基于继电器的库仑摩擦反馈补偿分析
Analysis of relay-based feedback compensation of Coulomb friction
摘要：
将具有库仑摩擦的单自由度机械系统的标准问题修正为基于继电器的反馈镇定。如文献[1]所示，具有库仑摩擦的系统通过基于继电器的输出反馈是渐近稳定的。假设库仑摩擦扰动为上界，通过最小化文献[2]中提出的扭转算法的李雅普诺夫函数的导数，得到了基于继电器的反馈控制的时间最优增益。此外，从不连续的库仑摩擦改变到一个更物理的不连续性，这意味着一个瞬态presliding阶段在运动反转，我们分析了剩余的稳态振荡。这是在稳定的极限环的意义上，除了由致动器动态引起的抖动。数值例子和实验案例研究伴随所提供的分析。
英文摘要：
Standard problem of one-degree-of-freedom mechanical systems with Coulomb friction is revised for a relay-based feedback stabilization. It is recalled that such a system with Coulomb friction is asymptotically stabilizable via a relay-based output feedback, as formerly shown in [1]. Assuming an upper bounded Coulomb friction disturbance, a time-optimal gain of the relay-based feedback control is found by minimizing the derivative of the Lyapunov function proposed in [2] for the twisting algorithm. Furthermore, changing from the discontinuous Coulomb friction to a more physical discontinuity-free one, which implies a transient presliding phase at motion reversals, we analyze the residual steady-state oscillations. This is in the sense of stable limit cycles, in addition to chattering caused by the actuator dynamics. The numerical examples and an experimental case study accompany the provided analysis.
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