A New Varying-Gain-Exponent-Based Differentiator/Observer: An Efficient Balance between Linear and Sliding-Mode Algorithms

It is well known that the supertwisting algorithm is robust to matched perturbation but is sensitive to measurement noise. Contrary to this, the classical linear algorithm is less sensitive to measurement noise but less robust to perturbation. To combine both the good accuracy of the supertwisting algorithm with respect to perturbation and the good performance of the linear algorithm with respect to measurement noise, this article proposes a new differentiator/observer with a varying exponent gain α whose variation depends on the magnitude of measurement noise (high-frequency signal). When the magnitude of measurement noise increases (respectively, decreases) α tends to 1 (respectively, tends to 0.5) and the proposed differentiator/observer behaves as a linear algorithm (respectively, as a supertwisting algorithm). Thus, by one parameter α, the differentiator/observer can take care of high-frequency noise and matched perturbations. A complete stability analysis of the proposed differentiator/observer is provided. To highlight the applicability of the proposed methodology, the dedicated differentiator/observer is, respectively, validated on the electropneumatic actuator and electric machine test benches. These experimental results are compared to those of linear and supertwisting algorithms.