Multivariable Control of a Submarine Using the LQG/LTR (Linear Quadratic Gaussian with Loop Transfer Recovery) Method

摘要

A multivariable control system for a deeply submerged submarine with active roll control is designed using the Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) method. A linear model of the submarine is developed for a 1 degree rudder deflection at a speed of 15 knots. The linear model is then scaled for units and input/output weightings and augmented with integral control in all four input channels. Using the properties of the linear model, a Model Based Compensator (MBC) is designed by shaping the singular values of a Kalman Filter to meet desired performance criteria and then recovering the singular value shapes using the Kwaakernaak recovery process. During extensive testing at speeds from 15 to 30 knots, the compensator performed well enough so that gain scheduling was not employed. Next, the compensator is compared to one designed for a 30 knot model. Finally, an Anti-Reset Windup (ARW) strategy is employed to counter the effects of control surface saturation.