The effect of time delay on control stability of an electromagnetic active tuned mass damper for vibration control

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Abstract
The aim of this paper is to investigate the effect of time delays on the stability of a zero-placement position and velocity feedback law for a vibratory system comprising harmonic excitation equipped with an electromagnetic active tuned mass damper (ATMD). The purpose of the active control is broadening the vibration attenuation envelope of a primary mass to a higher frequency region identified as from 50±0.5Hz with a passive tuned mass damper (TMD) to a wider range of 50±5Hz with an ATMD. Stability conditions of the closed-loop system are determined by studying the position of the system closed-loop poles after the introduction of time delays for different excitation frequencies. A computer simulation of the model predicted that the proposed control system is subject to instability after a critical time delay margin dependent upon the frequency of excitation and the finding were experimentally validated. Three solutions are derived and experimentally tested for minimising the effect of time delays on the stability of the control system. The first solution is associated with the introduction of more damping in the absorber system. The second incorporates using a time-delayed ATMD by tuning its original natural resonant frequency to beyond the nominal operational frequency range of the composite system. The third involves an online gain tuning of filter coefficients in a dual arrangement of low-pass and high-pass filters to eliminate the effect time delays by manipulating the signal phase shifts.

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