Semi-active vibration control via a magnetorheological damper and active disturbance rejection control

This work provides an alternative for the semi-active vibration control problem via state feedback plus an active disturbance rejection control (K-ADRC) for a multistory building structure equipped with one magnetorheological damper (MRD) located between the ground and the first story. This control law introduces a disturbance observer (DOB) to estimate the total disturbance in real time, produced by the earthquake perturbation, unmodeled dynamics, and parametric uncertainties, and then cancel their effect using a part of the control signal. Moreover, using a diffeomorphism, the K-ADRC provides a proportional derivative (PD) controller designed to improve internal stability. A prominent feature of the active disturbance rejection control (ADRC) algorithm is that the value of the DOB gain is selected according to the system bandwidth. The stability of the system is verified via Lyapunov analysis. Moreover, the building structure model and the MRD are accomplished by incorporating a nonlinearity state that represents the hysteresis effect to perform real behavior in addition to assuming that acceleration is the only available measurement of building structures. Thus, integral filters are provided based on the appropriate cut-off frequency to estimate displacement and velocity, avoiding bias, offset, and phase shifts. Experimental results from a reduced-scale two-story building prototype demonstrate that the proposed K-ADRC is promising for real applications, and it has better performance than the state feedback (K) and the linear quadratic regulator (LQR) control techniques.