Control And Application Of A Class Of Nonlinear Underactuated System

Nonlinear underactuated system is a type of nonlinear system with fewer control inputs than the system degrees of freedom and has the characteristic of strong coupling and strong nonlinearity.Although the underactuated system lack the corresponding driving equipment compared with the full actuated system,it brings difficulties to the design of the control scheme,but it is precisely this type of system that requires fewer drivers and can be assembled with a reduced number of drivers and actuators,thus reducing the size,weight and energy consumption of the system.Therefore,the research of nonlinear underactuated systems is of great practical significance.This paper studies a class of nonlinear underactuated systems that can be described by Euler-Lagrange equations.The inverted pendulum and the ball beam system are a typical nonlinear underactuated systems that are often used by scholars in control field to verify control methods.They are also abstract systems used in many practical engineering control problems.The research content of the paper is as follows:1.Decoupled sliding mode control of underactuated system based on the novel multipower reaching law.The principle of decoupled sliding mode control is described;in order to realize the simultaneous control of the non-actuated term and the actuated term of the nonlinear underactuated system,the decoupled method is used to derive decoupled sliding mode controller.At the same time,a novel multi-power reaching law is devised to restrain the chattering cause by sliding mode control.The results of simulation experiments show that this control method can reduce the steady-state error and chattering of the system and speed up the response speed of the system.2.Decoupled sliding mode control of underactuated system based on disturbance observer.A novel piecewise double-power reaching law is devised to restrain the chattering caused by sliding mode control.The characteristics of maximum convergence time of the reaching law that is not related to the initial value of the sliding mode surface and the fixedtime convergence are analyzed in detail.Considering the lumped disturbance problem in system,that is,the uncertainty of model parameters and external disturbance,a super twisting disturbance observer is devised.The results of simulation experiments show that the control strategy can reduce the system chattering,suppress the disturbance and enhance the robustness of the system.3.State error Port-Controlled Hamiltonian(EPCH)control and disturbance suppression of an inverted pendulum system with uncertain parameters.The closed-loop EPCH model of the underactuated inverted pendulum system is introduced;for the problem of the parameter uncertainty and external disturbance of the system,an adaptive law and a PI control law are devised respectively.The results of simulation and experimental show that this control strategy can enhance the anti-disturbance ability and reduce the steady-state error of the system.In this paper,the control strategy is verified by taking the inverted pendulum and the ball-bar system as the objects of simulation and experiment.Several control methods designed show excellent control performance,and realize the simultaneous control of the non-actuated term and the actuated term of the nonlinear underactuated system.Compared with other control methods,the designed control methods can improve the convergence speed of the system,reduce the steady-state error,and have a better ability to suppress the system chattering caused by sliding mode control,system parameter uncertainty and external disturbance of the system,and enhance the robustness of the system.