Backstepping adaptive control of quarter-vehicle semi-active suspension with Dahl MR damper model

This paper addresses the problem of controlling quarter-vehicle semi-active suspension systems. Presently, the suspension system involves a magnetorheologic MR damper featuring a hysteretic behavior captured through Dahl model. The control problem is dealt with backstepping control design. First, an observer is designed to get online estimates of the hysteresis internal state. Then, an adaptive state-feedback controller, that ensures a tight regulation of the chassis vertical position, is designed assuming all internal state variables to be accessible to measurements. Finally, an adaptive output-feedback controller is obtained combining the previous designed observer and state-feedback controller. It is formally established that the output-feedback controller asymptotically meets its control objectives. This theoretical result is confirmed by several simulation tests.