Study On The Non-linear Control Of Inverted Pendulum And Virtual Reality

The control of inverted pendulum system has long considered an intriguing problem for control theory and its applications. As a highly nonlinear, strong-coupling, multivariable and unstable system, the stabilization control of inverted pendulum system is a primary challenge for researchers in this field because of the difficulty of the problem. It becomes the wonderful experiment device to verify how about the control strategy in automatic control experiment.To the equilibrium control question of the double inverted pendulum, the author uses dynamic Lagrange equation to derive the mathematical model of the pendulum.In the vicinity of the equilibrium point,the model is linearized and the state-space equation is obtained. Then, the paper analyzes the stability, controllability and observability. For the control methods,the controller is designed by quadratic optimal control theory, and good effects of control are obtained. Because abilities of anti-jamming and robustness of the method are weak, so fuzzy control method is adopted. Towards to the multivariable double inverted pendulum system, this paper brings forward the control method of state varieties synthesis. It reduces the input variable dimension of the fuzzy controller, The question of "rule explosion" is solved successfully. As the strong-coupling, multivariable properties, control rules and membership functions are hard to confirm. ANFIS method has lots of strong point, such as creating less control rules, composing fuzzy controller simple, and having better character. Finally, this paper using the system's SIMULINK model realizes a virtual reality system, in which you can see the control procedure in 3D form.The research of this thesis based on definite theory, including the reasoning of mathematical model, discussion and the simulation. The result of simulation turn out that the control of the inverted pendulum using the controller designed in the paper is effective.