Research On Adaptive PI Control Of Switched Nonlinear Systems

Switched nonlinear systems are proverbially investigated since they can be used to model many practical engineering systems.At present,the research on switched nonlinear systems has achieved fruitful results,but the designed controllers are often more complex,and the physical significance is not clear.Therefore,how to design a simple controller for switched nonlinear systems under many kinds of difficulties such as external disturbance,system constraints and unmodeled dynamics has become a hot topic.Note that the PI control has a simple structure,which has been widely welcomed in engineering practice.In this paper,the adaptive PI control is investigated for switched nonlinear systems.The main research results are shown as follows:· The problem of adaptive fuzzy PI output feedback control is addressed for nonstrict-feedback switched nonlinear systems.An adaptive output feedback control scheme is developed,in which the virtual control laws and the final controller are bounded.The bounds are known in advance,and they can be ascertained using the feedback control gains.The first step is to construct a state observer that can estimate the unmeasurable states.The second step is to design an adaptive fuzzy PI output feedback bounded controller by using backstepping method and fuzzy logic systems technique.To guarantee the virtual control laws and the final controller with a specific range,hyperbolic tangent functions and projection operator are introduced.Subsequently,the boundedness of all signals of the closed-loop system is proven via the average dwell time method and Lyapunov stability theory.Finally,the effectiveness of the scheme is verified by two examples.· The problem of adaptive fuzzy PI output feedback tracking control is investigated for a class of uncertain switched nonlinear systems with unmodeled dynamics,unknown control coefficients and dead-zone output.Firstly,the unknown dead-zone output information is processed by adaptive estimation,and a filter is designed to estimate the reconstructed state.Secondly,an adaptive output feedback PI tracking controller is proposed by utilizing backstepping technique,where fuzzy logic systems are employed to approximate unknown nonlinear functions.Then,the boundedness of tracking error and all signals in closed-loop system is demonstrated via Lyapunov stability theory.Finally,the effectiveness of the proposed scheme is confirmed by means of two examples.· For a class of switched nonlinear systems with dead-zone input,unknown nonlinear functions and external disturbances,an adaptive fuzzy PI tracking controllers is proposed by using backstepping method with fuzzy logic systems,which have a simple structure and a clear physical meaning.The designed controllers don't need priori information of dead-zone input via introducing Nussbaum function scheme.To enhance the tracking performance,the prescribed performance technique is utilized to constrain the tracking error.The stability analysis of the closed-loop switched systems is established via common Lyapunov function,and the tracking error remains within a prescribed bound and all signals of the closed-loop system are bounded.Finally,simulation results are employed to verify the effectiveness of the developed scheme.