Research On Actuator Saturation And Control Of Delta Operator Systems

In the actual industrial production,many real-world physical processes are generally characterized by the presence of saturated nonlinearity.Because of actuator saturation,the actual equipment system is limited,and the performance of system will deteriorate.Delta operator which is a new discretization method has been combined continuous and discrete systems.Now delta operator systems are the method of a unified description between continuous-time and discrete-time systems.Delta operator solves a series of problems caused by the shift operator rapid sampling method.In recent years,a lot of research production has been obtained for saturated systems.However,there exist few works on delta system with actuator saturation,which motivates us to carry on this research work.The results of this paper are given as in the following.Firstly,the exact description of the null controllable domain is obtained by iterative algorithm for delta operator systems with actuator saturation.The boundary o f the null controllable domain is shown with theoretical analysis.The expression of the null controllable domain is given for delta systems with positive real eigenvalue or complex eigenvalue.Then we give the relation of different results for continuous time systems,discrete time systems and delta systems.Secondly,based on results of the null controllable region,the stabilization is discussed for saturated delta systems.A set of stable equilibriums of the delta operator systems under a constructed saturated linear feedback is given.For an anti-stable delta operator system,some different controllers have been constructed to achieve semi-global stabilization,respectively.For higher-order delta operator systems with one or two anti-stable modes,the semi-global stabilization has been established by explicit construction of feedback laws.Thirdly,we focus on practical stabilization of null controllable delta operator systems subject to actuator saturation and disturbances.Some properties of the domain of attraction for delta operator systems are shown by vector fields analysis.The practical stabilization is also given for planar delta systems.Moreover,a comprehensive controller is designed to guarantee performances of higher order delta operator systems.Both monotonicity and continuity are given for the domain of attraction on delta operator systems with actuator saturation.An aircraft model is given to show the effectiveness of the proposed method.Finally,a spacecraft attitude control system is studied with fuzzy control and delta operator approach.Based on a general continuous-time system of the rigid spacecraft model,a fuzzy delta operator system of spacecraft attitude was obtained under delta operator sampling.What's more,a theorem of stability for fuzzy delta operator systems is also given with control theory.The design of fuzzy state feedback controller is transformed into solving the problem on linear matrix inequality constraints.