| 基于虚拟完整约束的欠驱动起重机控制方法 |
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| 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. |
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| 作者姓名： | 赵晨 戈新生 |
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| 作者单位： | 1北京信息科技大学 自动化学院, 北京 100192;2北京信息科技大学 机电工程学院, 北京 100192 |
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| 基金项目： | 国家自然科学基金（11472058；11732005） |
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| 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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| 关 键 词： | 欠驱动 虚拟约束 部分反馈线性化 |
| 收稿时间： | 2018-06-14 |
A Control Method for Underactuated Cranes Based on Virtual Holonomic Constraints |
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| Affiliation: | 1School of Automation, Beijing Information Science and Technology University, Beijing 100192, P.R.China;2School of Mechanical and Electrical Engineering, Beijing Information Science and Technology University, Beijing 100192, P.R.China |
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| Abstract: | The control of underactuated systems was an important field of nonlinear control. The underactuated system refers to a nonlinear system with an input control variable number less than the degree of freedom number. At present, the main methods of dynamics and control research of underactuated nonlinear systems include the linear quadratic form optimal control method and the partial feedback linearization method, and how to make the system stabilize in the equilibrium position is always a difficult point. For the virtual constraint method, the periodic motion of the system is designed with a selected cyclic independent variable. Based on the typical underactuated model crane, the virtual constraint method was adopted to make the system stabilize or oscillate in equilibrium position. First, through establishment of the virtual constraints, the system’s degrees of freedom were reduced. Then, the system state equations were derived according to the partial feedback linearization theory. Finally, the feedback controller was designed with the linear quadratic form regulator. The simulation results show that, the weight can reach a stable state near the vertical position under the feedback control, which reflects the effectiveness of the virtual constraint method for underactuated systems. |
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