Research on the Control Strategy of Skyhook Inertance Semi-Active Suspension Based on Fractional-Order Calculus

The skyhook inertance (SHI) control strategy facilitates the real-time adaptation of inertance parameters to dynamic loading conditions, consequently enhancing vehicle ride comfort. It features a simple algorithm and strong robustness. However, traditional skyhook inertance systems only adjust the magnitude of the control force by changing the inertance, without regulating the control force phase, which limits the control effect of the SHI control strategy. To solve this problem, this study introduces a fractional-order skyhook inertance (Fo-SHI) control approach. This method substitutes the second-order differential terms appearing in the conventional equation of motion of the fractional-order skyhook inertance system with fractional-order derivatives of the displacement. Consequently, the proposed strategy enables continuous and independent tuning of both the amplitude and phase of the generated control force. To achieve a realistic representation of the Fo-SHI forces, a fractional-order model integrating an adjustable damper and an inerter was developed. This model was subsequently validated through prototype testing, and its parameters were identified via a fitting process. The results of Hardware-in-the-Loop experiments demonstrate that the semi-active suspension employing the Fo-SHI control strategy achieves significant performance improvements over the conventional SHI-controlled suspension: the root mean square of body acceleration is reduced by up to 18.12% under full-load conditions, while suspension working space and dynamic tire load also show favorable responses. These findings clearly underscore the advantages and rationale for incorporating fractional-order control into vehicle suspension systems.