Linearisation of a ship propulsion system model

The understanding, modelling and analysis of the behaviour of a non-linear ship propulsion plant are of great importance for conceptual system design, component selection, selection of control strategy and for propulsion control system tuning. Conceptual propulsion system design activities, such as deciding the combinator curve, require a relatively simple steady state simulation model, while propulsion controller design and tuning requires a non-linear time domain simulation model which captures the intricacies of the propulsion plant. In this paper a linearised model of the uncontrolled ship propulsion system is derived which can be used for analysis of propulsion system behaviour in waves and for initial controller design and tuning. Furthermore a thorough analysis is made of the conditions under which local instability of the system can occur. In a follow up paper the linearised model is extended and verified by means of comparison with a non-linear model. There it is furthermore used to investigate the effect of engine governor settings on a propulsion plant when sailing in waves at different encounter frequencies. The authors believe that, due to its transparency and clear link to well known parameters and variables, the linearised core propulsion system model as derived in this paper should appeal to marine system engineers, control engineers and hydrodynamicists alike. The linearised model should however not be seen as the replacement for a non-linear model, but rather as an additional tool that can be used.