Effect of a frequency adaptive control system on the modal control spillover of structures

Control strategies envisioned for the suppression of vibration of a structural system often cause adverse effects such as a control spillover. In this study, a systematic investigation was carried out on the modal control spillover based on a linear frequency adaptive control algorithm, designed in the independent modal space of a multi-degree-of-freedom structural system. A generalized closed form expression of the system transfer function and the optimal modal control force has been developed by separating the control and the spillover effects of a control force applied to a particular mode of the system. In addition, a linear quadratic Gaussian control algorithm has been considered in the study for comparison. Based on the formulation, a theoretical assessment has been developed showing the nature of the control spillover from different modes to a particular mode of the system considering both the algorithms. The comparative assessment has been extended through a numerical study on a ten-story shear frame structure subjected to thirty ground excitations by assuming a single actuator location. The effect of control spillover was also studied considering an attached component tuned to a particular mode of the system. It was observed from the study that the frequency adaptive control algorithm due to its appropriate control distribution over the frequency ranges, significantly reduces the control spillover and provides the desired responses as compared to the uncontrolled structure. The adopted control was found to be robust since it performed efficiently at a system perturbation. The comparative assessment revealed that the linear quadratic Gaussian control provided amplification of the structural responses, particularly sensitive to the spillover, while compared to the uncontrolled structural system.