Hopf bifurcation analysis for depth control of submersible vehicles
Bateman, Craig A.
Papoulias, Fotis A.
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Control of a modern submarine is a multi-dimensional problem coupling initial stability, hydrodynamic and control system response. The loss of stability at moderate to high speeds is examined using a nonlinear Hopf bifurcation analysis. Complete linear state feedback is used for demonstration purposes for depth control at level attitude and for a fixed nominal speed. Control time constant, nominal and actual speeds, metacentric height, and stern to bow plane deflection ratio are used as the main bifurcation parameters. A complete local bifurcation mapping provides a systematic method for evaluating the bounds of controllability for control system design parameters for a submarine with a given set of hydrodynamic coefficients. The submarine and its potential design modifications are then verified with a nonlinear simulation program.
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