Adaptive Backstepping Control with Time-Delay Compensation for MR-Damper-Based Vehicle Seat Suspension

Long-term vibrations endanger driver health and affect ride performance. Semi-active seat suspension systems equipped with magnetorheological (MR) dampers can effectively reduce vibrations transmitted to drivers, exhibiting excellent potential for widespread applications owing to their outstanding performance characteristics. In this paper, we propose an adaptive backstepping control system with time-delay compensation (ABC-C) for an MR-damper-based semi-active seat suspension system to enhance ride comfort and stability in commercial vehicles. The control framework integrates a reference model, an adaptive backstepping controller, a time-delay compensator, and an MR damper inverse model. The reference model balances ride comfort and stability using high-pass and low-pass filters, while the adaptive controller ensures robustness against parameter uncertainties and disturbances. A time-delay compensator mitigates delays in the control loop, improving system stability and performance. Numerical simulations under harmonic, bump, and random excitations demonstrated the superior performance of the ABC-C controller. The experimental results show that under random road excitation conditions, the frequency-weighted root mean square (FW-RMS) of acceleration was reduced by 26.9%, the vibration dose value (VDV) decreased by 29.3%, and the root mean square of relative displacement (RMS_rd) was reduced by 58.46%. The results highlight the practical effectiveness of the ABC-C controller in improving ride comfort and safety for drivers of commercial vehicles, offering significant potential for real-world applications.