The design trend of large industrial carriers brought out a new type of ship hull : high block coefficient and small length-beam ratio. Such hull proportions are liable to make a ship unstable on course. Since then minimum necessary course-stability has been of common interest.There are two criteria for the minimum necessary course-stability. The first relates to safe navigation normally under manual control. The second point is the propulsive power loss in a seaway under automatic coursekeeping ; the less stable is a ship, the more power loss from this reason assuming the same performance of the autopilot.The power loss is composed of three parts : elongation of ship path caused by course fluctuation, inertial drag caused by yawing and the drag of activated rudder. We'made theoretical analysis on them, taking account of the on-off (non-linear) performance of the “power unit”, a hydraulic servomechanism to control the steering gear. Also we paid attention to some non-linear elements normally called “weather adjust”, that is to avoid too frequent rudder activity in a seaway.Next we made numerical calculation of the power loss of a series of assumed ships whose course-stability vary systematically. Realistic sea and wind spectra are employed in this analysis.The conclusions are :(1) provided that the rudder gain and the yawrate gain of an auto-pilot is properly adjusted, even a very unstable ship can navigate with very small power loss, unless any low-frequency external disturbance exists ;(2) but this optimum rudder gain is so small that any frequency disturbance, very probably induced by wind gust, will cause a severe course deviation and then a considerable path elongation ;(3) from this reason, any spiral loop width (a measure of instability) greater than 15 degrees should not be permitted for fuel economy under automatic course-keeping in a seaway.

https://www.jstage.jst.go.jp/article/jjasnaoe1968/1982/151/1982_151_101/_pdf

Effects of Extra Sinusoidal Inputs to Nonlinear Systems

Power Loss Related to Automatic Course-keeping

An Approximate Method for Analysis of Stability and Step Response of the Nonlinear Second Order System with a Periodically Time-Varying Restoring-Force Term

On signal stabilization

—A model describing glitch disturbances is intro- duced and analysed. The model is used to find the response of glitch disturbances when adding a periodic dither to the input and applying low-pass filtering to the output. This averaged response is used to find a criterion to determine a sufficiently large dither amplitude that will make the averaged glitch disturbances appear as a constant on the output of the low- pass filter. An important resulting property is that the averaged response to glitch disturbances is independent of the model input. By fitting the model to the measured response of a common off-the-shelf digital-to-analogue converter, simulations are used to verify the analytical results.

Criterion for Sufficiently Large Dither Amplitude to Mitigate Non-linear Glitches

The minimum amplitude of the dither or the extra high frequency signal at the input to the nonlinear element, to quench the limit cycles present in the system, can be determined by the use of the DF theory. It can also be determined by the application of Popov's criterion, after replacing the original nonlinear element and dither by the altered nonlinearity. The results as obtained by the above two methods for several nonlinearities, are compared and analysed.

Effects of Extra Sinusoidal Inputs to Nonlinear Systems

Citations

Power Loss Related to Automatic Course-keeping

An Approximate Method for Analysis of Stability and Step Response of the Nonlinear Second Order System with a Periodically Time-Varying Restoring-Force Term

On signal stabilization

Criterion for Sufficiently Large Dither Amplitude to Mitigate Non-linear Glitches

Signal Stabilization Analysis by DF Method and Popov Method Compared

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