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倒立摆系统由于其多变量、非线性和强耦合性等特点而一直成为各国专家学者研究的热点。目前，一级、二级、三级倒立摆都已经有成功控制的实例，而单电机控制的四级倒立摆系统的控制还未见报导。本文首先推导了四级倒立摆系统的数学模型，并对倒立摆系统在平衡点附近进行了可控性研究。在此基础上，提出一种基于三维模糊组合变量的控制方法。仿真研究结果证明了所提出控制方法的有效性。
Inverted pendulum system due to its multivariable, nonlinear and strong coupling characteristics has become a hot spot for the study of experts and scholars from all over the world. At present, there are already examples of successful control of primary, secondary and tertiary inverted pendulums, and the control of a single motor-controlled four-stage inverted pendulum system has not been reported yet. In this paper, the mathematical model of the inverted pendulum system is deduced first, and the controllability of the inverted pendulum system is studied in the vicinity of the equilibrium point. On this basis, a control method based on three-dimensional fuzzy combination variables is proposed. Simulation results show the effectiveness of the proposed control method.