Fourier transform and 2nd derivative matrix corrections

[michaelcdevin]

Description

This corrects two mathematical issues in the code:

1. The core.td_to_fd function no longer multiplies the DC and Nyquist frequency by two, since these frequencies would not have Hermitian symmetry and therefore should not by doubled when converting from a double-sided to a single-sided spectrum
2. A second derivative matrix, core.derivative2_mat, has been added to correctly enable acceleration calculations from position. With Remove sine component of 2-point wave #191, the final velocity term is (correctly) zero, so performing derivative_mat @ velocity returns zero for the final acceleration term as well, though this should usually be nonzero. An explicit second derivative matrix allows for this term to be captured via derivative2_mat @ position instead of using derivative_mat twice on the position vector.

Type of PR

• Bug fix
• New feature
• Documentation
• Other: (specify)

Checklist for PR

• Authors read the contribution guidelines
• The pull request is from an issue branch (not main) on your fork, to the main branch in WecOptTool.
• The authors have given the admins edit access
• All changes adhere to the style guide including PEP8, Docstrings, and Type Hints.
• Modified the documentation if applicable
• Modified or added a new test
• All tests pass
• Reference or close any relevant issues

[cmichelenstrofer]

Didn't read all the tests but core and pto.py look good!

[cmichelenstrofer]

@michaelcdevin we still need to figure out why the PI controller still has arbitrary last frequency.

[michaelcdevin]

Agreed, I'm looking into this a bit now. Let's address that in #225