Time-delay based output feedback control of fourth-order oscillatory systems

TL;DR

This paper introduces a simple, robust time-delay output feedback control method for fourth-order oscillatory systems, effectively canceling resonance peaks and stabilizing systems with non-collocated sensing, demonstrated through experiments.

Contribution

A novel control approach using only oscillation frequency knowledge, avoiding derivatives and complex transfer functions, enhancing practical robustness for fourth-order systems.

Findings

Effectively cancels resonance peaks in fourth-order oscillatory systems.

Stabilizes inherently unstable PI feedback in non-collocated output scenarios.

Validated through experiments on a two-mass oscillator with uncertainties.

Abstract

We consider a robust stabilization of the fourth-order oscillatory systems with non-collocated output sensing. Worth recalling is that the fourth-order systems are relatively common in mechatronics as soon as there are two-mass or more generally two-inertia dynamics with significant elasticities in the link. A novel yet simple control method is introduced based on the time-delayed output feedback. The delayed output feedback requires only the oscillation frequency to be known and allows for a robust control design that leads to cancelation of the resonance peak. We use the stability margins to justify the transfer characteristics and robustness of the time-delay control in frequency domain. The main advantage of the proposed method over the other possible lead-based loop-shaping strategies is that neither time derivatives of the noisy output nor the implementation of transfer functions with a numerator degree greater than zero are required to deploy the controller. This comes in favor of practical applications. An otherwise inherently instable proportional-integral (PI) feedback of the non-collocated output is shown to be stabilized by the proposed method. The control developed and associated analysis are also confirmed by the experimental results shown for the low damped two-mass oscillator system with uncertainties.