## 7 Conclusions  
The paper proposes an airflow control strategy to deal with the undesired stalling phenomenon of the Wells-turbine-based oscillating water columns. The proposed strategy takes into consideration  
Figure 19: Airflow speed in uncontrolled and controlled cases with real wave data input.  
Figure 20: OWC torque and power outputs with real wave data input. (**a**) Torque in the uncontrolled case. (**b**) Power in the uncontrolled case. (**c**) Torque with ZN-PID. (**d**) Power with ZN-PID. (**e**) Torque with SGHS-PID. (**f**) Power with SGHS-PID.  
the aerodynamic characteristics of the studied Wells turbine and implements a control using a PID controller to govern an air valve situated within the capture chamber of the OWC system.  
To efficiently tune the parameters of the PID with such a complex system, a recourse to optimization theory has been proposed, specifically by using developed variants of the Harmony Search algorithm. The algorithms were implemented and tested to get to the final variant (i.e., SGHS). The parameters obtained by the SGHS algorithm were then used in the PID controller to simulate the OWC system with the proposed airflow control scheme.  
Finally, in order to show the effectiveness of the proposed strategy and tuning technique, two comparative study cases have been carried out between the uncontrolled OWC and the controlled OWC using the airflow control with a Zeigler-Nichols-tuned PID (ZN-PID) and a SGHS algorithm-tuned PID (SGHS-PID). The first case study considers two different sea conditions of regular waves, whereas the second case study considers real measured wave data. The results of the studies demonstrate successful avoidance of the stall effect with both airflow control cases. However, the control using the SGHS algorithm shows superior performance to the traditional tuning method.  
All authors contributed to the modeling and implementation of the OWC plant. All authors conceived, developed and implemented the control techniques. All authors analyzed and validated the results. All authors contributed to writing-review & editing the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
This work was supported in part by the Basque Government, through project IT1207-19 and by the MCIU/MINECO through RTI2018-094902-B-C21 / RTI2018-094902-B-C22 (MCIU/AEI/FEDER, UE).  
The authors declare no conflict of interest.  
The following symbols are used in this manuscript:  
\begin{tabular}{l l} \(\lambda\), \(A\), \(H\) & Wavelength, amplitude and height (m) \\ \(h\), \(z\) & Sea depth and wave surface elevation (m) \\ \(T_{w}\), \(\omega\) & Wave period (s) and wave frequency (rad/s) \\ \(g\) & Acceleration gravity (m/s\({}^{2}\)) \\ \(dP\) & Pressure drop (Pa) \\ \(w_{c}\), \(l_{c}\) & Capture chamber inner width and length (m) \\ \(V\), \(Q\) & Capture chamber volume (m\({}^{3}\)) and flow rate (m\({}^{3}\)/s) \\ \(\rho\), \(v_{x}\) & Atmospheric density (kg/m\({}^{3}\)) and airflow speed (m/s) \\ \(l,b,D\) & Blade chord length, blade span and turbine diameter (m) \\ \(n\), \(p\), \(k\), \(K\) & Blade number, pole number, wave number and turbine constant \\ \(T_{e}\), \(T_{t}\) & Electromagnetic and turbine torques (N.m) \\ \(J\) & Turbo-generator inertia (kg.m\({}^{2}\)) \\ \(C_{t}\), \(C_{a}\), \(\phi\) & Torque, power and flow coefficients \\ \(R_{s}\), \(R_{r}\) & Stator and rotor resistances (\(\Omega\)) \\ \(L_{s}\), \(L_{r}\) & Stator and rotor inductances (H) \\ \(i_{s}\), \(i_{r}\) & Stator and rotor currents (A) \\ \(\psi_{s}\), \(\psi_{r}\) & Stator and rotor flux (Wb) \\ \(\omega_{s}\), \(\omega_{r}\) & Stator and rotor rotational speed (rad/s) \\ \(e\) & Error between the reference variable and measured variable \\ \(u\) & Control signal obtained from the PID controller \\ \(K_{p}\), \(K_{i}\), \(K_{d}\) & Proportional, integral and derivative gains of the PID controller \\ \(\textbf{x}^{*}\) & Optimal solution for the problem \\ \(f\) & Cost function \\ \end{tabular}