Identification and Control of an MR Damper With Stiction Effect and its Application in Structural Vibration Mitigation

This paper presents the parameter identification and control of a magnetorheological (MR) damper with stiction effect and its application to seismic protection of a model two-story structure. This semi-active device is utilized to reduce the vibration of the model structure in response to earthquake excitations. First, modified Bingham and LuGre models which consider the stiction effect and the velocity-dependent nature of the damper force are proposed. The parameters of the models are identified by solving a nonlinear optimization problem. The Bingham model is considered because of its simple structure to be used in linear parameter varying (LPV) design framework. The parameter identification is performed while the MR damper is attached to the structure. These models are verified experimentally for different operating conditions showing an acceptable level of accuracy. The subsequent part of the paper addresses the design of different types of controllers to command the MR damper to suppress the structural vibrations of a model building due to earthquake excitations. Two types of controllers are considered in this study: 1) an
$H_{\infty }$
inverse control based on the mixed-sensitivity design and 2) a dynamic output-feedback LPV controller. In the former one, an
$H_{\infty }$
controller is designed for the linear structure and the modified LuGre-based inverse model is used to determine the required voltage from the commanded force. The LPV controller is designed for the combined structure and MR damper based on the modified Bingham model considering the damper velocity as the scheduling parameter. Both controllers are combined with a classical anti-windup scheme to compensate the effect of the saturation on the control voltage. An optimal passive damping design is also obtained for comparison purposes. The performance of the controllers is compared with the passive damping case and clipped-optimal controller for the El Centro and Northridge earthquake inputs with different intensities. The experimental results show the improved performance of the LPV controller design in terms of the maximum acceleration and the RMS values of the structure response.