## 留言板

 引用本文: 赵晨, 戈新生. 基于虚拟完整约束的欠驱动起重机控制方法[J]. 应用数学和力学, 2019, 40(3): 302-310.
ZHAO Chen, GE Xinsheng. A Control Method for Underactuated Cranes Based on Virtual Holonomic Constraints[J]. Applied Mathematics and Mechanics, 2019, 40(3): 302-310. doi: 10.21656/1000-0887.390163
 Citation: ZHAO Chen, GE Xinsheng. A Control Method for Underactuated Cranes Based on Virtual Holonomic Constraints[J]. Applied Mathematics and Mechanics, 2019, 40(3): 302-310.

• 中图分类号: TP273

## A Control Method for Underactuated Cranes Based on Virtual Holonomic Constraints

Funds: The National Natural Science Foundation of China（11472058；11732005）
• 摘要: 欠驱动系统的控制是非线性控制的一个重要领域，欠驱动系统指系统控制输入个数小于自由度个数的非线性系统.目前，欠驱动非线性系统动力学和控制研究的主要方法包括线性二次型最优控制方法和部分反馈线性化方法等，如何使系统持续的稳定在平衡位置一直是研究的难点.虚拟约束方法是指通过选择一个周期循环变化的变量作为自变量来设计系统的周期运动.该文以典型的欠驱动模型起重机为例，采用虚拟约束方法，使系统能够在平衡位置稳定或周期振荡运动.首先，通过建立虚拟约束，减少系统自由度变量；然后，通过部分反馈线性化理论推导出系统的状态方程；最后，通过线性二次调节器设计反馈控制器.仿真结果表明，重物在反馈控制下可以在竖直位置的附近达到稳定状态，反映了虚拟约束方法对欠驱动系统的有效性.
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##### 出版历程
• 收稿日期:  2018-06-14
• 修回日期:  2018-08-17
• 刊出日期:  2019-03-01

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