Finite-time Control For Linear Parameter-varying System And Its Application

Linear parameter varying(LPV)system is a very important class of time-varying system.It can describe both the nonlinear and time-varying characteristics of many practical systems,as well as with linear system structure.This makes it possible to use mature linear system theory to realize the control of nonlinear system,and builds a bridge between linear and nonlinear control.On the other hand,because LPV system itself contains nonlinear and time-varying characteristics,its control design is of great challenge and difficulties inherently.Therefore,LPV system control has become a hot topic in the field of control.The existing research results of LPV systems focus on the classical Lyapunov asymptotic stability,which deals with the behavior of a system within a sufficiently long(in principle,infinite)time interval.In practical engineering,we often need to pay attention to the behavior of the system within a finite(possibly short)interval.It is in this background that the theory of finite-time stability comes into being.Studying the finitetime control problem of LPV systems is not only of great significance in theory,but also of wide application prospect in engineering.However,the current research on this subject has not attracted enough attention.Based on the previous work,this thesis extends the theory of finite time stability to LPV systems.Focusing on state feedback and output feedback control and comprehensively considering the influence of time delays and disturbances,the finite time control problem of LPV systems is investigated systematically and applied to the design of missile control system.The main research contents and contributions are listed as follows:In Chapter 2,a new framework of finite time stability analysis and controller synthesis for LPV system is studied.Firstly,the concept of finite-time stability theory of linear time-invariant systems in the existing literature is extended to LPV system,and the definitions of finite time stability and finite time boundedness are proposed for LPV systems with and without disturbance terms,respectively.Based on Lyapunov function method,the sufficient conditions for finite time stability and finite time boundedness of LPV systems are given.On this basis,based on the gain scheduling idea,the existence conditions of variable gain controller are given to ensure the finite time stability and finite time boundedness of the closed-loop LPV system.The solutions of these nonlinear matrixinequalities and parametric linear matrix inequalities are explained.A simple and effective solution based on linear matrix inequality is given.Finally,a numerical system and two-mass-spring system are taken as examples to verify the effectiveness of the proposed method.Chapter 3 further considers the effects of disturbances and time delays on the basis of the work in Chapter 2,and studies the finite-time stabilization and finite-time H_?control of LPV systems with external disturbances and parameter-varying time delays.At first,the definitions of finite-time stability,finite-time boundedness and finite-time H_?performance for time-delay LPV systems are given.Then,based on the parameterdependent Lyapunov-Krasovskii functional,sufficient conditions of delay dependent finite time boundedness for time-delay LPV systems are given.On this basis,combined with variable gain control technology,an LMI-based finite-time stabilization controller design method for such systems is proposed.A similar idea is adopted to further consider the finite-time H_?control problem,and the sufficiency condition of the system with finite-time H_?performance and the finite-time H_?controller design method are given.Solving these problems have made full use of the parameter-and delay-dependent ideas and been combined with the free weight matrix method,which guarantees the less conservativeness of the proposed controller designs.Finally,a numerical example and a cutting process model of the milling machine are used for simulation.The simulation results verify the effectiveness of the proposed method.Taking into account of the situation that the states of the system are unavailable,Chapter 4 investigates the observer-based finite-time stabilization and finite-time H_?control of time-delay LPV systems.Based on the analysis results of finite time boundedness in Chapter 3,and combined with the parameter dependent full order state observer to reconstruct the state of the system,a design method of the observer-based finite time variable gain stabilization controller for time-delay LPV system is given.Further,the existence conditions of admissible controllers are converted into the feasibility of convex problems subject to linear matrix inequalities.Similarly,according to the analysis results of the finite time H_?performance and parameter-dependent full-dimensional state observers to reconstruct the system state,the problem of designing observer-based finite-time H_?controllers for time-delay LPV systems is solved.The obtained controller ensures the closed-loop system is finite time bounded and has finite time H_?performance.Finally,a numerical example and the cutting process of milling machine are simulated,and the simulation results verify the effectiveness of the theoretical results.The last chapter applies the idea of designing variable gain finite-time controllers to the design of the missile pitch channel control system.Firstly,the quasi-LPV model is developed for the nonlinear dynamic equation of the missile pitch channel.Then,the finite time variable gain controller and the finite time H_?variable gain control of the missile pitch channel are designed by using the Lyapunov function method and variable gain control method,so that the closed-loop system is finite time bounded and has finite time H_?performance.Finally,the designed controller is applied to the nonlinear model of the missile pitch channel for closed-loop simulation,and the simulation results verify the effectiveness of the proposed method.This part constitutes an attempt of applying the finite-time stability idea to practical engineering problems,which not only extends the finite-time stability theory,but also provides ideas.