1. Introduction
During the operation of wind turbines, uneven wind speeds within the rotating region are influenced by factors such as wind shear, tower shadow, and wind turbulence, leading to uneven structural loads on the turbine blades [
1,
2]. These loads exacerbate fatigue on the blades, pitch bearings, main shaft, and tower components, thereby reducing the expected service life of wind turbine generators (WTGs) [
3]. As WTGs increase in capacity and size, the disparity in wind speed across the rotating area intensifies, amplifying the issue of unbalanced blade structural loads [
4]. Consequently, studying active control technologies for managing WTG loads is crucial for enhancing the longevity of large-scale WTGs and lowering future power generation costs.
Independent pitch control (IPC) technology has emerged as a prominent area of research in active load control aimed at reducing unit loads [
5]. The traditional IPC strategy is to use the Coleman transform method to convert the blade root moment in rotating coordinates into the tipping moment and yaw moment in fixed coordinates [
6]. According to the analysis of control theory, Coleman coordinate transformation will bring serious coupling between the capsizing moment control closed-loop and yaw moment control closed-loop [
7]. The traditional single-input, single-output (SISO) independent pitch controller ignores this coupling, which makes it difficult to ensure the control performance of the system. Many studies optimize PID parameters using intelligent algorithms such as the fuzzy PID, ant colony algorithm, whale swarm algorithm, and immunogenetic algorithm [
8,
9]. While these approaches, combined with optimal control strategies like PID, yield improved results compared to traditional methods, they still ignore the inherent coupling between controllers.
Many scholars have employed multi-objective optimization methods, including game theory and multi-criteria decision-making, to design independent pitch controllers that achieve balanced optimization of load control responses [
10,
11]. A nonlinear pitch control strategy based on the dynamic inversion method has been proposed to enhance speed control performance and reduce tower load [
12]. However, the implementation of such nonlinear algorithms in engineering practice remains challenging. Lidar wind measurement technologies can enhance load control stability through feed-forward control, although they increase unit costs [
13]. Multi-objective optimization algorithms can leverage the coupled dynamics of wind turbine rotation and tower motion to achieve coordinated optimization of power loads [
14]. Linear quadratic regulators have garnered significant attention for their efficacy in stabilizing speed fluctuations and tower motion. Additionally, [
15] discusses pitch controllers designed for adaptive generator speed regulation and disturbance suppression in high wind speed regions. Robust control methods have also been incorporated into pitch controller designs for coordinated optimization of power loads [
16].
Wind disturbances can exacerbate tower loading and significantly impact the stability of wind turbine speed. Therefore, researching effective methods for suppressing wind disturbances is crucial for optimizing power and load fluctuations [
17]. The concept of disturbance adaptive controllers, first proposed by Johnson in 1976, has been successfully applied to the speed regulation of wind turbines [
18]. This concept was later expanded to multivariate control design methods to address sustained wind speed perturbations [
10,
11,
12]. For instance, reference [
19] introduced a state-space approach for managing the dynamic coupling of wind turbines using DAC to mitigate the effects of wind perturbations on overall system dynamics, thereby stabilizing speed and power output. However, this approach does not account for blade oscillations and edge loading. Refs. [
20,
21] applied DAC to regulate rotor speed and reduce blade waving loads at the rated operating point. Ref. [
22] employs a robust disturbance regulation controller in conjunction with an adaptive pitch controller for speed regulation and load management. Ref. [
23] extends observer-based pitch control to floating offshore wind turbines to enhance load alleviation and power regulation. Nonetheless, these controllers are designed for specific operating points and are ineffective under varying conditions. Since the operating point of a wind turbine varies with wind speed, an adaptive control strategy is needed. This strategy employs several parallel control loops, with only one connected to the output, and integrates multi-objective control to comprehensively address rotor speed fluctuations, tower load, and blade load.
Therefore, in order to improve the robustness and stability of the system, an adaptive control strategy is adopted, which uses several parallel control loops, but only one control loop is connected to the output [
24]. The multi-objective control to reduce the rotor speed fluctuation, tower load, and blade load is considered comprehensively. This paper develops an independent pitch adaptive control strategy based on full-state feedback (FSFB) and DAC on the basis of the above research, adopts the DAC to eliminate the dynamic effect of wind disturbance on the system and designs a set of IPC controllers, selects RBFNN for scheduling gain parameter adjustment, and the combination of the output values and controllers are switched to different operating points, which ensures the performance of the pitch system and the robustness between the appropriate trade-off between performance and robustness of the pitch system. The NREL 5MW wind turbine is simulated by FAST and Simulink and compared with the ROSCO controller and DAC controller under different wind conditions, and the simulation results show that the control strategy proposed in this paper can ensure the stability of the output power of the wind turbine, and can further reduce the fluctuation of the rotor speed, and the structural loads of the tower and blades.
The paper is structured as follows.
Section 2 describes the wind turbine model used in this paper.
Section 3 details the design of the FSFB controller and DAC controller.
Section 4 discusses the RBFNN based adaptive IPC controller in detail.
Section 5 presents the simulation results and their analysis under different operating conditions. Finally,
Section 6 presents the conclusions.
2. Wind Turbine Model
OpenFAST adopts a hypothetical modal approach to model the dynamics of the flexible components and uses the theory of foliation momentum to calculate the aerodynamic loads. For a three-bladed horizontal axis WT, OpenFAST uses 24 degrees of freedom (DoFs) for modeling. To simplify the model, Considering the model accuracy as well as the requirements of the control algorithm, six relevant DoFs are selected for the controller design. The selected DoFs encompass drive-train rotational flexibility, generator motion, e, the first blade flap-wise (F-W) bending modes, and the first tower fore-aft (F-A) bending mod. The generalized equation of motion for a wind turbine is expressed as [
25]:
where
is the vector displacement, where
,
,
are the corresponding blade F-W displacement,
is the tower F-A displacement,
is the drivetrain torsional displacement,
is the generator angle of rotation, and
f is the nonlinear function.
is the mass matrix coefficient,
is the vector velocity,
and
denotes the control input vectors and wind disturbance input vectors, respectively,
is the acceleration, and
is time.
OpenFAST was used to linearize the nonlinear model 1 around a steady-state operating point with a wind speed of 12 m/s, a rotor speed of 12.1 rpm, and a blade pitch angle of 4.06 degrees [
26]. A linearised model with small perturbations can be obtained to be used as a control object for pitch controller design. The generalized dynamical equations are described as follows:
where
denotes the linearised system state matrix,
,
denotes the control input matrix and the perturbation matrix,
,
,
all denote the output-related matrices, and
denotes the independent pitch angle of the perturbation
, the perturbed hub wind speed
is denoted by
, and the output measurements
denotes the generator rotational speed
and the blade F-W displacement
,
,
.
Transforming individual blade dynamics into a non-rotating coordinate system using the MBC transform is essential for facilitating the design of the IPC controller. Subsequently, The effect of azimuth on wind speed can be eliminated, thus reducing the effect of periodicity on the control model and improving the accuracy of the linear time-invariant model. The MBC coordinate transformation transforms as:
where
is the azimuth angle of the reference blade.
4. Adaptive Independent Pitch System Design
4.1. RBF Neural Network Architecture
A typical RBFNN topology comprises an input layer, a hidden layer activated by a radial basis function, and an output layer. The advantages of RBF neural networks include rapid learning speed, a simple structure, and superior approximation capabilities for nonlinear systems. Utilizing RBF neural networks for the learning and optimization of gain scheduling parameters can significantly enhance overall system performance. In this study, collective pitch angle and tower fore-and-aft displacement are employed as input parameters for training the RBFNN.
Figure 1 illustrates the schematic diagram of the RBFNN structure.
In the architecture of RBFNN,
denote the radial basis vector,
denote the input vector, and
denotes the Gaussian function.
where
denote the basic width vector. The expression of the network output vector is as follows:
where
denote the weight vector.
To ensure the accuracy of the Radial Basis Function (RBF) neural network training, The linearized collective pitch angle and tower fore-aft displacements are selected as inputs. The hidden layer utilizes a Radial Basis Function, while the output layer predicts the variable pitch angle and tower fore-aft displacement. Normalization is applied to facilitate the design of the controller, and the final output represents the value of the runnable controller. The training process focuses on determining the center and variance of the RBF, as well as learning the weights. During training, the update step size is set to 2000, and the sampling time is T = 0.00125 s, which is consistent with the time step used in the overall MATLAB/Simulink 2023 simulation system.
Initially,
randomly selected centers are chosen, and iterative optimization is performed to continuously update the clustering centers and reassign data points to the nearest centers until the optimal clustering effect is achieved. For the radial basis function of the Gaussian kernel, the variance is determined using Equation (14).
denotes the maximum distance between the selected center points.
The centers of the hidden neurons are determined using the k-means algorithm to cluster the input data. The average distance from each cluster center to its assigned data points, denoted by , is then computed. The specific steps of the algorithm implementation are as follows:
Step 0: Randomly initialize the clustering centers and weight matrix.
Step 1: Enter the loop and check if there is remaining data to be processed.
Step 2: Calculate the activation and output values according to Equation (13).
Step 3: Calculate the mean square error according to Equation (14). If the mean square error exceeds 1, iterate through each data point to update the centers.
Step 4: Evaluate the activation values and update the temporary cluster centers.
Step 5: Return to Step 2 and repeat the calculations until the cluster centers and weights meet the specified criteria.
Given the known center, variance, and weight vectors of the hidden layer basis functions, the outputs from the hidden layer are combined linearly to determine the gain that achieves the target value. Subsequently, the appropriate operating point for the outputs is selected in conjunction with an independent pitch controller.
4.2. Adaptive Independent Pitch Control System Design
When a wind turbine is in operation, variations in wind speed can alter aerodynamic loads, thereby impacting the stability and transient response of the turbine. Especially during gusts or extreme weather conditions, rapid fluctuations in wind speed may subject the mechanical structure to significant impacts or even lead to fatigue damage. Consequently, gain scheduling control is employed to design distinct controllers for varying wind speeds and to adjust controller gains based on the wind speed. This approach utilizes a range of linearized models that best represent the wind turbine. The linearized models used to design each individual pitch controller were extracted from the nonlinear wind turbine generator model (1), as shown in
Table 1, for various operating points. Each linear model, characterized by a constant wind speed and corresponding blade pitch angle, is used to derive the individual pitch controllers.
As shown in
Table 1, Seven independent variable pitch controllers are designed for wind speeds ranging from 12 m/s to 25 m/s to determine the operating point gain. A RBFNN is utilized to predict the approximate linear operating point. To better integrate with gain scheduling, the collective pitch angle, and tower displacement are selected as inputs to the RBFNN to determine the appropriate operating point for the wind turbine. Both scheduling parameters can be directly derived from rotor speed. Parameter values obtained from linearization are used as inputs
to the RBFNN.
denotes the tower F-A displacement, and denotes the collective pitch angle. The Gaussian function is chosen as the RBF for neural network training. To simplify controller selection, the output is set to a value indicating whether the controller should be activated, ranging from 1 to 7. The trained neural network model is converted into a Simulink visual model, facilitating its integration with the controller.
The structure of the adaptive independent pitch control system is shown in
Figure 2. The measured output y of the full-state feedback control loop varied by MBC passes through a low-pass filter and is used as the input to the controller, which updates the outputs
and
according to Equations (10) and (11) and combines them with the RBF training loop to form the adaptive control, and the outputs are inverted by the MBC and added with the reference value of the steady-state operating point of the pitch angle
and then pass through the pitch angle saturation module, the pitch input signals
,
,
of each blade are obtained from the pitch angle saturation module and the speed limiting module. The independent pitch angle modifies the collective pitch signal to create the control input for the FAST wind turbine model. Given that the IPC gain is designed using a control method that ensures closed-loop stability and targets specific objectives, the robustness and stability of the RBF + AIPC combined control strategy is assured.
6. Conclusions
To enhance system stability and robustness, a multi-objective control approach is employed to comprehensively address rotor speed fluctuation, tower load, and blade load. An independent pitch adaptive control strategy utilizing full-state feedback and perturbation regulation is proposed. A suitable linear time-invariant state space equation is established. Perturbation regulation control is implemented to mitigate the impact of wind disturbances. Additionally, a set of IPC controllers is designed for various operating points, RBF neural networks are employed to train scheduling parameters, and these components are integrated to form an adaptive control loop. The simulation results demonstrate that the proposed controller shows superior performance overall in reducing structural loads and controlling velocity. It is robust to wind turbine modeling errors and nonlinearities and adapts to operating point variations caused by wind disturbances. Additionally, it further reduces tower and blade loads and enhances the stability of wind turbine operation.
The primary limitation of this research is the use of a linearized reduced-order model in the controller design process, which may not fully account for the stability and uncertainty of the closed-loop system. Additionally, unstructured uncertainty has not been analyzed in detail. In practical wind turbine operations, the mobility of the blade pitch actuator is crucial, especially in high wind speeds and turbulent conditions. Future work could explore the use of robust controllers and the development of appropriate weighting functions to reduce the 1P frequency in the blades and enhance control performance. Furthermore, to better characterize uncertainty, future research could incorporate additional system parameter uncertainties, particularly when the wind turbine operates below rated power, which may enhance control robustness.