Force Control of an Active Suspension Hydraulic Servo System Based on BSO-Optimized ESO-Based SMC

To mitigate the significant impact of system nonlinearities, time-varying parameters, and external load disturbances on the output force of hydraulic servo systems in active hydraulic suspensions for engineering vehicles, this study proposes a beetle swarm optimization (BSO)-optimized extended state observer (ESO)-based sliding mode control (SMC) strategy. A comprehensive mathematical model of the hydraulic servo system is established, and an ESO-based SMC controller is designed, taking into account the coupled effects of chamber pressure dynamics and external loads on the uncertain output force. The stability of the closed-loop system is rigorously analyzed and verified using Lyapunov stability theory. The effectiveness of the proposed control strategy is verified through both numerical simulations and experimental tests. For step inputs of 5000 N and 8000 N, overshoot is significantly reduced compared with the conventional proportional–integral–derivative control and the standard extended state observer-based sliding mode control, while the settling time is shortened by more than 65% in simulations and up to 75% in experiments. Under sinusoidal force excitations at frequencies of 0.5 Hz, 1 Hz, and 2 Hz, the maximum tracking error, mean error, and standard deviation of the tracking error are substantially reduced, with the maximum error reduction exceeding 90%. These results demonstrate that the proposed method achieves high-precision force tracking under external disturbances and pronounced system uncertainties, providing an effective solution for force control of hydraulic servo systems in active suspension applications for engineering vehicles.