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arXiv · 2603.27615

Adaptive differentiating filter: case study of PID feedback control

Alexey Pavlov·Michael Ruderman
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Abstract

This paper presents an adaptive causal discrete-time filter for derivative estimation, exemplified by its use in estimating relative velocity in a mechatronic application. The filter is based on a constrained least squares estimator with window adaptation. It demonstrates low sensitivity to low-amplitude measurement noise, while preserving a wide bandwidth for large-amplitude changes in the process signal. Favorable performance properties of the filter are discussed and demonstrated in a practical case study of PID feedback controller and compared experimentally to a standard linear low-pass filter-based differentiator and a robust sliding-mode based homogeneous differentiator.

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Alexey Pavlov, Michael Ruderman. 2026-03-29. Adaptive differentiating filter: case study of PID feedback control. https://arxiv.org/abs/2603.27615

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