The effect of an adaptive feedback-control system in the structural vibration control

In this work, a novel frequency adaptive optimal control algorithm has been developed that aims to provide the desired response of the structural system with an ideal control effort, appropriate to every excitation frequency range. To achieve this objective, one part of the control gain has been developed to provide frequency response characteristics similar to the structural system. The modified system under the proposed control is verified for stability and the optimal gain constants are obtained by minimizing the H2 norm of the structural output. A thorough investigation of the system shows that the algorithm, at a certain excitation frequency, influences the appropriate dynamic properties of the system, sensitive in that region. This behavior is found to persist in case of a perturbation in the structural system. Next, a theoretical assessment of the proposed control is conducted considering an existing and popular linear- quadratic Gaussian (LQG) control algorithm. The comparative assessment is extended through a numerical illustration considering a simple structural system exposed to earthquake excitations of a varying range of frequencies. A huge reduction in the control force is observed for the proposed control as compared to the LQG control for the same response characteristics of the structure and the efficiency is retained in the case of a perturbation in the initial structural system.