Influence of Time-Delayed Fractional-Order PD Control on the Nonlinear Dynamics of a MAGLEV Vehicle Under Aerodynamic and Centrifugal Excitations

Time delays are inherently present in active control systems as a consequence of sensor acquisition, communication lags, and actuator dynamics, and their impact on system behavior cannot be overlooked. This paper examines the effect of delayed displacement and speed feedback gains on the nonlinear lateral and vertical vibrational behavior of a MAGLEV vehicle subjected to aerodynamic and centrifugal forces. A delayed nonlinear dynamic model incorporating a fractional-order PD controller under aerodynamic excitation is first established for the MAGLEV system. Subsequently, the method of multiple scales is employed to derive the frequency response relationships, while the corresponding steady-state solutions are analyzed to determine system stability. The investigation further explores how the delays alter the nonlinear dynamic response. It also considers the impact of changing the value of the fractional-order parameter α on the vehicle’s dynamics. The results showed that increasing controller delays reduces the stability region, with displacement-feedback delays having a more pronounced effect than speed-feedback delays, while fractional-order derivatives (0<α<1) further degrade stability; consequently, the integer-order case (α=1) is recommended to achieve lower vibration levels and improved dynamic stability. The outcomes of this work provide valuable understanding of vibration phenomena encountered in MAGLEV systems and contribute to the development of improved control and optimization strategies for safer, smoother, and more reliable vehicle performance.