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单级倒立摆迭代非线性滑模变结构位移控制

卜仁祥，刘正江，李铁山   

  1. 大连海事大学 航海学院，辽宁 大连 116026
  • 收稿日期:2006-04-20 修回日期:2006-11-07 出版日期:2007-05-31 发布日期:2007-05-31

Iterative Nonlinear Sliding Mode Control for Single Inverted Pendulum’s Position Tracking

BU Ren-xiang, LIU Zheng-jiang, LI Tie-shan   

  1. Navigation College, Dalian Maritime University, Dalian 116026, China
  • Received:2006-04-20 Revised:2006-11-07 Online:2007-05-31 Published:2007-05-31

摘要： 针对倒立摆的位移控制，提出一种非线性滑模变结构控制方法。通过对系统输出递归分解迭代设计，构成了扩展状态空间上的复杂非线性滑模，并结合增量反馈控制，无需对系统不确定性的估计，可以稳定摆的倒立并将小车驱动到任意的距离。非线性滑模分解迭代方法结构简单，容易实现，设计过程物理意义明显，利于参数整定保证控制系统稳定性以及分析输出特性。仿真结果表明，小车位移稳定时间、最大移动速度以及位移过程中摆角最大幅度均可通过设计参数调节，且控制器对倒立摆系统参数变化不敏感、具有强鲁棒性和良好的控制品质。

关键词: 单级倒立摆, 位移控制, 非线性滑模, 变结构控制

Abstract: A nonlinear sliding mode control method is presented for single inverted pendulum position tracking control. The nonlinear sliding mode is designed in the augmented states space using a decentralized and iterative procedure based on system output feedback. An increment feedback control law is then developed and proved to balance the pendulum-angle and drive the cart to track an arbitrary position without estimating the parameter uncertainties. Due to its simple structure and clear parametric functions, the controller is easy to be designed and adjusted for different control objectives. Numerical simulation results verify that the controller is robust to the systematic variations and both of the pendulum-angle and the cart velocity can be easily adjusted by parameters tuning in cart-position tracking.

Key words: single inverted pendulum, position tracking control, nonlinear sliding mode, variable structure control