Development of a New Inertial-based Vibration Absorber for the Active Vibration Control of Flexible Structures

In this paper, a new actively controlled inertialbased vibration absorber is proposed and used for controlling the mechanical deformations of flexible structures. To this end, a method for reducing the externally induced vibrations of structural systems is developed. The method employed in this paper is based on the numerical techniques of the applied system identification field and is grounded in the optimal control theory. A three-story shear building system with a pendulum hinged on the third floor is the flexible structure considered as the case study of this investigation. This mechanical system is constructed using rigid and flexible components in order to reproduce a simple three-dimensional structure. The base of the structural system is excited by a harmonic excitation combined with a noise excitation source in order to simulate the earthquake. By doing so, the worst case scenario in which the frequencies of the external excitation are close to the natural frequencies of the flexible structure is considered. The pendulum mounted on the third floor of the flexible structure serves as an actively controlled inertialbased vibration absorber. The control torque applied to the pendulum is actively controlled by using a brushless motor driven by a programmable digital controller. Therefore, the inertial effects of the oscillating pendulum directly contrast the externally induced vibrations of the three-story shear building system. The feedback control torque applied on the pendulum is obtained by monitoring the accelerations of the three floors of the flexible structure and is designed employing a realistic mechanical model of the dynamical system obtained by using a time-domain system identification approach. The numerical results found in this investigation by using a simple computer program coded in MATLAB show that the modal parameters identified for describing the dynamic behavior of the flexible structure are consistent with those predicted employing a simple lumped parameter model. Furthermore, in this investigation, an optimal closed-loop controller based on the Linear-Quadratic Regulator (LQR) method and an optimal state observer based on the Kalman filtering approach, also known as Linear-Quadratic Estimator (LQE), are designed employing the state-space model obtained from experimental data. Experimental results demonstrate that a considerable reduction of the structural vibrations of the three-story shear building system can be obtained by means of the introduction of the feedback controller combined with the state estimator.