Research On Finite-time Control Problem For Second Order System

When the model of a system is exactly known,the finite-time control that contains exponential parameters can guarantee the finite-time convergence of system states to the equilibrium point.However,the convergence time of an asymptotical control system to the equilibrium point is infinite in theory.In practical engineering,compared with the asymptotical control(such as PID control),the finite-time control has the advantages such as faster convergence speed,higher precision and less energy consumption.Second order system can discribe models of many moving body,such as satellites,vehicles and vessels.The study of finite-time control on second order system is also the base of high order system.The spacecraft attitude control system,which is the important part of the spacecraft system,is one of the classical second order systems.The attitude control scheme can affect the performance of the attitude system,even the success or failure of the space missions.This dissertation studies on the definition,theorem,performance,analysis method and design method of finite-time control for first order system,second order system and spacecraft attitude control system.The main research contents of each chapter are as follows.Study on what is finite-time control and the reasons why study on finite-time control.First,for the perturbed system,a new definition of finite-time convergent boundedness is given.This definition can differentiate the finite-time control and asymptotical control.Based on it,a new definition of finite-time is also given.Second,the theorems of extended local finite-time stability and extended finite-time convergent boundedness are given and proved.These two new stability theorem have less conservativeness than the traditional ones.Study on the finite-time state feedback control.For the general second order system,first,the problem that the homogeneous control cannot analyze the stability of perturbed system is investigated.By using Lyapunov method,it is proven that the perturbed system driven by the homogeneous control is finite-time convergently bounded.Second,the problem that the parameters of “adding a power integrator”(AAPI)control are greatly constrained is investigated.A method of simplifying parameters is given,and the stability of the system is analyzed in the absence or presence of perturbations.Third,the problem that the classical nonsingular terminal sliding mode(CNTSM)control cannot calculate the upper bound of settling time is investigated.A bounded upper bound of settling time is given by using AAPI method,and the stability of the system is analyzed in the absence or presence of perturbations.Fourth,for the attitude stabilization of spacecraft,by using above results,a homogeneous attitude controller,a AAPI attitude controller and a CNTSM attitude controller are designed respectively,and it is proved that the disturbed attitude system is finite-time convergently bounded.Study on the finite-time output feedback control.For a second order nonlinear system which has the observation error nonlinear term with any degree,a finite-time observer is designed to observe the velocity state,and the stability of the observation error system is analyzed in the absence or presence of perturbations.For a second order nonlinear system which has the nonlinear term with any degree,a finite-time output feedback filter-controller is designed,and the stability of the observation error system is analyzed in the absence or presence of perturbations.When considering the cases that the measuring equipment of angular velocity may fail or the measuring equipment of angular velocity may not be installed in the small spacecraft in the future due to cost-effective,the problem of angular-velocity-free finite-time attitude control is investigated.A finite-time angular velocity observer and a finite-time output feedback attitude controller are designed.The stability of the observation error system and the integrated closed-loop system are analyzed in the absence or presence of perturbations.In addition,a finite-time output feedback attitude controller is designed,and the stability of the attitude system is analyzed in the absence or presence of perturbations.Study on the fixed-time state feedback control.Fixed-time control is a special finite-time control,the bound of its settling time is independent from the initial states.For a general second order system,a nonsingular-terminal-sliding-mode(NTSM)based fixed-time controller and an AAPI based fixed-time controller are designed respectively.The stability of the system is analyzed in the absence or presence of perturbations.Then,for the attitude stabilization of spacecraft,a NTSM based FAttitude controller and an AAPI based FAttitude controller are designed respectively.The stability of the attitude system is analyzed in the absence or presence of perturbations.