Tube-based Model Reference Adaptive Control for Vibration Suppression of Active Suspension Systems

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With the developments of industrial automation in recent years, vehicle suspension systems have received a great deal of attention in industry and academia due to their critical role in the chassis performance of vehicles [1]. The suspension system is expected to guarantee the vehicle's maneuverability and provide satisfactory ride comfort by absorbing the vibrations arising from the road surface excitations and ensuring road-holding capability and suspension safety. Motivated by the desirable performance of the model reference adaptive control (MRAC) approach, various literature studies have investigated its performance in diverse linear and nonlinear practical systems [2], [3] (for more background review, see Supplementary material-Appendix A). Aiming to improve the conventional MRAC in terms of closed-loop stability, asymptotical tracking, and robustness against uncertainties and external disturbances, authors in [4] developed the tube-based MRAC (T-MRAC) approach. To simultaneously achieve the desired objectives, the developed scheme split the control signal into two main terms; an adaptive part and another part that corrects the control objective. In addition, an optimization problem is formulated to find the newly determined correction control component. However, although the method's performance was verified using some simple single-input single-output unstable systems [5], more extensive investigations on complex practical systems are needed to validate its performance. The main contributions of this paper are to develop a novel tube-based MRAC approach for multi-input multi-output active suspension systems; a realistic design that guarantees ride comfort and suspension safety and achieves better control performance with reduced control effort in the presence of external disturbances compared to conventional methods. Moreover, to validate the method's applicability in practical applications, three different road profiles are conducted to simulate distinct practical road situations, as the bump-dip road, random road, and sinusoidal profiles. Furthermore, the vibration suppression performance of the developed adaptive control scheme is investigated, and superior simultaneous ride comfort, road handling, and suspension safety are guaranteed compared to conventional MRAC [6] and SMC [7] approaches.