Experimental Modelling, System Analysis, and Actuator-Stroke Characterization of Flap-Type and Piston-Type Wave Makers

This study presents a comparative actuator-stroke analysis of flap- and piston-type wave makers using previously published experimental stroke–wave-height datasets acquired in separate campaigns on the same hydraulic wave channel. Matched checks using a Mamdani-type fuzzy position controller are reported separately. The hydraulic servo-cylinder (HSC) stroke under Mamdani control differed slightly from the reference stroke (maximum absolute differences: 0.70 cm for the flap and 0.14 cm for the piston), while the wave heights measured in both Mamdani-controlled configurations retained the same reported one-decimal values (0.1 cm precision) as the reference heights. A single common H column is used for these condition-matched values. This observation does not establish controller independence beyond the measured conditions or resolution. Previously identified third-order transfer functions were examined by pole-zero, Bode and Nyquist analysis. The principal analytical contributions are an empirically combined dimensionless actuator-stroke descriptor (Form1) and a comparison with the first-order wave-maker theory of Biésel and Suquet, with a kinematic conversion for the hinged flap. On the original 24-point datasets per configuration, the shared Form1 gave R2 = 0.924 for the piston and 0.733 for the flap, with pointwise leave-one-out R2 values of 0.908 and 0.685, respectively. The piston model was also checked against 16 previously acquired conditions at 60 cm depth (reported R2 = 0.90; RMSE = 0.021 for S/d). Classical-theory-normalized wave-height-to-stroke ratios were approximately 0.66 (piston) and 0.65 (flap at the nominal linkage position). Results apply to the tested geometry, frequencies and depths, and should not be interpreted as a controlled, same-campaign comparison or a measurement of energetic efficiency.