## 4 Results and Discussion  
In this section, the performance of the Controlled 4 OWC-based barge platform is compared with the uncontrolled standard barge platform. As it was explained in Section 3.2, in the switching control strategy, the OWCs' valves are open when the wave periods are shorter than 12.35 s, while the control switching commands to close the OWCs' valves for the wave periods longer than 12.35 s. In this control strategy, the green regions shown in Figure 5 are the optimal operating regions. The environmental conditions of zero degree wave direction and still air have been considered for the simulations. To show the capability of the control system for stabilization in time-time, two wave periods have been selected from shorter and longer periods than 12.35 s. In the considered scenario, the controlled 4 OWC-based barge and standard barge platforms are studied by two sea state conditions. The wave period of 10 s starting from 0-100 s with a 0.9 s amplitude and the wave period of 14 s starting from 100-240 s with the amplitude 0.9 s have been considered as shown in Figure 7.  
Due to the very low RAOs 'curves for sway, side-to-side, roll and yaw in Figure 4b,d,e,g, it is expected to see very small oscillations for both the standard barge and controlled 4 OWC-based barge platforms under different sea states. This aspect can be seen in Figures 8b, 9a,c and 10b for sway, roll, yaw and side-to-side motions where slight vibrations are observable. From Figure 4a, it is expected to observe the same oscillations in Surge in time-domain for periods of 10 s and 14 s for both controlled barge and standard barge platforms, shown in Figure 8a. In Figure 4c represented for the heave RAO, It may be observed that the controlled barge platform has lower oscillations in the wave period of 10 s from 0 s to 100 s, shown in Figure 8c. After switching to the wave period of 14 s at 100 s, the oscillations of the controlled barge and standard barge platforms in have are almost the same by consideration of Figures 4c and 8c. Figure 7: Considered wave input to the barge-based platforms. Figure 8: Platforms’ translational modes. (**a**) Surge. (**b**) Sway. (**c**) Heave. Figure 9: Platforms’ rotational modes. (**a**) Roll. (**b**) Pitch. (**c**) Yaw. Note that the aim of the the controlled barge platform is to reduce the oscillations in pitch and fore-aft motions under the considered environmental conditions. As it can be seen in Figures 4f and 5a, the PRAO for the open-OWCs-based barge platform is lower than that of the standard barge platform for the period of 10 s. At this period, the controller open all the valves in the platform so that the platform acts like the open-OWCs-based barge platform. Hence in time-domain shown in Figure 9b, the oscillations in Pitch declined by 30.8% from 4.106 degree for the standard barge platform to 2.841 degree for the controlled 4 OWC-based barge platform. On the other hand with consideration of Figures 4f and 5a, for the wave period of 14 s, the PRAOs for the closed-OWCs-based barge platform is lower than the open-OWCs-based barge platform. Hence, after 100 s when the wave period changes to 14 s in Figure 9b, the controller closes all the valves so that the platform acts like the closed-OWCs-based barge platform. In the figure, the oscillations of the standard barge and closed-OWCs-based barge platforms are almost the same. It was expected from the PRAOs that pitch of the mentioned platforms are almost identical for all the frequencies. For the period of 10 s, the FRAOs in Figures 4h and 5b for the open-OWCs-based barge platform is less than that of for standard barge platform. It means that it is expected to see less oscillations in fore-aft for the open-OWCs-based barge platform, compared to standard barge platform. In Figure 10a starting from 0 s to 100 s with the wave period 10 s, the controller opens all the valves so that the platform acts like the open-OWCs-based barge platform.