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基于虚拟完整约束的欠驱动起重机控制方法

赵晨 戈新生

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. doi: 10.21656/1000-0887.390163
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. doi: 10.21656/1000-0887.390163
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. doi: 10.21656/1000-0887.390163

基于虚拟完整约束的欠驱动起重机控制方法

doi: 10.21656/1000-0887.390163
基金项目: 国家自然科学基金(11472058;11732005)
详细信息
    作者简介:

    赵晨(1992—),男,硕士生(E-mail: 18811122609@163.com);戈新生(1957—),男,教授,博士(通讯作者. E-mail: gebim@vip.sina.com).

  • 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.
  • [1] MILLER S, MOLINO J A, KENNEDY J, et al. Segway rider behavior: speed and clearance distance in passing sidewalk objects[J]. Transportation Research Record,2008,2073: 125-132.
    [2] DRAZ M U, ALI M S, MAJEED M, et al. Segway electric vehicle: human transporter[C]// On Robotics and Artificial Intelligence, 〖STBX〗2012 International Conference.Pakistan, 2012.
    [3] CHWA D. Nonlinear tracking control of underactuate ships based on a unified kinematic and dynamic model[C]//2007 Mediterranean Conference on Control and Automation.Athens, Greece, 2017.
    [4] 高丙团, 黄学良. 欠驱动2DTORA基于部分反馈线性化的非线性控制设计[J]. 东南大学学报(自然科学版), 2011,41(2): 321-325.(GAO Bingtuan, HUANG Xueliang. Nonlinear control design of underactuated 2DTORA based on partial feedback linearization[J]. Journal of Southeast University(Natural Science Edition),2011,41(2): 321-325.(in Chinese))
    [5] BO L. Approximate linearization of a class of underactuated system and its application in the ball and beam system[J]. International Journal of Control and Automation,2015,8(12): 119-130.
    [6] GRIZZLE J W, ABBA G, PLESTAN F. Asymptotically stable walking for biped robots: analysis via systems with impulse effects[J]. IEEE Transactions on Automatic Control,2001,46(1): 51-64.
    [7] CANUDAS DE WIT C, ESPIAU B, URREA C. Orbital stabilization of underactuated mechanical systems[C]//15th IFAC World Congress. Barcelona, Spain, 2002.
    [8] SHIRIAEV A, PERRAM J W, CANUDAS DE WIT C. Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach[J].IEEE Transactions on Automatic Control,2005,50(8): 1164-1176.
    [9] SHIRIAEV A, ROBERTSSON A, PERRAM J, et al. Periodic motion planning for virtually constrained(hybrid) mechanical system[C]//Proceedings of the 〖STBX〗44th IEEE Conference on Decision and Control and the 〖STBX〗2005 European Control Conference. Seville, Spain, 2005.
    [10] SHIRIAEV A S, FREIDOVICH L B, ROBERTSSON A, et al. Virtual-holonomic-constraints-based design of stable oscillations of Furuta pendulum: theory and experiments[J].IEEE Transactions On Robotics,2007,23(4): 827-832.
    [11] FREIDOVICH L, ROBERTSSON A, SHIRIAEV A, et al. Periodic motions of the pendubot via virtual holonomic constraints: theory and experiments[J]. Automatica,2008,44(3): 785-791.
    [12] CONSOLINI L, MAGGIORE M. Virtual holonomic constraints for Euler-Lagrange systems[C]//8th IFAC Symposium on Nonlinear Control Systems.Bologna, Italy, 2010.
    [13] CONSOLINI L, MAGGIORE M. Control of a bicycle using virtual holonomic constraints[J]. Automatica,2014,49(9): 2831-2839.
    [14] CELLINA A. The validity of the Euler-Lagrange equation for solutions to variational problems[J]. Journal of Fixed Point Theory & Applications,2014,15(2): 577-586.
    [15] PERRAMJ W, SHIRIAEV A, CANUDAS DE WIT C, et al. Explicit formula for a general integral of motion for a class of mechanical systems subject to holonomic constraint[J]. IFAC Proceedings Volumes,2003,36(2): 87-92.
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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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