1. Introduction
In the past few decades, renewable wind energy has received much attention, and wind power generation technology has developed rapidly [
1,
2,
3]. As the power demand of wind turbines continues to increase, the size of wind turbine blades also increases with it. It is crucial to develop a feasible and reliable wind power system control strategy that matches it.
The PID controller has become an important strategy of wind turbine pitch angle control because of its simplicity and robustness. In [
4], a graphical method is proposed to determine the stable boundary value of the pitch angle PI controller, but its complexity increases exponentially with the increase in the system order. In [
5], an expert PID controller based on a track-differentiator is proposed, but the controller has difficulties in reasonably extracting the required differential signals. In [
6], gain and phase margins (GPMs) are introduced and effective graphical methods are used to determine the stable range of PI controller, but the optimal dynamic response cannot be achieved. In [
7], an accurate analysis method for correlation stability of a fractional order PID controller with a certain time delay is proposed. In [
8,
9], a delay margin calculation method is proposed that considers both the stability of a large wind turbine and GPMs in the frequency domain, but it is too complex to calculate. In [
10], a two-degree-of-freedom linearized model was constructed to capture the coupled effects of blade flap and tower fore-aft motions. In [
11], a novel PID controller was proposed, which considered PI parameter settings, unknown delay estimation and actual output delay compensation of a blade pitch angle control system. In general, the wind turbine pitch system can be described with a mathematical model, which is usually a high-order oscillating system with time delay. It increases the complexity of designing a PID controller. For this type of system, conventional PID cannot overcome various disturbances well, and its rapidity and tracking are not satisfactory.
With the emergence and rapid development of advanced control technologies, in order to achieve better control performance, they are gradually applied to the wind turbine pitch angle control system. The authors of [
12] proposed an adaptive fuzzy controller with self-tuning fuzzy sliding film compensation, but the additional noise of the fuzzy controller cannot be completely eliminated, and the expected control effect may not be achieved due to the influence of the pitch rate limitation. In [
13,
14,
15], a pitch angle control system based on a hydraulic valve control motor was proposed, but this system has too low of an operating efficiency and is unlikely to be used in practice. In [
16], the linear quadratic Gaussian (LQG) technique was proposed. The controller has good performance in terms of phase and gain margin, but it cannot adapt to the characteristics of nonlinear wind turbines. In [
17,
18], a collective pitch angle controller based on the Radial Basis Function Neural Network (RBFNN) was designed, and particle swarm optimization was used to optimize RBNFF. However, due to the complexity of the structure, it is hard to apply. The authors of [
19] proposed PSO-RBF algorithms that were successfully effective in wind turbine generator systems with and without time delay. These advanced control techniques cannot be immediately applied to practice due to the limitations of reality.
Considering the unsatisfactory performance of PI controllers and the complicated structure of advanced controllers, this paper proposes to apply the active disturbance rejection controller in wind turbine pitch control. Active disturbance rejection control (ADRC) technology is a simple and practical new control technology proposed by Han [
20]. It is independent of the system model and can better compensate the external disturbances and internal uncertainties of the system. Gao later proposed a linear active disturbance rejection controller (LADRC) [
21,
22], and the structure and parameters of LADRC have been greatly simplified. Because of its strong disturbance rejection ability and its simple structure, it has become a potential substitute for PID control [
23]. However, because the wind turbine pitch angle transfer function is a non-minimum phase, the traditional bandwidth method is difficult to use to tune its parameters; thus, this paper proposes to optimize the LADRC parameters under the robustness constraint.
The rest of this paper is arranged as follows:
Section 2 introduces the transfer function models of the pitch angle control system under different working conditions, and the frequency characteristics are analyzed.
Section 3 introduces the active disturbance rejection control technology, and under the given robustness, the parameters of the active disturbance rejection controller designed for the pitch angle control system are optimized by ES algorithm.
Section 4 simulates and compares the control performance and robustness of the designed LADRC and PI controllers, and shows that the LADRCs have better performance.
Section 5 summarizes and prospects the effects of the control method proposed in this paper.
2. System Model
Figure 1 is a block diagram of the entire wind turbine control system. First, the wind meter measures the speed and the direction information from the wind as an input signal and transmits it to the controller. The controller calculates the reference value of the pitch angle of the wind turbine according to the wind speed and direction information, and the pitch angle controller drives the actuator to change the pitch angle of the wind turbine according to the deviation between the actual pitch angle and the reference value of the pitch angle. The torque signal of the rotor affects the output power of the generator. There are delays in the wind speed measurement and in the pitch angle signal from the hydraulic drive unit. This brings great difficulties to the analysis and design of the pitch control strategy [
4,
17].
In order to make better use of control theory to design LADRC, the wind turbine pitch angle model can be identified. At some operation point, the transfer function from pitch to tower fore-aft deflection is as follows:
Here,
and
represent the time constant of the wind power model, and its value depends on the configuration of the wind power model.
is the overall delay in signal measurement.
The above transfer function was evaluated for various turbine configurations and operating conditions.
WT1: Rotor diameter = 70 m, tower height = 90 m, rated power = 1.5 MW, operating conditions: wind speed = 15 m/s, pitch angle = 0.
WT2: Rotor diameter = 15 m, tower height = 25 m, rated power = 50 kW, operating conditions: wind speed = 15 m/s, pitch angle = 0.75.
WT3: Rotor diameter = 27 m, tower height = 42 m, rated power = 275 kW, operating conditions: wind speed = 15 m/s, pitch angle = 0.
These wind turbine parameters are obtained from [
4]. The three transfer functions obtained are compared with the non-linear simulation prediction in the aeroelastic wind turbine simulator FAST [
24], and it is found that the responses are consistent.
All transfer functions have oscillatory modes with small damping ratios. The Bode diagrams of the three transfer functions are shown in
Figure 2. It is found that
G1 has an oscillatory mode around 7 rad/s.
G3 is similar to
G1, but its oscillation mode is higher (around 11 rad/s).
G2 is different from
G1 and
G3. It has two oscillation modes with smaller magnitude at 10 and 12 rad/s, respectively; thus, it will be more difficult to control
G2 than
G1 and
G3.
4. Discussion
This section compares the first-order LADRC based on PI transformation and ES optimization parameters and the traditional PI controller designed for three different wind turbines under specific working conditions to clarify the superiority of the LADRC control.
For tracking performance, a unit step setpoint is inserted at t = 0 s, and for disturbance rejection performance, a unit disturbance with an amplitude of −1 is inserted at 1 s. The setpoint responses and the disturbance responses of the three systems are shown in
Figure 7,
Figure 8 and
Figure 9. In addition, the robustness of each controller is analyzed.
For large wind turbine
G1,
Figure 7a shows that ES minimizes the cost Function (16) to LADRC parameters that produce a local minimum. In
Figure 7b, the robustness of the system under the control of a PI controller and the first-order LADRC is close; both are around 2.63. The optimized first-order LADRC robustness is lower than them, only 2.04, which means stronger robustness. At the same time, the LADRC itself has strong disturbance rejection performance, which can make up for the disadvantages of low robustness. As shown in
Figure 7c, the optimized first-order LADRC has reached a steady state in 5 s without overshoot, and the rise is stable. The first-order LADRC and PI controllers fluctuated greatly and slowed down during the rising process, and did not reach the steady state until 10 s. As shown in
Figure 7d, when the system is disturbed, the oscillation amplitude of the PI controller and the first-order LADRC is large and the speed to steady state is slow. However, the maximum amplitude of the optimized first-order LADRC is only half of them, and the time to reach steady state is nearly twice as fast and only takes 5 s, which greatly improves the disturbance rejection ability of the system.
For small wind turbine
G2,
Figure 8a shows that ES minimizes the cost function to produce a local minimum. It can be seen from
Figure 8b that
G2 has the worst robustness under PI controller. The robustness of the system under the control of the first-order LADRC is about 2.59, and the optimized first-order LADRC is about 2.0, the robustness is lower than the value of 5.1 for the PI controller. The dynamic characteristics of
G2 are different from
G1. There are two oscillation modes, which will oscillate violently under the disturbance. As shown in
Figure 8d, when the system is disturbed, the oscillation amplitude of the PI controller is the highest and the speed to the steady state is the slowest, while the oscillation amplitude of the first-order LADRC is only 2/3 of that of the PI controller, and the steady state time is also reduced by half. It only takes 3.5 s. The performance of the first-order LADRC optimized by the ES algorithm is greatly increased, and the maximum oscillation amplitude is only half of the original, which greatly improves the disturbance rejection ability of the system. In
Figure 8c, the optimized first-order LADRC has reached a steady state at 10 s, and its response speed is significantly faster than that of PI and first-order LADRC. The unoptimized LADRC and PI controller rise slowly, and still have not reached steady state at 20 s.
For medium wind turbine
G3, the convergence curve of the cost function of
G3 is shown in
Figure 9a. It can be seen from
Figure 9b that, compared with the PI control, the robustness of the first-order LADRC is similar to that of the optimized first-order LADRC, which is much lower than that of PI controller around 2. The response is shown in
Figure 9c. The response curves of the three controllers are compared. The optimized first-order LADRC is faster than the first-order LADRC and faster than the PI controller, and it only takes 3 s to reach the steady state. After the oscillation is caused by disturbance in
Figure 9d, the oscillation amplitude under the control of LADRC is similar and small, reaching steady state faster, which reflects the strong disturbance rejection ability.
It can be seen from the above simulation results that LADRC can achieve better control effects than PI for the pitch angle system with large time delay. It can be seen that LADRC is more prominent than PI in terms of regulation speed and has a shorter rise time. For disturbance rejection, LADRC can significantly reduce the drop rate of the system setpoint, reflecting strong disturbance rejection ability. The ES algorithm parameters are simply optimized, and the effect is good. The optimized first-order LADRC has better control performance than the first-order LADRC. The above examples show that LADRC can be applied to oscillating systems with large time delays and can achieve satisfactory control results.
To further clearly demonstrate the robustness of the system, step and disturbance response experiments were performed with the time delay of the controlled object changed by 30%. The step and disturbance response curves are shown in
Figure 10,
Figure 11 and
Figure 12. For
G1 shown in
Figure 10, the robustness of both the PI controller and the designed LADRC is acceptable, and the control effect is still ideal when the time delay changes. For
G2 shown in
Figure 11, the robustness of the PI controller is weaker against the time delay. The closed-loop system under the PI controller is unstable and diverges seriously. The first-order LADRC also exhibits divergence characteristics when the time delay increases. In contrast, the optimized first-order LADRC has excellent robustness and can quickly and smoothly reach the setpoint regardless of the time parameter changes. For
G3 shown in
Figure 12, the robustness of the PI controller is not desired. Although the closed-loop system is stable under PI when the delay time is increased by 30%, both the step and disturbance curves of the controlled system show a divergent trend when the delay time is decreased by 30%. As the delay time increases or decreases, the LADRC has a little overshoot, but the overall control effect is satisfactory, which shows that the designed LADRC has better robustness.
5. Conclusions
This paper proposes and designs a linear active disturbance rejection controller (LADRC) based on an extremum-seeking algorithm for a large wind turbine pitch angle model with delay under certain robust conditions. In order to facilitate the study, the pitch angle model is considered as a fourth-order oscillation system with time delay, and a first-order LADRC is designed for this model. Under a certain robustness constraint, the ES algorithm is used to optimize the parameters of the LADRC. Finally, the designed LADRC is compared with the traditional PI controller. The simulation results show that the setpoint tracking performance of LADRC is better than that of the PI controller, the rise time is reduced by half, and the steady state can be quickly reached. When the system is disturbed, its oscillation amplitude is small, and the speed of recovery to steady state is fast. When the delay of the system changes, LADRC has a better control effect than the PI controller, and the system always converges, reflecting better robustness. In the actual industrial process, many controlled systems have many disturbance factors, which are greatly affected by time delay, and even lead to system divergence in severe cases. Compared with PID control, LADRC has a simple structure, concise parameters, and strong disturbance rejection, and can solve this problem well. At the same time, the optimization of LADRC parameters by ES algorithm is effective and satisfactory. It can be seen that LADRC is a good choice to replace PID in practical control.