Submarine H({infinity} ) depth control under wave disturbances

The depth control of submarines in the absence of wave disturbances (deep submergence) is a straightforward task, but at periscope depth the submarine-wave dynamics become very complex. To solve the submarine depth-keeping problem, a procedure for designing H ({infinity}) controllers is proposed. This has been obtained by combining polynomial and state-space H({infinity}) methods. The polynomial approach allows the wave disturbances to be included in the design setting as design "parameters". Reformulating the polynomial description in a state-space configuration enables the controller to be calculated using standard design software, e.g., the mu-toolbox of Matlab. The wave disturbances model, which may be considered to be formed of first-order (oscillating) and drift (second-order) components, is crucial in the proposed design procedure, as it becomes a design "parameter". A successful representation of these disturbances is also included. The numerical problem caused by the ill conditioning of the standard interconnection system was solved by expressing the system in a "block observable" realization. The order of the controller was reduced by factorizing the common poles and zeros of the augmented plant. The criterion for selecting the cost-weighting functions is defined in terms of the dynamical system structure of the submarine. The success of the design procedure has been evaluated through a series of nonlinear simulations