## 5 Simulation Results under Irregular Conditionsfor Various Wave Period and Height  
Here, we analyze differences between two previously-mentioned types of controllers in the set time domain. We show that increasing the instant efficiency of the turbine or maintaining a certain angular velocity will effect the converting efficiency of the chamber stage. Therefore, an analysis of how the overall system, including the chamber stage, influences the overall power output is needed.  
In brief, our system consists of a chamber, turbine, DC electrical generator and terminal load attached to the generator. Due to the assumption that the only controllable parameter is the damping coefficient \(b_{g}\), which is produced by the generator and decided by the load, from the electrical analysis point of view, the analysis with the simplest electrical component should precede, and constant linear damping is produced from the simplest electric component, the resistor. Additionally, the constant resistor \(R_{e}\) in (16) provides the constant damping coefficient \(b_{g}\). Accordingly, we choose the results of constant damping \(b_{g}\) as the comparison results group for the controlled results. We set the standard as the maximum power extraction when \(b_{g}\) is at a constant.  
Similar to the previous simulation, we measure the average power extraction \(\bar{P}_{t}\) with the same chamber, turbine and ocean state, when \(b_{g}\) is held constant. We obtained the maximum power extraction when \(b_{g}=10^{-3}\sim 1\), for the various \(H_{s}\) and \(T_{p}\), by running a simulation for \(T_{m}=5000\) s, when \(H_{s}\) was between 0.4\(\sim\)5 m, for every 0.2 m, and when \(T_{p}\) was between 6\(\sim\)18 s, for every 1 s. For the sake of convenience, we set the maximum power extraction with fixed \(b_{g}\) as \(\bar{P}_{t,max}\) and calculate accordingly.  
\[\bar{P}_{t,\max}\left(T_{p},H_{s}\right)=\max_{b_{g}}\frac{1}{T_{m}}\int_{0}^{ T_{m}}b_{g}\Omega^{2}dt. \tag{31}\]  
The damping coefficient at maximum power is defined as \(b_{g,max}\). We also set the relative time average turbine efficiency as \(\bar{\eta}_{t}^{*}=\bar{\eta}_{t}/\eta_{t}(\phi_{0})\).  
Figure 11: Results of the CAV controller with various \(k_{p}\) under an equivalent irregular wave condition when \(\Omega_{d}=550\) rad/s: (**a**) relative root mean squared error of \(\Omega\); (**b**) average power extraction from the turbine; (**c**) average turbine efficiency and its maximum value.  
Figure 12 shows \(\bar{P}_{t,max}\), \(\bar{\eta}_{t}\) and \(b_{g,max}\) under irregular waves with a PM wave spectrum having various \(H_{s}\) and \(T_{p}\). As seen in Figure 12c, in most areas except for those having a long wave period (\(T_{p}\geq 16\) s) and a low wave height (\(H_{s}\leq 0.6\) m), \(\eta_{t}^{*}\) is higher than 0.9. From this, it can be inferred that tracking the turbine efficiency is somewhat consistent with tracking the overall system performance.  
The results from the controllers will only deal with the power extraction with respect to \(\bar{P}_{t,max}\), which is calculated as follows:  
\[\bar{P}_{t}^{*}\left(T_{p},H_{s}\right)=\frac{\bar{P}_{t}\left(T_{p},H_{s} \right)}{\bar{P}_{t,\max}\left(T_{p},H_{s}\right)}. \tag{32}\]