State-Derivative Feedback Control of Cable Vibration Using Semiactive Magnetorheological Dampers

Abstract:  This article presents the theoretical and in situ experimental studies on state-derivative feedback control of bridge cable vibration using semiactive magnetorheological (MR) dampers. The semiactive feedback control is accomplished using only one MR damper and one accelerometer collocated near the lower end of the cable. Within the framework of reciprocal state space (RSS), the linear quadratic regulator (LQR) control technique is applied to formulate state-derivative feedback control law and derive the feedback and estimator gains for real-time control of cable vibration using MR dampers. The state-derivative feedback control strategy directly uses acceleration information for feedback and state estimation, which is usually the only measure available in practical cable vibration control implementation. More importantly, the control force commanded by the state-derivative feedback control strategy based on energy weighting is a dissipative force except for low velocity and small force, which is therefore implementable by the semiactive MR dampers without clipping. Numerical simulations of state-derivative feedback control for a stay cable in the cable-stayed Dongting Lake Bridge are conducted under sweeping sine excitation and sinusoidal step relaxation excitation, and then the experimental validation of the prototype cable is carried out in the bridge site with the help of the real-time control system dSPACE. Good agreement between the simulation and experimental results is observed.