论文标题

二阶运动系统的最佳终端滑动模式控制

Optimal terminal sliding-mode control for second-order motion systems

论文作者

Ruderman, Michael

论文摘要

终端滑动模式(TSM)控制算法及其非斑点细化已被详细阐述了二十年,从那时起,属于更广泛的有限时间控制器,已知对匹配的扰动非常可靠。尽管TSM歧管允许不同形式的滑动变量,这些变量满足了可测量的输出状态的$ Q/p $功率比,但我们证明$ Q/p = 0.5 $是纽顿二阶运动动力学的最佳选择。本文分析了时间优势的滑动表面,并基于二阶运动系统的最佳TSM控制。强调的是,最佳的TSM控件完全与Fuller的最佳切换问题完全内联,该问题可以最大程度地减少沉降时间,即使用对不受干扰的双整合器的时间优势控制。还表明,对于给定的植物特征,即总体惯性和控制结合,不需要其他控制参数。单个表面设计参数可能(但不一定需要)用于在扭曲模式的边界层上驾驶系统,或者将其迫使其进入可靠的端子滑动模式。对TSM的有限时间收敛和鲁棒性对有限的扰动的有限时间收敛。证明了具有不同上限扰动的数值示例。

Terminal sliding mode (TSM) control algorithm and its non-singular refinement have been elaborated for two decades and belong, since then, to a broader class of the finite-time controllers, which are known to be robust against the matched perturbations. While TSM manifold allows for different forms of the sliding variable, which are satisfying the $q/p$ power ratio of the measurable output state, we demonstrate that $q/p=0.5$ is the optimal one for the second-order Newton's motion dynamics with a bounded control action. The paper analyzes the time-optimal sliding surface and, based thereupon, claims the optimal TSM control for the second-order motion systems. It is stressed that the optimal TSM control is fully inline with the Fuller's problem of optimal switching which minimizes the settling time, i.e. with time-optimal control of an unperturbed double-integrator. Is is also shown that for the given plant characteristics, i.e. the overall inertia and control bound, there is no need for additional control parameters. The single surface design parameter might (but not necessarily need to) be used for driving system on the boundary layer of the twisting mode, or for forcing it to the robust terminal sliding mode. Additional insight is given into the finite-time convergence of TSM and robustness against the bounded perturbations. Numerical examples with different upper-bounded perturbations are demonstrated.

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