Some Theoretical And Applied Research On Nonsmooth Control Based On Output Feedback

Nonsmooth control is an advanced nonlinear control method relative to smooth control.Its closed-loop control system is non-Lipshitz continuous.Compared with smooth control(such as PID control),nonsmooth control has a better transient performance,a better robustness,and a wider applicability.Because nonsmooth control removes the constraint of the smoothness condition(such as Lipshitz condition)in the smooth control on the system performance,it can be applied to strong nonlinear systems,and effectively improve the convergence performance and disturbance rejection performance of the closed-loop system.Due to these advantages,nonsmooth control has received great attention in both theory and application since the 1990 s.However,with the rapid development of information and intelligence in industrial systems,the structure,scale,and complexity of the actual system are increasing.System uncertainties,external disturbances,state estimation,state constraints,resource constraints also bring new challenges to the design of control systems.How to effectively solve these new problems has become a research hotspot and focus in the current control field.This dissertation focuses on some theoretical problems and application research of nonsmooth control based on output feedback.The contents mainly involve the design and analysis of output-based nonsmooth active disturbance rejection control for the second-order disturbed nonlinear uncertain systems,the design and analysis of output-based nonsmooth active disturbance rejection control for high-order disturbed nonlinear uncertain systems,the design and analysis of output-based nonsmooth constraint control for second-order nonlinear systems with output constraints,the design and analysis of nonsmooth observer-based sensorless speed control for permanent magnet synchronous motor systems,and the design and analysis of event-triggered nonsmooth attitude tracking disturbance rejection control for rigid spacecraft attitude systems and so on.The main results and contributions of the dissertation are summarized as follows:(1)For the problem of the finite-time output feedback control of a class of second-order nonlinear uncertain systems with disturbance,an output-based nonsmooth active disturbance rejection control method is proposed,which solves the problem of disturbance suppression and finite-time stabilization of the system.Firstly,without considering the external disturbance,a nonsmooth state feedback controller is constructed for the second-order nonlinear uncertain system without disturbance by using adding a power integrator technique,such that the finite-time stabilization of the closed-loop system is achieved.Secondly,the external disturbance is taken as an extended state of the system,and the nonsmooth observer theory is used to design a nonsmooth extended state observer to estimate the unknown disturbance and state at the same time.An output-based nonsmooth active disturbance rejection control method is obtained by combining the observer with the controller and adding the disturbance feedforward compensation term,The disturbance rejection performance and finite-time stability of the closed-loop system are analyzed by using the Lyapunov theory.Finally,the effectiveness of the proposed method is verified by the simulation of the inverted pendulum system.(2)For the problem of the finite-time output feedback control problem of a class of high-order nonlinear uncertain systems with disturbance,an output-based recursive continuous high-order nonsmooth active disturbance rejection control method is proposed,which solves the problem of disturbance suppression and finite-time stabilization of the system.Firstly,the system uncertainties are ignored,and the external disturbance is taken as an extended state of the system.By using the backstepping-like method,a recursive continuous nonsmooth extended state observer is constructed for the high-order disturbed nonlinear system to estimate the unknown disturbance and state simultaneously.Then,based on the adding a power integrator technique and homogeneous domination method,a recursive continuous high-order nonsmooth state feedback controller is designed to stabilize the nonlinear uncertain system without disturbance.An output-based recursive continuous high-order nonsmooth active disturbance rejection control method is obtained by combining the controller with the observer and adding the disturbance feedforward compensation term.The disturbance rejection performance and finite-time stability of the closed-loop system are analyzed by using the Lyapunov theory.Finally,the effectiveness of the proposed method is verified by numerical simulation.(3)For the problem of the finite-time output feedback control of a class of second-order nonlinear systems with output constraints,an output-based nonsmooth constraint control method is proposed to solve the problem of output constraint control and finite-time stabilization of the system.Firstly,the output constraint function is designed to provide sufficient reverse control energy when the state is close to the constraint boundary,and the output filter is designed to estimate the unknown state.Then,the output constraint function and the output filter are integrated into the traditional homogeneous finite-time control law.The finite-time stability of the closed-loop system is guaranteed and the constraint of the system output is achieved.The rigorous theoretical analysis shows that the system output can not only be kept in the preset constraint range but also converge to zero in finite time.Finally,the effectiveness of the proposed method is verified by numerical simulation.(4)For the problem of the nonsmooth speed control of permanent magnet synchronous motor systems without sensors,a nonsmooth observer-based sensorless speed control method is proposed to solve the problem of the position estimation,speed estimation,and sensorless control of the motor system.Firstly,based on the measurable motor current and voltage,a nonsmooth back electromotive force observer is designed to estimate the back electromotive force of the motor,and the rotor position of the motor is calculated by using the algebraic equation.Then,based on the calculated value of the rotor position,a nonsmooth extended state observer is designed to estimate the speed and the lumped disturbance of the motor at the same time.The disturbance estimation is used as feed-forward compensation and the speed estimation is used as a nonsmooth feedback design,then a composite sensorless speed control method is obtained.The stability and disturbance rejection performance of the closed-loop system are analyzed by using the Lyapunov theory.Finally,the proposed control method is applied to a permanent magnet synchronous motor system.The simulation results and experimental results show that the proposed method can improve the convergence performance and disturbance rejection performance of the system.(5)For the problem of the nonsmooth attitude tracking disturbance rejection control of rigid spacecraft attitude systems,an event-triggered nonsmooth attitude tracking disturbance rejection control method is proposed,which solves the problem of discrete-time attitude controller design and disturbance suppression of spacecraft attitude system.Firstly,a nonsmooth attitude observer is proposed to eliminate the zero-drift bias of the gyro sensor,so that the attitude and angular velocity of the aircraft can be estimated accurately.Then,a discrete-time nonsmooth attitude tracking disturbance rejection controller is obtained by using the emulation method of a continuous-time nonsmooth attitude tracking disturbance rejection controller.Considering the problem of limited onboard resources,an event-triggered mechanism without Zeno behavior is proposed.The event-triggered nonsmooth attitude tracking disturbance rejection controller is obtained by combining the mechanism with the discrete-time attitude controller.By using the Lyapunov theory,the stability and disturbance rejection performance of the closed-loop system are analyzed.Like the case of a continuous-time nonsmooth attitude controller,it is proved that the event-triggered nonsmooth attitude controller maintains a better disturbance rejection ability.Finally,the numerical simulation verifies the feasibility and effectiveness of the proposed method.