal system and uncertain system are derived respectively,and the proposed result has less conservatism than the existing one.Thirdly,the sampled-data control and quantization problem for nonlinear singular system based on Takagi-Sugeno(T-S)fuzzy models is discussed.The nonlinear singular sampled-data system without quantization is discussed firstly.By adding important or useful items,such as integral items of sampled-data state,the time-dependent Lyapunov function is constructed,and the available characteristics of the actual sampling pattern can be fully captured,less conservativeness can be achieved and longer sampling period can be obtained.The admissible condition is derived and the design methods of fuzzy sampled-data controller is given.Then,the sampled-data control problem for a class of nonlinear singular system with quantization based on T-S fuzzy model is studied.Considering the effect of the quantization for the system,the logarithmic quantizer is introduced to the controller.Meanwhile,by adding the quadratic integral terms of sampled-data state into the Lyapunov functional,an augmented Lyapunov functional is constructed.By using reciprocal convex combination method,the quantized fuzzy sampled-data controller is designed to guarantee that the system is admissible.Fouthly,some of the theoretical results are applied to the ship dynamic positioning system to deal with the sampled-data control problem.At First,the nonlinear ship dynamic positioning system with sampled-data is discussed.By using the input delay approach,the system is transformed into closed loop system with time-varying delays,which is represented by T-S fuzzy models.Sufficient conditions are given to make the system to be asymptotically stable with a prescribed H? performance level.The simulation results show that the proposed method can make the position,speed,heading angle etc.of the ship dynamic positioning system stable under the influence of external disturbances.Then,based on the methods mentioned above,the robust fault-tolerant sampled-data control problem for linearlized ship dynamic positioning system is discussed.The fault-tolerant sampled-data mode with the tracking error integral is established,and the corresponding fault-tolerant sampled-data controller is obtained.The simulation results show that the designed controller can guarantee that the output of the system can track the reference signal without steady-state error.