Design Of Switching System Based On Controller Parameterizations

With the development of modern industrial process towards large-scale and integration,the requirements for control precision of systems are becoming higher and higher.It is necessary to continuously optimize the controllers to ensure system stability or certain performance indices to meet the high requirements.It is difficult to design a traditional single controller to meet the multi-performance requirements of an actual industrial system.In order to overcome the shortcomings of a single controller,a series of sub-controllers are designed and switched with pre-defined rules.Then,the system can cope with the interference of many complex factors in the external environment.Although the switching controller can meet the various performance requirements of complex systems,the traditional Lyapunov function based design methods of switching controller put more emphasis on global performance of the closed-loop system.However,the local performance optimization of the switching controller still needs to be further studied.To ensure the global and local optimal performance of the control system,Youla parameterization method was introduced into the design of switching controller.The Youla parameterization method can guarantee the stability,achieve the established control objectives and improve the local optimal performance of the system by optimizing the free parameters.Furthermore,the Youla parameterization based switching controller can not only ensure the stability of the whole closed-loop system or meet some performances under switching,but also guarantee the corresponding optimal performance indices of local subsystems.In this thesis,the design of switching controllers for linear time invariant?LTI?and linear parameter-varying?LPV?systems were studied with Youla parameterization method.The main contents of this paper are as follows:Firstly,for an LTI controlled plant,a switching controller is designed based on Youla parameterization method.The sufficient conditions of Youla free parameters of the switching controller are given to ensure the H₂ control performance of subsystem under arbitrary switching.In addition,a state-space realization of free parameters for switching controller is given according to the corresponding relationship between the free parameters and the H₂performance of the closed-loop system.The state-space realization can not only guarantee the H₂ performance satisfaction of the whole closed-loop system but also ensure that the local subsystem satisfies the corresponding H₂ performance.Secondly,the design of arbitrary switching H?performance controller for LPV systems based on Youla parameterization is studied.Since a single LPV controller cannot guarantee the same control performance in all parameter regions when the time-varying parameters change in a wide range,the variable region of the time-varying parameter is divided into several sub-regions,and the Riccati inequality is used to find the central controller to ensure the global H?performance of the system.The state space realization Q???of Youla parameters for the central controller is obtained by linear fractional transformation.Then,the switching controller design problem is transformed into the switching between free parameters to ensure that each subsystem and the whole closed-loop system can satisfy the corresponding H?performance under arbitrary switching.Thirdly,aiming at the noise rejection problem of LPV control system,the design of the smooth switching LPV controller for H₂ control performance is studied combining with the Youla parameterization method.The free parameter Q???with H₂ control performance is obtained by linear matrix inequality.The central controller is obtained primarily by Lyapunov inequality to ensure the stability of the system.The variable region of the time-varying parameter is divided into several sub-intervals and the central controller is parametrically decomposed.The design of free parameters for smooth switching controller can achieve smooth transition switching as well as obtain better noise rejection ability.Finally,switching LPV controller may cause large disturbances during switching.The smooth switching controller is design based on the Youla parameterization method to meet the system H?control performance.The parameter variation range is divided into several sub-areas,and the central controller is obtained by Riccati inequality to ensure the global H?performance.Then,the convex combination form is constructed using the coprime factorization technique.The proposed method can not only ensure the global H?performance of the system,but also ensure the H?performance of the local subsystem.Besides,only small disturbance is caused during switching.