Several Control Methods Research On Linear Inverted Pendulum

Inverted pendulum, which is an unstable system, can effectively reflect many key problems in process control, such as stabilization problem of the linear and nonlinear system, robustness problems, servo problems and tracking problems. To design the controller of inverted pendulum system, its stable effection is very clear, which can observe through the angle of the swinging rod, the displacement of the trolley and the setting time, the control effect is clear at a glance.This thesis primary researches the 1-stage and 2-stage inverted pendulum system. In the first, the structure and mathematical model of inverted pendulum is analysis, and we have the mathematical model of the 1-stage and 2-stage inverted pendulum. From the mathematical model, we also have the transfer function of the inverted pendulum system. Secondly in the stability control of the 1-stage inverted pendulum, we first use the single PID control method for inverted pendulum control, and then use double closed loop PID control method for its control. On the issue of the selecting and determination of the PID parameters, we use the optimal control and its mathematical methods. By using the integral criterion of time multiplies the absolute error, we design the linear 1-stage inverted pendulum PID controller. At last, use Ackermann's algorithm to design controller of pole placement to control the inverted pendulum.In the second, for 2-stage inverted pendulum, we use the linear quadratic optimal control method. Through the selection of matrix Q and R, and by using MATLAB soft to calculate the feedback linear matrix K, use state feedback to control the 2-stage inverted pendulum.Finally, describe the control platform MATLAB software. The experiment of realtime-control of inverted pendulum shows that the system is stable, thus indicating that the controller is affection. Though different controller control the inverted pendulum, show the difference between the different controllers.