The parameter settings for each algorithm.

Traditional PID control faces challenges in addressing parameter uncertainty and nonlinearity in active suspension electrohydraulic servo actuators, leading to suboptimal performance. To address these challenges, a fractional-order PID (FOPID) controller optimization method based on the Multi-Strategy Improved Beluga Whale Optimization (MSIBWO) algorithm is proposed. Simulation results in MATLAB/Simulink demonstrate that the MSIBWO-FOPID controller significantly outperforms traditional PID and BWO-FOPID controllers in force tracking and robustness. For step input, the rise time and the root mean square error(RMSE) are reduced by 66.7 and 70.3, respectively, compared to BWO-FOPID. For sine inputs, the system achieves better disturbance rejection and higher precision. Using a half-car model, the MSIBWO-FOPID controller improves ride comfort significantly. Under random road excitation, the RMSE values of the vehicle body’s vertical acceleration and pitch angle acceleration are reduced by 51.7 and 13.1, respectively, compared to passive suspension, outperforming both PID and BWO-FOPID controllers.