Adaptive fixed-time sliding mode control and optimal force allocation for nonlinear full-vehicle active suspension considering lumped uncertainties

This article proposes a robust nonlinear control strategy for a full-vehicle active suspension system equipped with hydraulic actuators to improve ride comfort and enhance vehicle body stability under road disturbances, model nonlinearities, and lumped uncertainties. A seven-degree-of-freedom full-vehicle model is established, including heave, roll, and pitch motions of the sprung mass, vertical dynamics of the four unsprung masses, and hydraulic actuator dynamics, while nonlinear spring and damping characteristics are explicitly considered. To simultaneously guarantee heave, roll, and pitch stability with minimum actuator effort, an optimal active force allocation method based on the Moore–Penrose pseudo-inverse is introduced to distribute the generalized control forces among four independent hydraulic actuators. A cascade control structure is then developed, in which adaptive fixed-time sliding mode control (AFxTSMC), integrated with active disturbance rejection control (ADRC), is employed in the outer loop to generate the desired control force. At the same time, an inner-loop proportional–integral–derivative (PID) controller regulates the hydraulic servo valve for accurate force tracking. Lyapunov stability analysis is performed to verify the boundedness of all closed-loop signals and the fixed-time convergence of the tracking errors. Comparative simulations under sinusoidal and random road excitations are conducted against PID-ACO, ADRC, and SM-DRC methods. Under sinusoidal excitation, the proposed controller achieves the lowest root mean square (RMS) vertical body acceleration of 0.014 m/s², corresponding to reductions of approximately 17.6%, 26.3%, and 75.0% compared with SM-DRC, ADRC, and PID-ACO, respectively. Under random road excitation, the vibration dose value (VDV) decreases to 0.506 m/s^1.75, representing improvements of 35.5%, 39.9%, and 85.2% over SM-DRC, ADRC, and PID-ACO, respectively. Furthermore, the roll and pitch angles are effectively constrained to 0.012° and 0.003°, demonstrating the robustness of the proposed control strategy under complex operating conditions.