引用本文:梅珂琪,马莉,丁世宏,刘陆.滑动变量受限情况下的二阶滑模控制设计[J].控制理论与应用,2018,35(3):414~420.[点击复制]
MEI Ke-qi,MA Li,DING Shi-hong,LIU Lu.Second-order sliding mode control design subject to sliding variable constraints[J].Control Theory and Technology,2018,35(3):414~420.[点击复制]
滑动变量受限情况下的二阶滑模控制设计
Second-order sliding mode control design subject to sliding variable constraints
摘要点击 2303  全文点击 1244  投稿时间：2017-04-06  修订日期：2017-10-24
查看全文  查看/发表评论  下载PDF阅读器
DOI编号  10.7641/CTA.2017.70232
  2018,35(3):414-420
中文关键词  二阶滑模  有限时间稳定性  加幂积分  状态受限
英文关键词  second-order sliding mode  finite-time stability  adding a power integrator  state constraints
基金项目  国家自然科学基金项目(61573170, 31571571), 江苏高校优势学科建设工程项目和江苏省“六大人才高峰”项目(XNYQC–006) 资助.
作者单位E-mail
梅珂琪 江苏大学  
马莉* 江苏大学 mali@mail.ujs.edu.cn 
丁世宏 江苏大学  
刘陆 江苏大学  
中文摘要
      在实际系统中状态受限普遍存在, 因此考虑状态受限下的控制设计问题具有重要的理论意义和工程价值. 本文考虑了滑动变量受限情况下的二阶滑模控制设计问题. 首先, 在不考虑滑动变量受限的情况下, 基于Lyapunov 方法, 给出了一种新的二阶滑模控制器构造方法, 并严格证明了在该控制器的作用下滑动变量将在有限时间内稳定 到平衡点. 其次, 考虑滑动变量受限情况, 证明了在受限区域内存在一个与控制参数相关的吸引域, 使得当初始状 态在该吸引域内时其相轨迹不会逃离它. 最后, 状态受限情况下倒立摆系统的控制设计验证了该算法的有效性.
英文摘要
      In real system, the state constraints are ubiquitous. Thus it is of great theoretical and engineering significance to consider the control design problem under state constraints. In this paper, the problem of second-order sliding mode (SOSM) controller design under sliding variable constraints is considered. Firstly, by using the Lyapunov method, a kind of new SOSM controller is presented without considering the sliding variable constraints. It is proved that the sliding variable will be stabilized to the equilibrium point in a finite time under the designed SOSM controller. Secondly, considering the case that the sliding variable is restricted to be in a preset region, it is also proved that there is a domain of attraction associated with the control parameters in the restricted region so that its phase trajectory will not escape from the attractive domain when the initial states are within it. Finally, the control of the inverted pendulum under state constraints is given to demonstrate the effectiveness of the proposed algorithm.