[Paper Review] Modelling and Control of Blowing-Venting Operations in Manned Submarines

Font, Roberto, José A. Murillo+2 more|arXiv (Cornell University)|Jul 4, 2011

Fluid Dynamics Simulations and Interactions9 references3 citations

TL;DR

This paper develops a comprehensive nonlinear mathematical model of 24 ordinary differential equations for blowing and venting operations in manned submarines, integrating them with a variable-mass hydrodynamic model. It proves existence of solutions for both the dynamics and an optimal control problem, demonstrating numerically that controlled blowing and venting can effectively assist in roll control during emergency surfacing maneuvers.

ABSTRACT

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.

Motivation & Objective

• To develop a detailed mathematical model of blowing and venting operations in manned submarines for use as a complementary or alternative control system.
• To integrate these operations with a variable-mass hydrodynamic model (Feldman-based) to capture the full dynamics of submarine motion.
• To formulate and analyze an optimal control problem for emergency rising maneuvers, focusing on roll control using only blowing and venting.
• To prove the existence of solutions for both the dynamic model and the optimal control problem.
• To numerically solve the control problem using a descent algorithm and evaluate its feasibility in practice.

Proposed method

• Formulates a system of 24 nonlinear ordinary differential equations to model the coupled dynamics of submarine motion and ballast tank blowing/venting operations.
• Integrates the blowing-venting dynamics with the Feldman variable-mass hydrodynamic model to account for mass and center of mass changes during operations.
• Models control inputs as variable apertures of valves in each ballast tank, enabling precise manipulation of air and water flow.
• Formulates a constrained, nonlinear optimal control problem where the objective is to achieve desired roll control during emergency surfacing.
• Applies a descent algorithm for numerical resolution of the optimal control problem, ensuring convergence to a feasible solution.
• Performs numerical experiments to evaluate the effectiveness of the control strategy under emergency conditions.

Experimental results

Research questions

• RQ1 Can blowing and venting operations in ballast tanks be effectively modeled as a control system for submarine maneuvering?
• RQ2 Does the integration of blowing-venting dynamics with a variable-mass hydrodynamic model yield a consistent and solvable system of equations?
• RQ3 Is there a solution to the optimal control problem that enables roll control during an emergency rising maneuver using only blowing and venting?
• RQ4 Can numerical methods successfully resolve the optimal control problem and demonstrate practical feasibility?
• RQ5 To what extent can controlled blowing and venting contribute to stabilizing roll during emergency surfacing?

Key findings

• The complete model consists of a system of 24 nonlinear ordinary differential equations that accurately describe the coupled dynamics of submarine motion and ballast tank operations.
• The existence of a solution to the dynamic model is rigorously proven, ensuring mathematical consistency.
• The existence of a solution to the constrained, nonlinear optimal control problem for emergency roll control is also proven.
• Numerical experiments using a descent algorithm indicate that blowing and venting can effectively contribute to roll control during emergency rising maneuvers.
• The results suggest that blowing and venting operations can serve as a viable control mechanism in emergency scenarios where traditional control systems may fail.
• The proposed control strategy demonstrates potential as a complementary or alternative method for submarine maneuvering, particularly in critical situations.