Flexible Inverted Pendulum Control

Inverted pendulum system is a higher-order, nonlinear, strongly coupled and absolutely instable system. It is an effective tool for validating new control theories and methods.The paper takes the linear 1-stage flexible-joint inverted pendulum as a research object. At first, it establishes the model of the inverted pendulum system based on the Lagrange equation and analyzes its performance. Secondly, it also talks about how the PD control method, the fuzzy control method and the sliding mode control method control the flexible-joint inverted pendulum system. Specific means are as follows:(1) The three loop PD controllers are designed to control three variables of the flexible joint inverted-pendulum system and then the pole assignment is used to design the parameters of controllers. The designed controller is applied to actual inverted pendulum system. The real-time experiment result shows that the PD controller can also control multivariable, nonlinear and absolutely instable system.(2) Based on the linear 1-stage flexible-joint inverted pendulum system property of multivariable, a fuzzy controller based on fusion function is proposed. Specific process is as follows: the feedback gain matrix is figured out, which makes the system stable by utilizing optimal control theory, and then makes up the fusion function by utilizing the feedback gain matrix which reduces the input variable dimension of the fuzzy controller,"rule explosion" problem is solved. The simulation experiment and the real-time experiment prove its validity and the correctness.(3) The sliding model variable structure control (SMVSC) algorithm is applied to flexible joint inverted pendulum system, and sliding mode controller based on reaching rate is designed. And by introducing saturation function to the SMVSC based on reaching law, the system's chattering is solved. The result of simulation shows that the algorithm is feasible and efficient.