Sliding motion accuracy of proxy-based sliding mode control subjected to measurement noise and disturbance

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.