Modelling and Control of Blowing-Venting Operations in Manned Submarines

Motivated by the study of the potential use of blowing and venting operations of ballast tanks in manned submarines as a complementary or alternative control system for manoeuvring, we first propose a mathematical model for these operations. Then we consider the coupling of blowing and venting with the Feldman, variable mass, coefficient based hydrodynamic model for the equations of motion. The final complete model is composed of a system of twenty-four nonlinear ordinary differential equations. In a second part, we carry out a rigorous mathematical analysis of the model: existence of a solution is proved. As one of the possible applications of this model in naval engineering problems, we consider the problem of roll control in an emergency rising manoeuvre by using only blowing and venting. To this end, we formulate a suitable constrained, nonlinear, optimal control problem where controls are linked to the variable aperture of blowing and venting valves of each of the tanks. Existence of a solution for this problem is also proved. Finally, we address the numerical resolution of the control problem by using a descent algorithm. Numerical experiments seem to indicate that, indeed, an appropriate use of blowing and venting operations may help in the control of this emergency manoeuvre.