Allowing negative saturation multipliers could improve power performance

[rebeccamccabe]

Currently the saturation multiplier is formulated to stay between 0 and 1 in dynamics.m.
For a wave with given frequency \omega, the ideal Kp is:
$K_{p,ideal} = m \omega^2 - K_h$

For the nominal design, $K_h = 7.6e6, m=6e6$, and $\omega$ ranges from 0.5 to 1.5 rad/s, so Kp_ideal ranges from -6.1 at low $\omega$ to +6.4e6 at high $\omega$. Since $K_{p,ideal}$ changes sign, that means having a saturation multiplier with a different sign would be beneficial. (See the notional hand-drawn plots on p228 of my notebook).

This could also be addressed by changing the problem formulation so that instead of choosing a single Kp for all sea states and then introducing sea state dependence through saturation only, a variety of design variables could be used to encode a $K_p(\omega)$ relationship. Changing the problem formulation is out of scope at this time.