Stability optimization of time-delay systems with zero-location constraints applied to non-collocated vibration suppression

• Published in: Mechanical systems and signal processing Vol. 208; p. 110886
• Main Authors: Saldanha, Adrian, Michiels, Wim, Kuře, Matěj, Bušek, Jaroslav, Vyhlídal, Tomáš
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15-02-2024
• Subjects: Spectral optimization; Time-delay systems; Vibration suppression; Zeros placement; Time-delay systems; Vibration suppression; Spectral optimization; Zeros placement
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2023.110886

We present an active control method for achieving non-collocated vibration absorption, implemented on a lumped mass system. The task of suppressing vibrations at a number of frequencies, at a target mass is recast into a problem of assigning zeros of the transfer function from the external excitation force to the position of the target mass. The controller design involves computing the controller parameters by utilizing the available output feedback to directly assign a set of zeros on the imaginary axis while simultaneously preserving the overall stability with a sufficient margin. The design also takes into account delays in the feedback path. The presence of delays leads to an infinite dimensional system for which, there exists in general, infinitely many characteristic roots. The requirement of achieving sufficient damping in the resulting closed-loop system together with suppressing vibrations of the desired frequency leads to a constrained optimization problem of minimizing the spectral abscissa function subject to zero-location constraints. These constraints exhibit polynomial dependence on the controller parameters. We present two approaches for controller parameterization for the single and multiple input case. Both approaches are based on constraint elimination and exploit the property that the constraints are affine in a selection of the gain parameters. Finally, the methodology is verified by simulating on a spring–mass–damper system following which, it is then validated experimentally on a laboratory setup.