## 4 Simulation Results  
To assess the effectiveness of the proposed MFC (PMFC) technique, simulations were conducted using the MATLAB/Simulink environment. The simulations are based on the system depicted in Figure 11. The power conversion system's parameters are detailed in Table 1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbol** & **Value** \\ \hline Kite’s area & \(A\) & 3 m\({}^{2}\) \\ Air density & \(\rho_{air}\) & 1.225 kg/m\({}^{3}\) \\ Lift coefficient & \(C_{L}\) & 1 \\ Drag coefficient & \(C_{D}\) & 0.33 \\ Pole pair number & \(p\) & 2 \\ System total inertia & \(I\) & 0.03 kg m\({}^{2}\) \\ Viscous damping & \(D\) & 0.005 N.m.s \\ Machine inductance & \(Ls\) & 6 mH \\ Machine resistance & \(Rs\) & 0.2 \(\Omega\) \\ Machine flux linkage & \(\varphi_{m}\) & 0.6 Wb \\ DC-link capacitance & \(C\) & 4700 \(\mu\)F \\ Grid-side filter inductance & \(L_{f}\) & 20 mH \\ Grid-side filter resistance & \(R_{f}\) & 0.5 \(\Omega\) \\ Carrier frequency & \(F_{c}\) & 5 kHz \\ Sampling time & \(T_{S}\) & \(5\times 10^{-6}\) s \\ \hline \hline \end{tabular}
\end{table}
Table 1: Kite generator system parameters.  
Figure 10: Control diagram of the proposed MFC.  
Figure 9: TD output curves for linear and nonlinear variation in \(\lambda\).  
Here, the PMFC strategy is being compared to the integral-proportional (IP) regulator depicted in Figure 12, and with the conventional MFC without the TD.  
The IP controller is chosen over the PI controller to eliminate the zero typically present in the closed-loop transfer function of PI controllers in order to mitigate overshoot during transient phases [40]. The IP controller parameters are obtained by synthesizing the closed-loop system with a response of a second-order system of the following canonical form.  
The parameters of the integral-proportional (IP) controller are obtained by synthesizing the closed-loop system response to match a canonical second-order system form [15].  
\[H(s)=\frac{1}{1+\frac{2m}{\omega_{n}}s+\frac{1}{\omega_{n}^{2}}s^{2}} \tag{42}\]  
This approach ensures the IP controller is designed to deliver the desired transient characteristics, such as natural frequency \(\omega_{n}\) and damping ratio \(m\). Then, the proportional and integral parts are obtained as follows:  
* \(K_{p\omega}=\frac{2D}{3\varphi_{m}}(2m\tau_{m}\omega_{n}-1)\)
* \(\tau_{iw}=\frac{3K_{p\omega}P_{m}}{2D\tau_{m}\omega_{n}^{2}}\).  
where \(\tau_{m}=J/D\), and \(\varphi_{m}\) is the machine flux linkage. The parameters for IP controller are then selected as \(\omega_{n}=10\) and \(m=1.1\), providing the desired system dynamics.  
The gains of the MFC are manually tuned following the procedure outlined in [26]. The tuning process begins by selecting a very large \(\alpha\) and a high \(K_{p}\), ensuring a minimal steady-state error. Next, \(\alpha\) is gradually reduced to achieve a quick, oscillatory response, enhancing the system's speed. Finally, \(K_{p}\) is decreased incrementally to stabilize the system, balancing responsiveness and stability.  
To ensure a fair and meaningful comparison of the control strategies, the parameters for the MFC were adjusted, before introducing the TD, so that the system exhibits the same  
Figure 11: Global diagram of the grid-connected PKGS control.  
Figure 12: Block diagram of the IP controller.  
dynamic response as when the IP controller is used with its selected parameters. After tuning, the MFC parameters were determined to be \(K_{p}=8\) and \(\alpha=1.5\times 10^{5}\).  
The TD parameters are chosen as \(\rho=40\), \(c_{1}=2\), \(c_{2}=20\), \(a=0.4\), \(b=0.5\), and \(\xi=0.03\).  
For the DC-link and current regulation within the GSC control, as well as for the inner current loops in the MSC control, the control strategy employs the classical PI control method. This configuration is depicted in Figure 11.