Study on second-order sliding mode control law for affine nonlinear system
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摘要: 分析现有滑模控制算法特别是二阶滑模控制算法在抑制抖动和鲁棒性等方面所存在的问题,以仿射非线性系统为对象,针对近似时间最优的二阶滑模控制律收敛速度慢和抖振较大的问题,提出改进控制算法,通过设计适当的约束条件和修正滑模趋近加速度,提高了二阶滑模的响应速度,并在不损失鲁棒性的前提下削弱了抖振的频率和幅度.以单摆模型为例,分别对该算法和二阶Lyapunov函数法以及一阶指数趋近法进行仿真研究,仿真结果表明该算法适用于具有不确定性的非线性系统,并在削抖和快速响应方面具有相对优势.Abstract: The chattering and robustness issues of the existing sliding mode control especially second-order sliding mode (SOSM) control algorithms were analyzed. Aiming at the problems of slower convergence and stronger chattering in the nearly time-optimal SOSM control law, an improved control method was developed for the affine nonlinear systems through redesigning restrictive conditions and modifying reaching acceleration of sliding mode, which can effectively enhance responding speed of second-order sliding mode, as well as reduce the frequency and amplitude of chattering without losing the robustness of system. Taking a pendulum model as example, the simulation studies on the proposed algorithm were carried out, simultaneously comparing with the first-order exponential reaching law and the Lyapunov function-based SOSM control law. The simulative results demonstrate that the improved nearly time-optimal SOSM control law is appropriate for the uncertain nonlinear systems, and has the relative advantages on the aspects of chattering reduction and rapid response.
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Key words:
- nonlinear systems /
- sliding mode control /
- time-optimal /
- robustness
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