Stability Analysis And Application Of 2-D Delta Operator Systems With Actuator Saturation

With the rapid development of industrial technology,two-dimensional(2-D)systems have attracted more and more attention due to complex system characteristics.A 2-D system is a dynamic process in which information is transmitted in two independent directions,and2-D models widely exist in modern engineering field.As one of the typical application examples for the 2-D system,a repetitive system has important value in both theory and application.In fast sampling cases of industrial fields,a traditional discrete-time system is difficult to guarantee its performance,so a delta operator is used to discretize continuous-time systems in order to adapt to the fast sampling frequency.As one of the common problems for control systems,problems with actuator saturation have also attracted much attention of scholars.Therefore,the following researches have been done in this dissertation:Firstly,this dissertation introduces the research backgrounds,significances and current situations for a 2-D system,a repetitive system and a delta operator system.At the same time,stability analysis,controller design,stability region estimation and performance index optimization problems are discussed for the above mentioned systems with actuator saturation.Secondly,both approximate radius and monotonicity of the domain of attraction are considered for a delta operator system with actuator saturation.Based on an optimal control problem,the approximate radius of the domain of attraction is obtained,a necessary and sufficient condition is also discussed for the equivalence of the approximate radius and the exact one.On the basis of the above approximate radius,monotonicity of the domain of attraction is discussed.The correctness and the effectiveness of the results are verified by the simulation results.Thirdly,stability and stabilization are analyzed for a 2-D delta operator system with time-varying delays and actuator saturation.In order to adapt to a fast sampling frequency,the 2-D system is applied to delta domain.Using a Lyapunov-Krasovskii functional,a state feedback controller is designed for the 2-D delta operator system.By means of free weight matrices,2-D Jensen inequalities and linear matrix inequalities(LMIs),the stability and stabilization are discussed for the 2-D delta operator system.The correctness and the effectiveness of the results are demonstrated by simulation examples.Finally,a robust model predictive control(RMPC)strategy is proposed for a repetitive system with input constraints and uncertain parameters.In order to reduce complexities of the repetitive system,an augmented state approach is given.At the same time,a convex bounded uncertain domain is introduced to deal with uncertain parameters for the repetitive system.Based on the RMPC strategy,a state feedback controller for the closed-loop system is designed,and the robust stability and iteration feasibility of the closed-loop system are discussed.The correctness and the effectiveness of the discussions are verified by an example of a metal rolling process.