Model-based resonance tracking of linear systems

TL;DR

This paper introduces recursive, model-based algorithms for real-time resonance frequency tracking in linear systems, overcoming limitations of phase-based methods by using a complex-valued system representation.

Contribution

It presents a novel transformation into complex space enabling more robust resonance tracking algorithms that handle complex scenarios like MIMO systems and nonmonotonic phase differences.

Findings

Algorithms successfully track resonance shifts in simulations

Proposed method outperforms phase-based approaches in challenging cases

Stability of the scheme is theoretically supported

Abstract

The present paper develops recursive algorithms to track shifts in the resonance frequency of linear systems in real time. To date, automatic resonance tracking has been limited to non-model-based approaches, which rely solely on the phase difference between a specific input and output of the system. Instead, we propose a transformation of the system into a complex-valued representation, which allows us to abstract the resonance shifts as an exogenous disturbance acting on the excitation frequency, perturbing the excitation frequency from the natural frequency of the plant. We then discuss the resonance tracking task in two parts: recursively identifying the frequency disturbance and incorporating an update of the excitation frequency in the algorithm. The complex representation of the system simplifies the design of resonance tracking algorithms due to the applicability of well-established techniques. We discuss the stability of the proposed scheme, even in cases that seriously challenge current phase-based approaches, such as nonmonotonic phase differences and multiple-input multiple-output systems. Numerical simulations further demonstrate the performance of the proposed resonance tracking scheme.