On Control Srategy Of Planar Double Inverted Pendulum

Inverted pendulum system is typical test equipment in the automatic control fields. It has many characteristics such as multi-variable, nonlinear and strong coupling. Planar double inverted pendulum is one of the systems which are difficult to control.Stable control of the inverted pendulum has more application in engineering.The mainly work of this thesis is focused on the study of the inverted pendulum control. Four control algorithms are designed, and MATLAB simulations show that the four designed controllers can stabilize planar double inverted pendulum. The mathematical model of planar double inverted pendulum is established by means of analytical dynamics method,Linearization of the mathematical models around the balance position results in the decoupled linear models in X and Y directions of double inverted pendulums respectively. Firstly, three-loop PD controller is designed for this multi-variable model. It can use pole assignment method to determine the parameters, PID control of a multi-variable system is achieved.Secondly, LQR self-adjusting controller is presented with the linear quadratic optimal theory, further the output of the LQR controller is refined through coordinated factor, which is the function of the states of planar pendulum, and on account of that, control action exerted on the pendulum is improved, and car position tracking reference input is realized. Based on basic fuzzy control, the parametric self-adjusting fuzzy controller is presented. It can automatically adjust the size of quantify factor and scale factor parameters according to error, and stable control of the inverted pendulum is achieved.Based on sliding mode control, the adaptive fuzzy sliding mode controller (FSMC) is designed further. It can adjust the convergence rate and realize fuzzy approximate of switching control via fuzzy system, Lyapunov function is used to prove the stability of the controller. Simulation results also show that this controller can weaken chattering, has good speed and robustness.Three-loop PD controller and LQR self-adjusting controller are applied to Googol planar double inverted pendulum system. Experimental results verify that the controllers are effective, and have a faster response time, good stability.