The proxy-based sliding mode control (PSMC) is a previously-proposed controller for the position control of robotic manipulators. It is an alternative approximation of a simple sliding mode control (SMC) of which the set-valuedness is relaxed in a particular differential-algebraic manner, and has been found useful for many applications especially in robotics. This paper presents the results of frequency-domain analysis and simulations to clarify the mathematical nature of PSMC subjected to measurement noise and disturbance. The results show that, in the presence of measurement noise and disturbance, the sliding motion realized by PSMC is closer to that of the ideal SMC than those of conventional implementations of SMC with the boundary-layer approximation and low-pass filtering. Comparisons in terms of the chattering intensity and the sliding motion accuracy are also presented. Moreover, it is shown that PSMC’s response to disturbance in the sliding motion is quite different from that of the conventional implementations.

基于代理的滑模控制（PSMC）是先前提出的用于机械手位置控制的控制器。它是简单滑模控制（SMC）的一种替代近似方法，其设定值以特定的微分代数方式被放宽，并且已发现对许多应用特别是机器人技术有用。本文介绍了频域分析和仿真的结果，以阐明受到测量噪声和干扰的PSMC的数学性质。结果表明，在存在测量噪声和干扰的情况下，与边界层近似和低通滤波的传统SMC实现相比，PSMC实现的滑动更接近理想SMC。还给出了颤动强度和滑动运动精度方面的比较。而且，表明PSMC对滑动运动的干扰的响应与传统实现方式有很大不同。