Research On Modeling And Model Predictive Control For Stabilization Of Double Inverted Pendulum

Abstract:Straight double inverted pendulum is a kind of typically nonlinear object which is multivariable, less-driven and strong-coupling. Its nature is extremely similar with many industrial systems. So the research of the inverted pendulum is not only an important way to verify the validity of control algorithm, but also has a value in engineering applications.The traditional modeling method of the straight double inverted pendulum is physical modeling. The model is got by analyzing the forces of the pendulum. As some assumptions are made and some nonlinear factors are ignored, the physical model is not very accuracy.Due to the demerits of physical model, the ARX modeling method and RBF-ARX modeling method are applied to the double inverted pendulum for the first time. ARX model is a kind of linear models whose parameters can be obtain from the linear least squares method(LSM). While RBF-ARX model is a kind of state-dependent models which are varying according to the state of system. The structured nonlinear parameter optimization method(SNPOM) is applied to estimate the parameters of RBF-ARX model. The results show that two models of double inverted pendulum have high precision.Based on the ARX model and RBF-ARX model, the model predictive controller(MPC) is designed for the double inverted pendulum. There also gives the detailed design methods of the two controllers and the influence of control parameters on the control effect.The simulation study for the stabilization of straight double inverted pendulum is realized with the model predictive control method based on ARX model and RBF-ARX model. The results show that two methods all have strong anti-interference abilities, and double inverted pendulum can reach to the steady state quickly with the MPC method. On the basis of simulation experiments, the RBF-ARX model-based predictive control method is first applied to the real-time control for the stabilization of straight double inverted pendulum successfully. The result further demonstrate that the predictive control based on the RBF-ARX model is effective in nonlinear and fast systems.