**1. Introduction**

Wind power generation systems (WPGSs) have become competitive and attractive as exhaustless and clean power sources [1–6]. According to the objectives of variable speed variable-pitch wind turbines (WT), three main operating regions can be observed [7], as illustrated in Figure 1. In Region 1, wind speed is lower than cut-in wind speed (*V*ci), and the WT does not operate; in Region 2, wind speed is between cut-in wind speed (*V*cut−in) and rated wind speed (*V*rated), and the maximum wind power is required to be extracted by rotor speed control; in Region 3, wind speed is between rated wind speed (*V*rated) and cut-out wind speed (*V*cut−out), and its main control objective is maintaining extracted wind power around rated power via blade pitch control and electromagnetic torque control.

**Figure 1.** Main operating regions of the wind turbine.

To keep the wind turbine (WT) within its design limits in Region 3, blade pitch and electromagnetic torque control is primarily applied in limiting the extracted wind power [8]. As the electromagnetic torque has much faster response than the mechanical torque, the decoupled control between the WT and generator can be applied [9]. When wind speed is above rated wind speed, for the WT, the control of the mechanical rotation speed is applied to achieve the required pitch angle. The extracted wind power will vary only in proportion to mechanical rotation speed when the mechanical torque keeps at its rated value. Therefore, extracted wind power regulation is entirely dependent upon mechanical rotation speed regulation. A good tracking of a power reference can be achieved while keeping the rotor speed close to its nominal value. The variable of rotor speed reaches large values that can damage the wind turbine behavior performance in rotor speed regulation by pitch controller [10,11]. For the generator, the electromagnetic torque is required to be maintained at its rated value. When the electromagnetic torque or q-axis stator current and mechanical rotation speed are well regulated, the rated mechanical torque can be achieved. Numerous studies have used the linear techniques and designed controllers based on an approximated linear model for pitch-angle control, such as the linear quadratic Gaussian [12], conventional vector control with proportional-integral (PI) loops [13,14] and PI controller with gain scheduling (GSPI) [10,15]. As the WT contains aerodynamic nonlinearities, the linear controllers designed based on a specific operation point cannot obtain satisfactory performance under time-varying wind speed.

To enhance the performance of the conventional VC and LQG, a nonlinear controller is necessary to be designed for the WT pitch control. One effective solution is employing the feedback linearizing control (FLC) approach. The FLC has been widely and successfully applied in solving many practical nonlinear problems [8,16–18]. Compared to the controllers using linear technique and approximated linear model, a better dynamic performance of nonlinear systems can be achieved under the FLC [19]. The FLC provides fully decoupled control of the original nonlinear system and optimal performance for time-varying operation points. In reference work literature [8], an FLC with an Extended Kalman Filter has been successfully applied in the WT control. In the FLC design, full state information is required to be known. Although the FLC provides better performance than the linear quadratic regulator at low wind speeds, no enhanced performance is achieved at high wind speed, because of model uncertainties. The accurate system model is required to be known in the FLC design [20]. To make up these drawbacks of the FLC, robust control [21–23], fuzzy logic control [10,24,25], sliding mode control [26,27], and neural network control [28], have been proposed. Recently, control methods based on observers have been successfully used to reinforce the robustness of disturbances and model uncertainties in power system [29], permanent magnet-synchronous motor [30,31], photovoltaics inverters [32] and WT [33].

In this paper, a nonlinear adaptive controller (NAC) based on observers is investigated for permanent magnet-synchronous generator-based WT (PMSG-WT) to limit the extracted wind power and provide high performance in Region 3. In the designed NAC, it contains one rotor speed controller and two stator current controllers. One third-order states and perturbation observer (SPO), and two second-order perturbation observers (POs) are employed for the estimations of perturbation terms, including parameter uncertainties, coupling nonlinear dynamics, and disturbances of the PMSG-WT. The estimated perturbations are used for compensating the real perturbation and obtaining adaptive linearizing control of the PMSG-WT. The comparisons of simulation studies among the proposed NAC, FLC, VC and GSPI under three different scenarios, e.g., ramp wind speed, random wind speed and field flux variation, are carried out to verify the effectiveness of the proposed NAC.

The remaining parts of this paper is organized as follows. The model of the PMSG-WT is presented in Section 2. Section 3 presents the design of the NAC. In Section 4, simulation studies are carried out for verifying the effectiveness of the proposed NAC in comparing with the FLC, VC and GSPI. Finally, conclusions of this work are presented in Section 5.
