Tracking Control Of Double Pendulum On A Cart System Based On Output Regulation Method

The double pendulum on a cart system is a typical underactuated mechanical system,which has been widely used in the fields of robotics and aerospace,and is often applied to verify various advanced control algorithms.Because the double pendulum on a cart system has the characteristics of multivariable,nonlinear and strongly coupled,its position tracking problem is challenging.At the same time,because the output regulation theory can achieve trajectory tracking and disturbance rejection simultaneously,it has attracted extensive attentions from the control community and has been applied to solve various control problems in engineering applications.However,there is often a lack of experimental verification.Therefore,it is of great significance to adopt the output regulation method to solve the position tracking problem of double pendulum on a cart system under time-varying reference signals.This thesis mainly studies the position tracking problem of double pendulum on a cart system,and carries out related experimental research on the experimental platform of the double pendulum on a cart system.The main research work is as follows:(1)Based on the polynomial approximation method,the position tracking problem of the double pendulum on a cart system under time-varying reference signal is solved.First,the position tracking problem of the double pendulum on a cart system is formulated as an approximate nonlinear output regulation problem.Then,the polynomial approximation method is applied to obtain the approximate solution of the regulator equations.Finally,a tracking controller based on the polynomial approximation method is designed to solve the approximate nonlinear output regulation problem and hence solve the position tracking problem of the double pendulum on a cart system.Simulation results verify the effectiveness of the proposed control algorithm.(2)Based on the neural network approximation method,the position tracking problem of the double pendulum on a cart system under time-varying reference signals is solved.First,the position tracking problem of the double pendulum on a cart system is formulated as an approximate nonlinear output regulation problem.Then,the neural network approximation method is applied to obtain the approximate solution of the regulator equations.Finally,a tracking controller based on the neural network approximation method is designed to solve the approximate nonlinear output regulation problem and hence solve the position tracking problem of the double pendulum on a cart system.Simulation results verify the effectiveness of the proposed control algorithm.(3)Two tracking controllers designed in this thesis were studied on the experimental platform of the double pendulum on a cart system.The experimental results verify the effectiveness of the proposed two position controllers.