Tracking Control Of Inverted Pendulum System Based On Discrete-Time Output Regulation Approach

Inverted pendulum system is regarded as a typical benchmark system to test various advanced control methods.It is widely used in the field of robot control,aerospace technology and so on.Since inverted pendulum system is a class of unstable,multivariable and strong coupling nonlinear system,it is challenging to synthesize a feedback control law to achieve its stabilization and tracking control problem based on non-simplified nonlinear model.Besides,most of the nonlinear control laws are realized by digital controiler.Traditional control methods have some limitations in dealing with the high-precision control problem of inverted pendulum system.Nevertheless,nonlinear output regulation theory can achieve multiple goals including accurate tracking of reference trajectory,disturbance rejection,and parameter robustness.Therefore,it is very important to study the position tracking problem of inverted pendulum system based on discrete-time nonlinear output regulation theory.This thesis mainly studies the position tracking problems of two categories of inverted pendulum system.The main research work is as follows:(1)This thesis studies the position tracking control of a multi-input,multi-output spherical inverted pendulum system.This problem can be formulated as a typical discrete-time nonlinear output regulation problem.The key for solving the discrete-time nonlinear output regulation problem lies in how to solve a set of algebraic functional equations called discrete regulator equations.In this thesis,we first show that the discrete regulator equations associated with the spherical inverted pendulum system are solvable by the center manifold theorem and then use the neural network approach to tackle with the tracking problem.Finally,we compare the neural network method with traditional linear control method.Simulation results demonstrate the effectiveness and superiority of our design.(2)This thesis studies the position tracking control of a single-input,single-output linear motor inverted pendulum system.This problem can be formulated as a typical discrete-time nonlinear output regulation problem.Compared with traditional rotational motor,the linear motor has many advantages such as high precision,fast response,good reliability,and small disturbance.However,the frictional force on the rail still has great impact on the control accuracy of inverted pendulum system.Therefore,this thesis proposes a discrete-time neural network controller by combining neural network approach and frictional force feedforward compensation approach,which can realize precise position tracking control of linear motor inverted pendulum system.Finally,we compare the neural network method with traditional linear control method.Simulation and experimental results demonstrate the effectiveness and superiority of our design.