Submarine Autopilot Performance Optimization with System Identification

Computer simulation models play a vital role in the assessment of a ship’s autopilot design. A well-tuned autopilot will contribute to reducing rudder activity, thereby minimizing wear on the actuation plant and also generally reducing fuel consumption. The equations that describe the ship motion dynamics contain a large number of hydrodynamic coefficients that must be calculated as accurately as possible to justify the use of a simulation model and its relevance to predicting the ship manoeuvring characteristics. Proper prediction of the ship performance is an essential pre-requisite in the process of tuning the autopilot.  

The hydrodynamic coefficients can be calculated by using theoretical methods or by carrying out experiments on the actual ship or on a scaled model of the ship. System Identification (SI) is an experiment-based approach and in this paper the authors present an algorithm that can estimate the coefficients with great accuracy. These coefficients can classically be obtained in a towing tank using a captive model, and with a planar motion mechanism and a rotating arm. Generally, these systems are costly and entail expensive trials programs, and SI methods have been developed in an effort to obviate some of those problems and limitations. They typically process ship manoeuvring data obtained from a free-running scaled model or full-scale trials.  

While similar to a surface ship, the motion dynamics of a submarine introduce additional challenges for SI methods. This is because the submarine manoeuvres in “three dimensions”, which adds complexity and more hydrodynamic coefficients to the equations. The standard submarine simulation model, also referred to as the Gertler and Hagen equations, incorporates over 120 coefficients. To calculated these coefficients, the SI algorithm uses a Square-Root Unscented Kalman filter (SR-UKF). One of its appealing features is that it calculates all the coefficients by processing data from a single submarine manoeuvre that has a repeating sinusoidal pattern in both depth and course. The manoeuvre can be performed in a towing tank by a free-running scaled model of the submarine, or it can be performed at sea on the full-scale submarine as part of the sea trials schedule.