Nonlinear Control For Two Types Of Underactuated Systems

The under-actuated systems are special kinds mechanical systems which have fewer independent control inputs than the degrees of freedom(DOF).Compared with the fully actuated systems,the under-actuated systems have fewer actuators,which reduce the complexity of the system,the mechanical failure rate and the energy consumption etc.,and widely used in many areas such as agriculture,industry and aerospace.However,the control of an under-actuated system has always been a challenging issue.The controllers are required not only to stabilize fully actuated subsystems but also realize the self-stabilization of the under actuated subsystems.Furthermore,the under actuated systems are characterized as nonlinear,coupled which make the control issue more difficult.Therefore,the investigate on the control of under actuated system has great theoretical and practical significancesThis dissertation takes the multi-link underactuated offshore crane system and the motion limited underactuated quadrotor unmanned aerial vehicle(UAV)system as the control objectives and studies the heave compensation and anti-swing control for an offshore crane and the trajectory tracking control for a quadrotor UAV respectively Although the control for the two under actuated systems has been extensively investigated,there still some problems to be solved(1)Most offshore crane anti-swing control papers treat the hook-cable-cargo system as a single pendulum system.However,when the mass of the hook cannot be ignored or the cargo is large in size.the hook-cable-cargo system may exhibit double pendulum effects.The single pendulum-based control approaches are not suitable in such cases.(2)The existing offshore crane heave compensation controllers take the ship heave displacement as the input and make the cargo moves in opposite direction to realize heave compensation.However,the under-water cargo may suffer from ocean current which has little effect on the ship which lead to that the existing approaches have poor robustness to the ocean current disturbances.(3)The hydraulic motors/winches are common actuators in the offshore crane systems.However,the hydraulic motors/winches usually have nonlinear characteristics such as dead-zone and saturation,and the correction of the nonlinear characteristics is a tough problem to be solved.(4)For the trajectory tracking control of a quadrotor UAV,most control approaches are based on accurate model parameters.However,the measurement of the model parameters is not an easy task which not only requires specific equipment but also repeated experiments.Furthermore,when the quadrotor UAV is fulfilling some specific missions such as aerial shooting,pesticide spraying etc.,the model parameters will change during the flight.In such cases,the accurate model parameters-based control approaches are not suitable.Motivated by the desire to solve the aforementioned problems,this dissertation carries out some studies in designing advanced controllers to solve the anti-swing and heave compensation for the offshore crane and the trajectory tracking control for the quadrotor UAV.The main contributions of this dissertation are as follows(1)Stable control for a double pendulum offshore crane.Aiming at the problem that the single pendulum-based control approaches cannot be applied in the anti-swing control for a double pendulum offshore crane,this dissertation proposes a partially constraint control approach.First,by using the Lagrange's method,the dynamic model of a double pendulum offshore crane is established in the presence of ship roll and heave motion-induced disturbances.Second,without any linearization to the dynamic model and in the presence of input constraint,a partially constraint controller is designed to regulate the hook and cargo to desired positions without swing.The stability of the closed-loop system is strictly proven by using the Lyapunov theory and Lasalle's invariance theorem.Finally,extensive numerical simulation results are presented to verify the effectiveness and robustness of the proposed controller.(2)Active heave compensation control for the offshore crane in the presence of actuator saturation.In consideration that the existing heave compensation approaches have limited robustness to the current disturbance and the hydraulic motors/winches have nonlinearities such as dead zone and saturation,a state observer based active disturbance rejection control-equivalent saturation model predictive control(ADRC-ESMPC)scheme is designed.Different from the existing approaches,this control scheme transforms the heave compensation problem into the payload trajectory tracking control problem.First,the motion equation of the payload is established Furthermore,in consideration that the accurate position of the payload is difficult to measure,a state observer is designed to estimate the payload position.Second,by using the output of the state observer,an active disturbance rejection controller(ADRC)is designed to compensate for the external current disturbances and generate desired angle trajectory for the hydraulic winches.Third,an equivalent saturation model predictive controller(ESMPC)is designed to correction the dead zone and saturation nonlinearities of the hydraulic winch and ensure the winch track the desired trajectory quickly and accurately.Finally,simulation results are provided to show the effectiveness of the proposed control scheme(3)Disturbance observer based adaptive quadrotor UAV trajectory tracking control.The backstepping control and sliding mode control(SMC)are two common nonlinear control approaches in the quadrotor UAV tracking control.However,the two control approaches require accurate model parameters.However,the quadrotor UAV model parameters are difficult to measure which not only require specific equipment but also repeated experiments.In addition,the quadrotor UAV system is sensitive to external disturbances.To solve these problems,a disturbance observer based adaptive trajectory tracking controller which has an outer-inner loop structure is designed.By introducing virtual control inputs,the quadrotor UAV system is divided into outer loop position control subsystem and inner loop attitude control subsystem.In the outer loop,adaptive laws are designed to estimate the unknown aero damping factors and then backstepping controller is designed to stabilize the outer loop system.Furthermore,a disturbance observer is designed to compensate for external disturbance and enhance the robustness.In the inner loop,proper adaption laws are designed to estimate the unknown inertia moments,aero damping factors and the upper bounds of lumped disturbances.Then an adaptive non-singular terminal sliding mode controller is designed to ensure the states converge to their desired values in finite time.Finally,simulation results have verified the effectiveness of the proposed controller.(4)Model parameters independent nonlinear trajectory tracking control approach In practice,the model parameters of the quadrotor UAV such as mass,inertia may be time-varying and the linear parameterization condition cannot be satisfied.In such case,the adaptive technique-based control approaches cannot achieve good performances To solve this problem,a model parameters independent controller is designed.In the outer loop,the Proportion-Differentiation(PD)controller is used to replace the equivalent control part of the sliding mode controller(SMC)to stabilize the system without the requirement for model parameters.Furthermore,an adaptive radical basis neural network is designed to compensate for the external disturbances to enhance the robustness.In the inner loop,a robust integral of sign of error(RISE)controller which not only do not need the information of model parameters but also has continuous control signals is designed to ensure the inner loop tracking desired trajectory accurately.Finally,the effectiveness and the robustness of the proposed controller is verified via simulation experiments.