# Adaptive Pitch Control of Variable-Pitch PMSG Based Wind Turbine
## 4 Simulation Results
### Robustness Against Parameter Uncertainty  
For a practical PMSG-WT system, the operating temperature, manufacturing tolerance and magnetic saturation effect may result in the variation of system parameter values. The control  
Figure 8: Estimations of states and perturbations. (**a**) Estimation of mechanical rotation speed \(\omega_{\text{m}}\). (**b**) Estimation of perturbation term \(\Psi_{1}\). (**c**) Estimation of \(i_{\text{md}}\). (**d**) Estimation of perturbation term \(\Psi_{2}\). (**e**) Estimation of \(i_{\text{md}}\). (**f**) Estimation of perturbation term \(\Psi_{3}\).  
Figure 7: Responses of the PMSG-WT to random wind speed. (**a**) Wind speed V. (**b**) Mechanical rotation speed \(\omega_{\text{m}}\). (**c**) Relative error of \(\omega_{\text{m}}\). (**d**) Power coefficient \(C_{\text{p}}\). (**e**) Active generating power \(P_{\text{m}}\). (**f**) Reactive generating power \(Q_{\text{m}}\).  
performance of the VC, FLC and proposed NAC is tested under field flux variation. Please note that the wind speed is kept at 18 m/s. The variation of field flux \(K_{e}\) is shown in Figure 9a.  
In Figure 9b, the proposed NAC can provide better tracking performance of the mechanical rotation speed \(\omega_{\rm m}\), compared with the VC and FLC. The maximum relative error (\(\frac{\omega_{\rm m}-\omega_{\rm mt}}{\omega_{\rm mt}}\times 100\%\)) reaches approximately 5% and 1% under the FLC and VC, respectively. The control performance of the VC and FLC are both affected by field flux variation. In Figure 9c,d, the responses of the required pitch angle \(\beta_{\rm r}\) and power coefficient \(C_{\rm p}\) are shown. The active generating power \(P_{\rm m}\) and reactive generating power \(Q_{\rm m}\) of the PMSG-WT are shown in Figure 9e,f, respectively. The active generation power \(P_{\rm m}\) cannot be kept at its rated value under these three controllers, especially under the FLC. The reactive generating power \(Q_{\rm m}\) is almost unaffected under the NAC.  
In addition, Table 3 shows the control performance of these three controllers via integral of absolute error (IAE) in different simulation scenarios. Here, \(IAE_{x}=\int_{0}^{T}|x-x^{*}|\). The reference value of the variable \(x\) is \(x^{*}\). The simulation time \(T\) is set as 20 s. It can be seen from Table 3 that in first and second simulation scenarios, the \(IAE_{i_{d}}\) and \(IAE_{i_{d}}\) are both almost around 0 A.s under these three controllers. Compared with the VC and FLC, the \(IAE_{\omega_{\rm m}}\) is smaller under the proposed NAC. In the field flux variation simulation scenario, the NAC can provide much smaller \(IAE_{i_{d}}\) and \(IAE_{\omega_{\rm m}}\) than  
Figure 9: Response to field flux \(K_{e}\) variation under constant wind speed. **(a)** Variation of field flux \(K_{e}\). **(b)** Relative error of mechanical rotation speed \(\omega_{\rm m}\). **(c)** Required pitch angle. **(d)** Power coefficient \(C_{\rm p}\). **(e)** Active generating power \(P_{\rm m}\). **(f)** Reactive generating power \(Q_{\rm m}\).  
those achieved by the VC and FLC. Compare with the VC, the FLC is more significantly affected by field flux variation.  
The proposed NAC can always provide a satisfactory performance. This is because the proposed NAC can estimate all uncertainties without knowing detailed system model. Therefore, it has better robustness than the FLC, which requires accurate system parameters. Meanwhile, the control performance of the VC is affected under parameter variations [29].