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310   Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics






















                        Figure 19.8 Suspension space of semi-active suspension systems.


                        19.5 CONCLUSION

                        In this chapter, an adaptive estimation and control for vehicle semi-active
                        suspension system with MR damper is proposed. A hyperbolic model is
                        suggested to describe the hysteresis behavior of MR dampers. The un-
                        known parameters of the MR damper model are estimated by using a re-
                        cently introduced adaptive algorithm based on the estimation error. More-
                        over, the MR damper is further incorporated into the vehicle suspension
                        system, and an adaptive control is developed to regulate the vertical dis-
                        placement of the vehicle body. Regulation of vehicle vertical displacement
                        and parameter estimation can be achieved simultaneously by introducing
                        a leakage term of the estimation error in the adaptive law. The suspen-
                        sion requirements of ride comfort and vehicle safety are also studied. The
                        proposed approaches are validated by comparative simulations based on a
                        quarter-car model.



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