Linear Quadratic Integral Control for Longitudinal Stability of a Fully Submerged Hydrofoil Craft

This paper presents a normalized discrete linear quadratic integral (DLQI) control scheme for the longitudinal stabilization of a fully submerged hydrofoil craft under wave disturbances and actuator constraints. A control-oriented heave-pitch model is formulated from a nonlinear hydrofoil simulation plant that includes wave orbital velocities, near-free-surface hydrodynamic attenuation, actuator lag, and deflection saturation. Based on the trimmed cruising condition, the reduced subsystem is normalized and discretized using zero-order hold (ZOH), and a DLQI output-regulation controller is designed with a pseudo-inverse anti-windup safeguard. Comparative nonlinear simulations show that the proposed DLQI provides better heave and pitch suppression than a continuous-time LQI baseline when actuator bandwidth is limited. Quantitative indices are used to evaluate the performance difference under varying wave heights and actuator response coefficients.