For a point mass subject to Coulomb friction in feedback with a PID controller, we consider a model based on a differential inclusion comprising all the possible magnitudes of static friction during the stick phase and having unique solutions. We study the set of all equilibria and we establish its global asymptotic stability using a discontinuous Lyapunov-like function, and a suitable LaSalle's invariance principle. The well-posedness of the proposed model allows to establish useful robustness results, including an ISS property from a suitable input in a perturbed context. Simulation results are also given to illustrate our statements.

中文翻译：

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具有库仑摩擦的 PID 控制系统的全局渐近稳定性


对于受 PID 控制器反馈的库仑摩擦影响的点质量，我们考虑基于微分包含的模型，该模型包含粘滞阶段期间所有可能的静摩擦大小并具有唯一的解决方案。我们研究所有平衡点的集合，并使用不连续的李雅普诺夫函数和合适的拉萨尔不变原理建立其全局渐近稳定性。所提出模型的适定性允许建立有用的鲁棒性结果，包括来自扰动环境中合适输入的 ISS 属性。还给出了模拟结果来说明我们的陈述。