## 4 Simulation Analysis  
### System Parameters  
According to reference [32], the parameters of the SOFC system can be obtained as in Table 2.  
Since an SOFC is a system with strong nonlinearity, it is not easy to tune the LADRC using the primitive mathematical model, so it needs to be linearized. In this paper, the IFA is used to optimize the parameters of the LADRC controller, and the method is compared with the traditional PID. Various aspects analyze the performance of FA-PID, FA-LADRC, IFA-PID, and IFA-LADRC control schemes in the offshore wind power SOFC system. The LADRC structure of the SOFC system is shown in Figure 5.  
In this paper, the transfer function of the SOFC system is obtained using the model in reference [32] after linearization. The expression is as follows:  
\[G(s)=\frac{2.417s+0.8276}{s^{3}+0.716s^{2}+0.1808s+0.006914} \tag{26}\]  
The objective function, constraints, and termination conditions are set as follows:  
1. Objective function: To quantify the performance of the control system, the deviation performance index IAE is used to evaluate the performance of the LADRC. That is, it  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Value** \\ \hline \(K_{H_{2}}\) & 0.843 mol/(s atm) \\ \(K_{H_{2}O}\) & 0.281 mol/(s atm) \\ \(K_{O_{2}}\) & 2.52 mol/(s atm) \\ \(K_{r}\) & 0.993 \(\times\) 10\({}^{-3}\) mol/(s A) \\ \(\tau_{H  
is used as the fitness function of the algorithm, and the expression of the minimum objective function to be optimized is \[J=\int\limits_{0}^{t_{a}}|e(t)|dt\] (27) where \(e(t)\) is the SOFC control error. The smaller the value of the expression \(J\), the better the control effect.
2. Constraints: The parameters of the firefly algorithm are set as follows: The number of firefly populations nPop is 5, and the number of dimensions nVar is 3, where the three variables to be optimized are \(\omega_{0}\), \(\omega_{C}\), and \(b_{0}\), and the range of decision variables Var is empirically set as \[0.05\leq\text{Var}\leq 0.75\] (28) The initial value of step length is 0.2, the initial attraction value is 2, and the light absorption coefficient is 1.
3. Termination criterion: To make the parameters close to the optimal values, the maximum number of update iterations of the firefly algorithm is set to 50.  
In the process of continuous iteration, the objective function will gradually converge to a minimum value, at which time, the optimal solution is found, and the specific adaptation value convergence curve is shown in Figure 6.  
As seen in Figure 6, the IFA has a faster convergence rate in the early iteration process than the common FA. After about 20 iterations, it can be seen from the convergence results that the error integral convergence function value of the PID scheme is higher than that of the LADRC scheme. Therefore, it is known that LADRC has better adaptability to the FA, has a better convergence rate to the IFA, and can reach the optimal solution faster to avoid the \"premature\" phenomenon.  
The optimization parameters obtained by four specific control algorithms after 50 iterations are shown in Tables 3 and 4. After 50 iterations, the system with the control algorithm using IFA-LADRC has a smaller value of the error integral convergence function. Specifically, the system with the IFA-LADRC control algorithm outperforms the FA-LADRC control algorithm and the IFA-PID control algorithm by 0.49% and 68.62%, respectively. This shows that the system with the IFA-LADRC control algorithm has stronger stability and better control effect.  
Figure 6: Convergence curve.