The paper will be too far into the deep end if you are new to the subject, but could be a chance to follow references. I'd look at the second of the two design-optimization methods it describes, the H-infinity method. If we strip out the optimization step for the time being, this contains within it a "classical" 2D control setup that seems like it would be appropriate. It is shown broken into two coupled 1axis loops on page 8 of that paper...
Your situation would, I think, differ in 4 ways: (1) the dynamics of the ship's response, (2) the character of the disturbances (sea state 5 acting on the ship), (3) the control objective- you are less interested in tracking a moving control target, as far as I can tell, and (4) the delays or lags (unwanted plant poles) in your system , which may be dominating your performance....
But it depends on the dynamics and time constants of your system, which you could hopefully fish out of the measurement data you have
Also I looked at the IEEE link you sent (Rajesh 2015) - Not entirely clear but it looks looks like 2 independent 1-axis loops for the two axes of the gimbal/platform relative to the ship
That may be good enough depending on the dynamics. If it is, it would simplify things tremendously
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