Improving Vehicle Dynamics: A Fractional-Order PIλDμ Control Approach to Active Suspension Systems

This paper presents a comprehensive vehicle model featuring an active suspension system integrated with semi-active seat and engine mounting controls. The time-domain stochastic excitation of the four tires was modeled using the filtered white noise method, and the required road excitation was simulated using MATLAB software R2022b. Four comprehensive performance indices, including engine dynamic displacement, vehicle body acceleration, suspension dynamic deflection, and tire dynamic displacement, were selected and made dimensionless by the performance indices of a passive suspension under the same working conditions to construct the fitness function. A fractional-order PIλDμ (FOPID) controller was proposed, and its structural parameters were optimized using a gray wolf optimization algorithm. Furthermore, the optimized FOPID controller was evaluated under five road conditions, and its performance was compared with integer-order PID control and passive suspensions. The results demonstrate that the FOPID controller effectively improves the smoothness of the vehicle by reducing engine mounting deflection, vehicle body acceleration, suspension deflection, and tire displacement. Moreover, the simulation results indicate that, compared to the passive suspension, the FOPID-controlled suspension achieves an average optimization of over 42% in the root mean square (RMS) of body acceleration under random road conditions, with an average optimization of more than 38% for suspension deflection, 4.3% for engine mounting deflection, and 2.5% for tire displacement. In comparison to the integer-order PID-controlled suspension, the FOPID-controlled suspension demonstrates an average improvement of 28% in the RMS of acceleration and a 2.1% improvement in suspension deflection under random road conditions. However, the engine mounting deflection and tire displacement are reduced by 0.05% and 0.3%, respectively. FOPID control has better performance in vehicle acceleration control but shows asymmetrical effects on tire dynamic deflection.