Research On Saturation Control And Finite Frequency Domain Performances For Delta Operator Systems

As a unified description method of continuous and discrete time models,a delta operator is a link between continuous and discrete time systems.Under fast sampling conditions,discrete time models described by the delta operator tend to the corresponding continuous time models,which avoids numerical instability caused by the use of a shift operator to describe discrete time systems.Note that actuator saturation is ubiquitous in actual control systems.When a input of an actuator reaches a certain limit and enters a saturated state,further increase of the input does not have any effect on an output of the actuator.Actuator saturation degrades dynamic performance of systems and even causes instability for closed-loop systems.Frequency domain analysis is a basic research method in the field of control theory and engineering.Many control problems are attributed to the analysis and synthesis of finite frequency domain performance.Therefore,a performance optimization problem is investigated for delta operator systems with actuator saturation in time and finite frequency domains.Some interesting analysis results are further obtained for H_?performance under finite frequency domain constraints.Moreover,a generalized KYP lemma is used to transform frequency domain conditions into time domain linear matrix inequality conditions to design controllers,so that the delta operator systems with actuator saturation are stabilized quickly.The main research results are given as follows.Firstly,a overall convergence rate for a delta operator system with actuator saturation is considered.Based on an explicit definition of the overall convergence rate,a controller gain is obtained to make the overall convergence rate optimal for the closed-loop system,and a solution is further given under the optimal control.Based on some related properties of the overall convergence rate,a functional relationship is obtained between the overall convergence rate and the domain of attraction for the actuator saturated delta operator system.By a compromise optimization of the overall convergence rate and the domain of attraction,an optimal controller design method is shown for the closed-loop system with a certain overall convergence rate.Secondly,a fuzzy control problem is considered for a spacecraft attitude actuator saturation system based on a delta operator method.For the spacecraft attitude control system after a linearization,a delta operator model with actuator saturation is obtained by a discrete sampling processing using delta operator.A T-S fuzzy rule is designed to further obtain a comprehensive fuzzy control law which satisfies desired control performance for the closed-loop system.Using a Lyapunov method in delta domain,a global asymptotic stability criterion is given for the spacecraft attitude actuator saturation system.A convex hull method is used to transform a fuzzy state feedback controller design problem into a linear matrix inequality problem.Thirdly,stability analysis is investigated for a networked control system with actuator saturation under a high frequency constraint.Through a delta operator method,the high frequency networked control system is discretized into a delta operator actuator saturation system with a high frequency constraint.By an extended integral quadratic constraint framework,the closed-loop system with time-varying delay and actuator saturation is transformed into a double closed-loop feedback configuration form,and its frequency domain inequality criterion is obtained in high frequency domain.Using a generalized KYP lemma,frequency domain inequality conditions is transformed into some linear matrix inequality conditions which are easy to solve.Finally,a static output feedback controller is designed based on a decentralized event trigger mechanism for a low frequency networked control system with a disturbance input.The decentralized event trigger mechanism is adopted so that only measurement outputs that satisfy trigger conditions are transmitted at each sampling instance,and network resources are saved by reducing unnecessary data transmissions.By an integral quadratic constraint method and a generalized KYP lemma,a linear matrix inequality criterion is obtained for the closed-loop system to satisfy a desired low frequency H_?performance.Moreover,a heuristic algorithm is designed to deal with bilinear matrix inequality problems in the criterion to obtain a static output feedback controller.