Anti-Noise and Anti-Disturbance Properties of Differential-Algebraic Relaxation Applied to a Set-Valued Controller

This paper presents illustrative analytical and numerical results regarding the noise and disturbance response characteristics of a proxy-based sliding mode control (PSMC), which is a position controller for robot manipulators proposed a decade ago. The PSMC can be viewed as a simple sliding mode controller of which the set-valuedness is relaxed in a particular differential-algebraic way. This paper compares this “differential-algebraic relaxation” scheme with conventional managements of the set-valuedness, specifically, the use of boundary layers and low-pass filters. Results of frequency-domain analysis and simulations illustrate that PSMC realizes better noise rejection capability than conventional approaches and that its disturbance response characteristics are quite different from those of conventional ones.