Control Realization And Chaotic Analysis Of Inverted Pendulum

Inverted pendulum is a control system, with the feature of high order, instability, multi-variable, non-linearity and tight coupling. In this paper, it analyzes the experiment platform system of the single inverted pendulum, and programs the computer to control the system. The nonlinear dynamics of the double inverted pendulum system is also studied, and the results show that there are chaotic motions in some parameter regions. The contents and the major results of the paper are as follows: First of all, the research background and the practice significance of the inverted pendulum system are introduced. And this paper presents the applications in the engineer and the research developments of the inverted pendulum system in recent years. It also points out the developing trend in future and the study necessity in the nonlinear dynamics of the inverted pendulum system. Secondly, the experiment platform of the single inverted pendulum is set up. And it analyzes the controllability and the control principle of the single inverted pendulum system. It also analyzes the practical control system based on four aspects of machine, sensor, control equipment and actuator. Thirdly, it analyzes the mathematical model of the single inverted pendulum system, and completes the status feedback and system simulation with MATLAB. Based on the experiment platform system, the program is compiled to control the system making used of LQR method. And the Simulation result is effective. The software part is programmed by Visual Basic and the practical result indicates that it makes the inverted pendulum steadily stabilized at "inverted" state and concerning actual time parameters showed in program interface. Fourthly, utilizing Lagrange Equations, it establishes the mathematical model and obtains the nonlinear equations of motion for the double inverted pendulum system. And the equations of motion are simplified and then the dimensionless equations of notion are acquired. Using the method of multiple scales, the averaged equations of the double inverted pendulum system are obtained in 1:1:1 internal resonance.