A Lyapunov based multi-level controller for a semi-active suspension system with an MRF damper

In this work, we study the implementation of magnetorheological fluid (MRF) to the semi-active suspension. Owing to the nonlinear hysteretic phenomenon, the analysis and synthesis of a controller is not trivial. The kinematic energy and spring potential function of the suspension system plus an integral term of the hysteretic component of an MR damper is chosen as the Lyaupnov function to verify the stability and dissipativity of the system. Then a multi-level controller, which is constructed in virtue of stability analysis, turns out to be effective in vibration suppression. In addition, the controller algorithm is simple and easy to implement, requires only the measurements of relative displacement and velocity between sprung and unsprung masses, and the damping force of the MR damper.