Research On Cloud Model PID Control Of Double Inverted Pendulum

Inverted pendulum system is nonlinear, multivariable, strong coupling and naturally unstable. It is an ideal experimental platform in the field of control engineering. The stability control of the inverted pendulum can effectively reflect many key problems in the control process, such as the non-linear problem, the system robustness problem, the servo performance problem, the stabilization problem and the tracking problem. This paper focuses on the optimization modeling and adaptive cloud model PID control for linear double inverted pendulum system.Firstly, this thesis analyzes the inverted pendulum system structure and characteristics, establishes the nonlinear mathematical model of the linear double inverted pendulum by using Lagrange equation and carries out the linearization process in the vicinity of equilibrium position. On this basis, a qualitative analysis of the linear model is implemented by using modern control theory. It is proved that the linear double inverted pendulum system is a naturally unstable system near the equilibrium point, but completely controllable and observable.Secondly, considering the multi-output characteristic of inverted pendulum system, based on the idea of information fusion, this thesis designs the state feedback matrix by using the LQR algorithm to build fusion function. Consequently, the 6 state variables of the original system are simplified into 2 variables, which are called comprehensive error and comprehensive error rate, so the controller input variable dimension can be extremely reduced. In the applying process of LQR algorithm, Genetic Algorithm is combined to optimize weighting matrices Q and R for an inverted pendulum system, the method simplifies the design process of feedback matrix and enhances the rapidity and robustness of the control system.Finally, combined with the cloud model theory and PID control strategy, the design method of cloud reasoning rule based PID controller is put forward and applied to the linear double inverted pendulum control system. This method takes cloud model as an effective tool in uncertain transformation between qualitative concepts and quantitative expressions, integrates human control experience in the rules for cloud reasoning. In the control system, synthesis error and synthesis error rate are adopted as the inputs of cloud rule reasoning, the outputs of cloud rule reasoning can adjust PID control parameters adaptively. The simulation results show that the control effect of the proposed cloud model PID controller is better than that of ordinary PID control. With its good adaptive ability, the dynamic performance and robustness of the control system are significantly improved. The application of cloud model theory provides a good solution for dealing with nonlinear uncertainty in intelligent control system.