Resonance Suppression of Flexible-Transmission Servo Systems with Fractional-Order Dual-Inertia Modeling and Singular Perturbation

Abstract

Mechanical resonance limits the tracking bandwidth of flexible-transmission servo systems. This limitation stems from the coupling between rigid-body motion and flexible vibration, which gives rise to high-order dual-inertia dynamics and complicates direct controller synthesis. To represent the flexible-transmission dynamics more accurately, a fractional-order dual-inertia model is adopted to capture the viscoelastic and memory-dependent behavior of the transmission. Singular perturbation is applied to a control-oriented approximation of this model, yielding quasi-steady-state load-position dynamics and boundary-layer resonance dynamics. The quasi-steady-state dynamics are used to design a cascade controller comprising a proportional (P) position loop and a proportional–integral (PI) velocity loop, hereafter termed the P-PI cascade controller. The boundary-layer resonance dynamics are used to design a fractional-order active damping law. Simulation results indicate that, under the considered conditions, fractional-order active damping with a properly selected value for the fractional order attenuates load-side resonance more effectively than integer-order active damping while maintaining tracking performance.