## 3 Results
### Time-Domain Analysis  
Subjecting both the _WEC-Sim_ and _Gazebo_ model to the same monochromatic waves allowed for a direct comparison of their behavior. Each model was run with monochromatic waves varying from 0.25 to 2.0 m wave heights and 4 to 14 s wave periods, a scale factor of 1.0 (as discussed in Section 2.2.2), a closed heave cone door status, and a 0.8 m initial mean piston position. The top portion of Figure 6 shows the time signals for the piston position and velocity, motor speed, and electric power output by the _WEC-Sim_ and _Gazebo_ models when subject to a monochromatic wave with a height of 1 m and period of 8 s close to the resonance frequency of the heave cone [3]. For a non-resonant case, the bottom of Figure 6 shows these same signals when the models were subject to a monochromatic wave with a height of 1 m and period of 6 s. Table 1 shows statistical measures for the time signals in each wave case to provide quantitative measures for comparison.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Wave Case** & \multicolumn{2}{c}{**Mean Piston pos. [m]**} & \multicolumn{2}{c}{**RMS Piston vel. [m/s]**} & \multicolumn{2}{c}{**RMS Motor Speed [RPM]**} & \multicolumn{2}{c}{**Mean Electric pow. [W]**} \\ \hline \((\mathbf{H},\mathbf{T})\) & **Gazebo** & **WEC-Sim** & **Gazebo** & **WEC-Sim** & **Gazebo** & **WEC-Sim** & **Gazebo** & **WEC-Sim** \\ \hline
1 m & 8 s & 0.76 & 0.82 & 0.06 & 0.06 & 648 & 663 & 32.5 & 2.7 \\
1 m & 6 s & 0.7 & 0.73 & 0.09 & 0.11 & 1059 & 1247 & 221 & 291 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Statistical measurements for monochromatic wave time signals in Figure 6 for _Gazebo_ and _WEC-Sim_ models.  
As described in Section 2, a key difference between the _WEC-Sim_ and _Gazebo_ models is their approaches to modeling the dynamics of the air spring. These effects are illustrated in Figure 6. For each wave case, the differences in piston position highlighted the varying spring stiffness between the models. However, the time signals of the piston velocity and motor speed between both models largely agreed, indicating that these dynamics were not significantly influenced by spring stiffness. Studying the quantitative measurements between both models in Table 1 revealed that _WEC-Sim_ maintained a closer mean piston position value to the desired value of 0.8 m. It also showed that the RMS value of piston  
Figure 6: Time signals for piston position and velocity, motor speed, and electric power for _WEC-Sim_ and _Gazebo_ models when subject to two monochromatic waves (top: \(H=1\) m, \(T=8\) s; bottom: \(H=1\) m, \(T=6\) s). Both models generally exhibit similar dynamics for piston velocity and motor speed, signifying both models’ insensitivity to spring stiffness despite modeling unique spring behavior.  
velocity and motor speed between both models were in close agreement. The time signal of the electric power output in both models generally exhibited a similar pattern, with negative power values resulting from loss calculations. It was also noted that the electric power for both models was lower during piston retraction (positive motor speed) due to the 60% reduction in winding current that was imposed as mentioned in Section 2.1.1.  
Figure 7 provides a detailed examination of the electric power, plotting it against motor speed from data obtained in the 1 m, 6 s monochromatic wave case. Both the _Gazebo_ and _WEC-Sim_ models showed similar dependence with motor speed, an expected result as they employed the same control algorithm.