Research Of The Linear Single Inverted Pendulum System

As a multivariate and unstable nonlinear system, Inverted Pendulum is a typical experimental platform for research on control theory. As many abstract concepts of control theory, such as stability controllability, anti-jamming capability etc. can be reflected by Inverted Pendulum, it is often used to test the properties of complex system. Besides, because the control system of Inverted Pendulum is similar with those of rocket vehicle and robot walk, its control theory and control method are applied widely in the areas of military industry, spaceflight and robot. According to the number of pendulum, Inverted Pendulum can be ranked into first, second and third class, which are jointed freely mutually, means there are no motors or other drive components. Whether it is first-class Inverted Pendulum or not, its basic control problem is to make the pendulum reach the equilibrium position vertically as soon as possible with little vibration.As a typical controlled object, Inverted Pendulum can be controlled by various theories and methods. And the most common way among them is the PID control. As one of the earliest control strategies, PID control is widely used in the industrial control for its simple algorithm, good robustness and strong adaptability. Because both of its input and output are single, PID control can only control the angle of the pendulum but cannot control the position of the controlled car at the same time. Through the analysis of physical model of Inverted Pendulum, state space feedback control can set up kinetic model, determine state variable and deduce state and output equation. As a way with multiple input and output, state space feedback control can control the angle of pendulum and the position of the controlled car. Therefore, it is a relatively mature control method. LQR, LQR can get the optimal control law of state space feedback control, thus, it is easy to constitute the closed-loop optimal control. This article analyzes some typical control strategies, including the establishment of mathematical model, MATLAB simulation and their controlling results. Based on these control strategies, this article designs an experimental platform of linear single inverted-pendulum, and builds the model of linear single inverted-pendulum in ADAMS. Through the united simulation of MATLAB and ADAMS, real-time control of linear single inverted pendulum is realized by the way of state space feedback control.