Hierarchical Fractional-Order Disturbance-Rejection Control of an Electro-Hydrostatic Actuator for Marine Steering Gear

Abstract

Disturbances from multiple sources propagate through coupled motor, hydraulic, and mechanical channels in electro-hydrostatic actuators, while increasing observer bandwidth introduces a trade-off with sensitivity to high-frequency components. To address these challenges, this study proposes a cascaded control method that integrates parallel disturbance estimation with fractional-order error damping. A detailed model incorporating the instantaneous flow rate of a piston pump, leakage, fluid compressibility, and dynamic friction is developed, and a control-oriented model is derived through time-scale separation. A three-channel parallel observer is constructed according to the locations at which disturbances enter the state equations, enabling corresponding compensation within a position–pressure difference–rotational speed backstepping control cascade. A Caputo fractional derivative is introduced into the motor-level error feedback to shape the magnitude and phase characteristics within the target frequency band by adjusting the fractional order and damping gain. This term is implemented using a rational approximation over a finite frequency band. The approximation filter states are incorporated into a composite Lyapunov function. Under prescribed filter dissipation conditions, positive feedback gains, and uniformly bounded equivalent residuals, uniform ultimate boundedness of the augmented continuous-time closed-loop error dynamics is established, together with residual-dependent error bounds. Co-simulation results show that the position root-mean-square error during multilevel step tracking is 5.68 mm, representing reductions of 45.8%, 24.6%, and 12.6% relative to proportional–integral–derivative control, fractional-order linear active disturbance rejection control, and cascaded sliding-mode control with multiple-disturbance observation, respectively. In semi-physical experiments, the steady-state position error during the plateau phases remains largely within ±2 mm under loads of 5 kN and 10 kN. During motion-reversal tracking under variable loads, the position root-mean-square error is reduced by 26.8% and 14.8% relative to the first two baseline methods, respectively. These results demonstrate that, under the tested conditions, channel-specific disturbance compensation combined with fractional-order dynamic shaping improves actuator tracking performance and provides a basis for fractional-order controller design and finite-dimensional implementation analysis in coupled electrohydraulic systems.