## 5 Internal Control Techniques
### RSC Control
#### 5.2.2 Nonlinear RSC Internal Control  
Since conventional PID controllers are designed based on linearized system models, they usually show poor performance during severe grid faults. Thus, many nonlinear control methods were proposed to provide better control effect for DFIG-WTs under large disturbances.  
Sliding mode control (SMC) is an intermittent control signal-based nonlinear control method. In Reference [73], SMC was applied in DFIG-WTs to restrict the oscillations in electromagnetic torque and stator active power, which improved the system robustness. However, the application of SMC may lead to the decreasing capability to generate power under large disturbances. A decentralized nonlinear control (DNC) method was proposed in Reference [74] to improve the transient stability of DFIG-WTs. Based on the differential geometry theory, this LVRT technique can linearize the complex DFIG model and realize optimal control for DFIG-WTs. This exact linearization based method can significantly improve the LVRT capability compared to the conventional PI controller. However, due to the fluctuation in stator terminal voltage, the strict assumption of exact linearization is hard to achieve, which limits the application of the proposed method.  
Input-to-state stability (ISS)-based control was applied to DFIG-WTs in Reference [75]. Based on the mechanism where the existence of ISS control Lyapunov functions can be used to demonstrate the input-to-state stability of nonlinear systems, a decentralized ISS control law was proposed for the RSC to enhance the transient stability of wind turbines. However, ISS-based controllers can only ensure the inverse optimality, while combination with other control techniques is needed to further optimize the ISS control parameters. By reasonably designing the state-dependent coefficient (SDC) matrices and weighting matrices, an effective RSC control scheme based on the state-dependent Riccati equation (SDRE) technique was proposed in Reference [19]. The implementation of the SDRE control method can simplify control and mitigate the impact of grid voltage dips. Moreover, different selections of SDC matrices lead to different control performance, whereas the extra freedom in selecting non-unique SDC matrices makes the robust H\(\infty\) controller design more flexible [76].  
Fuzzy control can provide desirable control performance for DFIG-WTs during severe disturbances such as three-phase short-circuit faults and sudden changes in wind speed, while linear control schemes cannot predict the behavior of DFIGs correctly in this case [77; 78]. The fuzzy logic controller is known for its adaptability to nonlinear systems and the function of reducing computational complexity. In Reference [78], two fuzzy logic controllers were implemented in RSCs. One was applied to control the direct current proportional to the generated reactive power, and the other was applied to control the quadrature current proportional to the generated active power. Simulation and experimental results showed that the fuzzy logic controller has a faster and a more accurate response when compared with PI controllers. Compared with the fuzzy logic controller, the interval type-2 fuzzy PI controller (IT2-FPI) is generally more robust and has a smoother control surface around the steady state [79]. Thus, the IT2-FPI can also be applied in DFIGs to provide ideal capability of handling uncertainties during grid voltage dips. The proposed strategy can provide a satisfactory performance in power oscillation damping without the need to retune controller parameters. Furthermore, a fuzzy operator was applied in DFIG-WTs to scale the variables of optimization including PI gains of DFIG controllers and SFCL parameters in Reference [53]. The fuzzy operator scaled the objective functions within the range of [0, 1], and the max-geometric mean operator aggregated the scaled objective functions. This optimization algorithm could smooth output power and improve the LVRT capability through multi-objective optimization.