A Unified Design Method for FOPID Controllers in Active Suspension Systems

This study explored the use of fractional order PID (FOPID) controllers for active vehicle suspension, addressing the challenges of discretization for real-time application. Simulations on a quarter-car model were conducted to compare the performance of a novel direct delta domain FOPID (delta-FOPID) with traditional z-domain FOPID and continuous time FOPID implementations. The results indicated that the delta-FOPID outperformed the other methods, especially at very low sampling times, where the z-domain FOPID showed numerical instability. The delta-FOPID’s improved accuracy and stability, achieved by closely approximating continuous time control behavior as the sampling time (delta) approaches zero, led to significant enhancements in ride comfort, road handling, and suspension deflection. These findings underscore the potential of fractional order control and direct delta domain discretization for creating advanced and robust active suspension systems.