引用本文:董领逊,窦丽华,陈杰,夏元清.含间隙机械系统的混杂模型预测控制器[J].控制理论与应用,2009,26(12):1378~1382.[点击复制]
DONG Ling-xun,DOU Li-hua,CHEN Jie,XIA Yuan-qing.Hybrid model-predictive-control for mechanical system with backlash[J].Control Theory and Technology,2009,26(12):1378~1382.[点击复制]
含间隙机械系统的混杂模型预测控制器
Hybrid model-predictive-control for mechanical system with backlash
摘要点击 2434  全文点击 1375  投稿时间：2008-04-23  修订日期：2009-03-05
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DOI编号  10.7641/j.issn.1000-8152.2009.12.CCTA080369
  2009,26(12):1378-1382
中文关键词  混杂模型预测控制  间隙模式  PWA模型  动态规划
英文关键词  hybrid model predictive control  backlash mode  PWA model  dynamic programming
基金项目  北京市教育委员会共建基金资助项目(XK100070532).
作者单位E-mail
董领逊* 北京理工大学 信息科学技术学院 donglx@bit.edu.cn 
窦丽华 北京理工大学 信息科学技术学院  
陈杰 北京理工大学 信息科学技术学院  
夏元清 北京理工大学 信息科学技术学院  
中文摘要
      研究含间隙机械系统的混杂模型预测控制问题. 首先, 将含间隙机械系统的运行模式分为“间隙模式”和“接触模式”. 其次, 建立了含间隙机械系统的混杂分段仿射(PWA)模型. 然后, 利用模型预测控制(MPC)的方法对约束PWA系统的最优控制进行求解, 通过动态规划与多参数二次规划方法, 得到了MPC的离线解. 最后, 通过将分段二次(PWQ)Lyapunov函数的求解转换成半正定规划, 找到了确保闭环控制稳定性的PWQ Lyapunov函数. 跟踪参考速度的实验结果表明, 混杂模型预测控制器对含间隙机械系统的跟踪控制具有较好的效果, 能够满足小采样时间系统的实时控制要求.
英文摘要
      The hybrid model-predictive-control for mechanical system with backlash is studied. The operation model of a mechanical system with backlash is distinguished into the “backlash mode”and the “contact mode”, and a piecewise affine(PWA) model of the mechanical system with backlash is built. For controlling this constrained PWA system, the optimal control law is derived by using the model predictive control(MPC) method; the offline solution of which is obtained by using the dynamic programming and the multi-parametric quadratic programming method. Finally, a piecewise quadratic(PWQ) Lyapuno function for the stability of the closed-loop system is found by transforming its searching process to a semi-definite programming. Experiments in tracking a reference speed signal demonstrate that the hybrid MPC gives desirable performances for the mechanical system with backlash, satisfying the real-time control requirements for systems with small sampling time.