Adaptive Fractional-Order Damping via Extremum Seeking Control for Intelligent Vehicle Suspension Systems

Conventional vehicle suspension systems, often relying on integer-order models with fixed damping coefficients, struggle to deliver optimal performance across diverse and dynamic road conditions. This paper introduces a novel intelligent adaptive suspension framework that leverages fractional-order calculus and real-time optimization. The core of the system is a damping model employing a Caputo fractional derivative of order $\alpha \in \left(1,2\right)$ , where $\alpha$ itself is dynamically tuned. This adaptation is driven by an Extremum Seeking Control (ESC) algorithm, which continuously adjusts $\alpha$ to minimize a predefined cost function reflecting ride comfort and road holding, based on fused sensor data (e.g., from IMUs and wheel encoders processed via a Kalman Filter). This model-free online optimization allows the suspension to adapt its fundamental damping characteristics to changing terrains without requiring explicit road classification models. Simulation results for a quarter-car model demonstrate the ESC’s ability to converge towards an optimal $\alpha$ , enhancing the suspension’s adaptability and performance across varying operating scenarios, thereby indicating a promising path for next-generation terrain-aware vehicle dynamics control. This model-free, online optimization allows the suspension to adapt its fundamental damping characteristics to changing terrains without requiring explicit road classification models. Real-time feasibility is achieved through computationally efficient numerical approximations of the fractional derivative and the inherent filtering within the ESC loop, making the framework suitable for implementation on modern automotive controllers. Simulation results for a quarter-car model demonstrate the ESC’s ability to converge towards an optimal α, enhancing the suspension’s adaptability and performance across varying operating scenarios, thereby indicating a promising path for next-generation terrain-aware vehicle dynamics control.