Abstract
The inverted pendulum is a classic problem in dynamics and control theory and is widely used as a benchmark for testing control algorithms. This paper studies the use of fuzzy control method to study the stability control problem of a triple inverted pendulum system. By the linear model of the system, the feedback weight matrix of the LQR optimal control and the feedback parameters of the linear optimal control are designed to determine the parameters of the fuzzy controller. The simulation results show that the proposed method can achieve the stability control of the three stage inverted pendulum, and has good dynamic performance with simple parameter selection.
Highlights
The inverted pendulum system is a typical nonlinear, strong coupling, multivariable, naturally unstable system [1]
The design of a fuzzy controller based on the fusion structure for the triple inverted pendulum system is analyzed; the fusion weights of the multi-variables are based on the linear model
In order to facilitate the study for the triple inverted pendulum system shown in Figure 1, assumptions of the following conditions are true [9]: 1) Friction torque and the relative speed of each part are proportional; 2) There is no slip between the belt pulley and the drive belt; 3) Link 1, Link 2, or Link 3 can be regarded as a rigid body; The nonlinear dynamic model of the three stage inverted pendulum system is:
Summary
The inverted pendulum system is a typical nonlinear, strong coupling, multivariable, naturally unstable system [1]. The inverted pendulum can effectively be used for studies key issues such as the quality of stability, robustness, mobility, tracking and that is why, it is the ideal model for testing various theories in control engineering [2] [3]. It has been used in classical control, modern control and intelligent control for stability analysis with techniques such as LQR control [4] [5] fuzzy control method [6], fuzzy neural network method [7] etc. Theodomile has the advantages of simple structure, stable control and better convergence
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