Abstract: In this paper, the balance control problem of set-point is studied about the ball and beam system based on the joint constraint. According to the position of the ball, the structure of the ball and beam system is divided into two types：the normal ball and beam system and the single pendulum system. The motion characteristics of both the two systems and their switching are analyzed. A control scheme based on the Lyapunov method is proposed to solve the balance problem of the ball and beam system based on the joint constraint. It is proved that the solutions make the closed-loop system converge to the desired balance state exactly by using the proposed control scheme. The simulations result is given.

Key words: joint constraint, balance control scheme, energy control, ball and beam system

摘要： 研究了节点约束的球杆系统的定点平衡控制问题。根据球的位置，球杆系统分为两种类型的结构模式：普通球杆系统和单摆系统。对两种结构的运动特性以及它们之间的切换进行了分析，使用了基于Lyapunov方法的控制策略来解决节点约束球杆系统的平衡问题。通过理论分析和实验，证明了提出的闭环系统控制策略完全收敛于预期的平衡状态，给出了相应的仿真结果。

关键词: 节点约束, 平衡控制策略, 能量控制, 球杆系统