The RBF-ARX Model-based LQR Control Applied To Inverted Pendulum System

Inverted pendulum is a typical research object with characteristics of high-order, nonlinear, strong-coupling and instability, which is worthy of our study.At first, the background and development is introduced, and the structure and the principle are discussed.Then, the model and controlmethods on 1-stage inverted pendulum are given. The traditional way on the inverted pendulum is mainly based on physical model. The process of building up a physical model is not an easy thing, some system factors have to be omitted, and lots of derivative equations are needed to be solved. However, the result of physical model is notverysatisfied. The identification way can eliminate the defects brought by physical model. In this paper, ARX and RBF-ARX model are proposed. The ARX model is a linear model, whose parameters are searched by LSM. While on the other hand, the RBF-ARX model is a time-varied nonlinear model, the SNPOM is used in parameter optimization, and it works quickly and perfectly. The model results of the 2 models show ideal performance, which lay a solid foundation for the closed loop control.And then the LQR controller is detailedly studied. According to the ARX and RBF-ARX model, the LQR controllers are designed. The simulation results show that the system is stable and convergent, and has a good dynamic response.At last, the ARX and RBF-ARX model based real-time experiments are carried out. Through the results we can see that: both of the 2 models have a good performance in the real-time control, and can make the system go to stable. But the RBF-ARX model is better, so the RBF-ARX model is superior in the application of nonlinear system.