## 3 Problem Statement
### Control Statement  
In this part, a switching control strategy is proposed in order to have a system with lower oscillations, particularly in the pitch and fore-aft motions. In the previous subsection, three platforms' performance under different sea states have been evaluated. Among different modes with consideration of the environmental condition described in the last section, the PRAO and FRAO have been selected for more detailed evaluations in this section.  
In the Section 3.1, it was illustrated that the standard barge and closed-OWCs-based barge platforms' RAOs have almost identical curves with slight differences. It proves that the behaviour of the platforms are the same for different modes.  
Figure 5a,b show the PRAO and FRAO for the closed-OWCs-based barge and open-OWCs-based barge platforms in blue dash and red, respectively.  
The closed-OWCs-based barge platform represents a barge platform equipped by four OWCs when the valves are closed, while the open-OWCs-based barge platform represents a barge platform housing four OWCs when the valves are open. It can be seen in Figure 5a,b that the PRAO and FRAO for the open-OWCs-based barge platform have lower values compared to the open-OWCs-based barge platform when the wave period is shorter than 12.35 s. On the other hand, for the wave periods longer than 12.35 s, the PRAO and FRAO for the closed-OWCs-based barge platform are higher than those of for the open-OWCs-based barge platform. It means that for the wave periods shorter than 12.35 s, the open-OWCs-based barge platform has less oscillation (better performance) than the closed-OWCs-based barge platform. Also for the wave periods longer than 12.35 s, the closed-OWCs-based barge platform has less oscillation (better performance) than the open-OWCs-based barge platform. Hence, the green regions in Figure 5a,b represent the optimal operating regions with better performance.  
The performance analysis of the platforms in Figure 5 gives the idea of the control strategy for reducing oscillations in the system. Block diagram of the controlled FOWT is represented in Figure 6. In this control system, there are the FOWT with a sensor attached to the bottom of the platform for measuring the wave periods. The measured values of the sensor goes to the switching control. The switching control commands the system to open the valves when the wave periods are shorter than 12.35 s. On Also, the valves are commanded to be closed when the measured wave periods are longer than 12.35 s. This control strategy gives this ability to the system to have the optimal performance in the green regions.  
The sensor used in the control system for measuring the wave periods can be an Acoustic Doppler Current Profiler (ADCP) which is a device to measure the water speed transferring through the whole water column [32]. An ADCP attached to the seabed may  
Figure 5: RAOs for (**a**) Pitch. (**b**) Fore-aft.  
Figure 6: Block diagram of controlled FOWT.  
measure current velocity at the bottom as well as equal intervals all the way up to the surface. In very deep areas, they can be lowered on a cable from the surface. In our case, the ADCP is mounted at the bottom of the barge platform facing downwards, similar to those mounted into ships.  
By Doppler effect phenomena, water currents can be measured by the ADCP with sound by means of a principle of sound waves. Pings of sound are sent at a constant frequency to the water and then they are rebounded off the particles suspended in the moving water and reflected to the device. Because of the Doppler effect, there is a slight deference in frequency between the waves that the profiler transmits and the waves it receives which is known as Doppler shift. Using this shift, the device calculates the velocity of the particle and the water around it.