Backstepping Angle Control of a Marine Hydraulic Ramp Based on a Nonlinear Extended State Observer

Marine hydraulic ramps exhibit pronounced nonlinear behavior arising from configuration-dependent transmission geometry, gravitational torque, and servovalve flow–pressure coupling. Accurate angle regulation is further complicated by external disturbances and unavailable internal states. This study develops a nonlinear extended state observer (NLESO)-assisted backstepping control strategy for marine hydraulic-ramp angle regulation. A coupled mechanical–hydraulic model is formulated while retaining the nonlinear transmission geometry, rotational dynamics of the ramp, and hydraulic-actuator dynamics. When only the ramp angle is measured, the local distinguishability between the physical load pressure and the lumped mechanical disturbance is examined to establish a structural basis for their joint reconstruction. A fourth-order NLESO is then developed to reconstruct the angular velocity, load pressure, and lumped disturbance, and the resulting estimates are incorporated into an estimated-state backstepping controller. A Lyapunov-based analysis establishes sufficient conditions for bounded observation errors and boundedness of the observer–controller cascade. Comparative simulations with cascaded feedforward proportional–integral–derivative control, linear active disturbance-rejection control, and linear-ESO-based backstepping control show that the proposed method yields smaller angle-tracking errors under the considered operating conditions. The observer comparison further shows improved reconstruction of the mechanical motion states and a lower average disturbance-estimation error, while revealing a channel-dependent trade-off in load-pressure estimation. Overall, the proposed method enhances closed-loop tracking and disturbance rejection without a substantial increase in RMS control effort.