Nonlinear Disturbance Observer-Based Control For The Trajectory Tracking Control Of Underactuated Systems

Underactuated systems are a class of control systems characterized by the presence of more degrees of freedom than control inputs,and are very common in the field of control research and practical application.Cart-pole inverted pendulum,as a kind of typical underactuated system,has important theoretical value.The control technology derived from the cart-pole inverted pendulum can be applied in many industrial and engineering products.Two-wheeled inverted pendulum is a complex nonlinear underactuated system with the typical characteristics of instable and nonholonomic,and has become an ideal experimental platform for the study of control theory and control methods.Meanwhile,it has application value because it can work well in a small or a relatively dangerous place.Considering the fact that the model of the real system is not exactly exact and the problem that the system exists parameter perturbation and external disturbance,the control methods are studied on trajectory tracking of tht cart-polt inverted pendulum and two-wheeled inverted pendulum.The main research contents of this article are as follows:1).Trajectory tracking control of cart-pole inverted pendulumA nonlinear disturbance observer-based control scheme was proposed for the trajectory tracking of cart-pole inverted pendulum systems.Firstly,a tracking error-based output function was proposed and the equation transformation and Butterworth low-pass filter are applied to solve the problem of unknown control directions.By introducing a tracking differentiator-based nonlinear disturbance observer,which is used to compensate for unknown system model and disturbance,the need to know the structure of the system and its parameters was obviated.The internal and external dynamics are rigorously analyzed,thereby proving the uniform ultimate boundedness of the error trajectory.Finally,the effectiveness of the method presented in this study was proved with the simulation research of cart-pole inverted pendulum.2).Trajctory tracking control of two-wheeled inverted pendulumA nonlinear disturbance observer-based hierarchical sliding mode control scheme was proposed for the trajectory tracking of two-wheeled inverted pendulum systems.Firstly,the nonholonomic system is divided into speed inner loop system and posture outer loop system,then design the controller separately.The inner loop system is composed of rotational actuated system and longitudinal underactuated system.A sliding mode control was proposed for the speed tracking of actuated system with the help of the NDO to deal with disturbance in system.A hierarchical siliding mode control was proposed for the speed tracking of underactuated system with the help of the NDO to deal with disturbance in system.Two inner loop systems are simulated respectively,which proves that the controller has good anti disturbance ability.Then the inner loop controller and outer loop posture controller are combined to achieve the purpose of tracking any trajectory as well as keeping upright.The stability of the controller is proved by Lyapunov method in every part of the controller design.Finally,the validity of the system is proved by MATLAB simulation.