Research On Sampling Control System Based On Discretization Method

With the rapid development of digital computer technology and network technology,computer control is widely used in industrial control,scientific experiments,national defense construction and other fields related to actual production and life.Sampling system control theory is the basis of computer system control,Wide practical application requires higher and higher performance of computer system,which also promotes the development of sampling control theory.The coexistence of Continuous System and Discrete System is the characteristic of the sampled-data system,for this reason,the research of sampling system has its own complexity.At present,the main methods to study sampled-data system include sampling signal lifting method,impulse system modeling method,input delay method and convex polyhedron method,the research of first three approaches has some achievements,however,the application of convex polyhedron approach to sampled-data system has not been studied much,the main goal of this work is to fill this gap.Concrete work for this topic can be summaried as follows.Firstly,the Finite-Time Stability(FTS)of uncertain sampled-data systems is studied.Discrete the sampled-data system and transfer it into the ploytopic uncertainty system,put the uncertain sampling interval information into convex polyhedron model,norm bounded uncertainty is used to deal with the errors in the conversion process.With this discretization method,the finite-time stability conditions of sampled-data control systems are studied,a feedback controller for finite-time stability of sampling system is designed.Secondly,the finite-time boundedness(FTB)problem of uncertain sampled-data systems is considered.The external disturbance of the system is considered during the design of the controller.The interference item is put into the input item and discretized,the convex polytopic uncertainty method can be successfully applied into the sampling system without changing the interference information.Based on Lyapunov-like method,the condition of finite-time boundness is given in the form of linear Matrix Inequalities(LMI).An example is given to show that the obtained conditions can effectively solve the finite-time bounded problem of sampled-data systems with interference.Lastly,The application of convex polytopic uncertainty approach in model predictive control(MPC)of sampled-data system is further extended.The idea of Min-Max and rolling optimization is applied to minimize the secondary performance index of the sampling system at each sampling time.An online optimal state feedback controller with uncertainties is designed,and the feasibility and stability of the proposed algorithm are proved.An example is given to illustrate the influence of the upper bound of sampling interval,input constraints and Taylor expansion order on the system performance index in the process of changing the sampling system into a convex polytopic system with uncertainties.