Stable Control On The Ring Double Inverted Pendulum

Ring double inverted pendulum system is a typical model of single-input and multi-outputs, multivariable, nonlinearity, strong-coupling and absolutely instability naturally. The research on the accurate control of the inverted pendulum has great engineering value to the control of the complex industrial object. What is more, the research of inverted pendulum has many important realistic meaning in the research such as, the walking of biped robot, the launching process of rocket and flying control of helicopter.In order to make the ring double inverted pendulum stable on the equilibrium position. Firstly we build up the math model of the ring double inverted pendulum and prove its controllability. Secondly, according to the model, three methods about how to control the ring double inverted pendulum are given, which are the infinite time linear quadratic optional controller, weighted integral-type variable universe adaptive fuzzy controller and weighted sum-type variable universe adaptive fuzzy controller. Thirdly, we act the control on the inverted pendulum in simulation using those methods respectively, the simulation results not only illustrate the effectiveness of the control methods, but also manifest the method that integral variable adaptive fuzzy controller is better than the LQR controller; at the same time, the weighted sum-type variable universe adaptive fuzzy controller is designed, which not only solve the slightly complicated structure and large calculation of weighted integral-type variable universe adaptive fuzzy controller, but also obtain better effectiveness than the weighted integral-type variable universe adaptive fuzzy controller; what's more, we deeply discuss two contraction-expansion factors in order to make the ring double inverted pendulum have rapider speed; At the last, we make the inverted pendulum control experiment under the weighted sum-type variable universe fuzzy controller and analysis the result.