Nonlinear disturbance observer-based robust backstepping control for active pneumatic suspension systems with unknown dynamics

Reliable vibration control for active pneumatic suspension systems remains challenging due to inherent nonlinearities, parameter variations, and road-induced disturbances. This paper proposes a nonlinear disturbance observer (NDO)-based robust backstepping controller (NDORBC) scheme for a quarter-vehicle active pneumatic suspension model. Parametric deviations, unmodeled dynamics, and equivalent road effects are lumped into a single disturbance acting on the sprung-mass dynamics, which is reconstructed online by the NDO using only directly measurable states—without acceleration measurement or numerical differentiation—thereby avoiding sensor-noise amplification through a compact observer structure. A Lyapunov-based analysis establishes the uniform ultimate boundedness of the tracking and disturbance-estimation errors. Comparative simulations under sinusoidal and random road excitations show that the proposed NDORBC improves ride comfort, suspension deflection, tracking accuracy, and disturbance estimation while maintaining acceptable tire dynamic load, compared with passive suspension configuration (PSC), robust backstepping controller (RBC), and neural-network-based robust backstepping controller (NNRBC) baselines.