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Multivariable robust blade pitch control design to reject periodic loads on wind turbines

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Abstract

The demand on sustainable operations of large-scale wind turbines necessitates the concurrent advancement of power regulation and load mitigation through blade pitch control. Traditional collective pitch control (CPC) mechanisms can only deal with symmetric disturbances. The advent of individual pitch control (IPC) provides new opportunities to mitigate asymmetric or periodic loads on blades. Nevertheless, difficulties in control synthesis remain. In order for IPC to be truly effective, the complicated dynamic coupling between turbine components has to be accounted for. Moreover, wind turbine dynamics is highly nonlinear, and significant modeling uncertainties exist. In this research, a multivariable robust IPC framework is developed, aiming at rejecting periodic loads. The inter-blade coupling is explicitly modeled to provide response characteristics in the frequency domain. Subsequently, the structured singular values (μ)-synthesis strategy is adopted, as it shows distinct capability of dealing with periodic loads. In particular, weighting functions can be tailored to suppress response peaks at periodic frequencies with guaranteed robustness. Systematic case investigations indicate that, with the proposed IPC strategy, one can achieve significant periodic load mitigation as well as fatigue alleviation in speed-varying wind fields.
Multivariable Robust Blade Pitch Control Design to Reject Periodic Loads on Wind Turbines
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Abstract
      2      .  3  2      
32
*&, 32  
    *4&,    3                 2
5             4      4&    2      
   23 2    2     3
2                  6  3    2
34224&37
0.26
    8  28     *9,.
      3 2   3 2  
8432
 7   8 3  2   
34&3
.3
Keywords: :2  2 0   2  9.

1. Introduction
;3223
 8 2 22
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 *&,  3    2  0   3  
   3  <-.+>        
    2     A  6  ;  B4%C          3
.68*A.CB ,
223<$> %2327
2323
3<)!>%32
*%,23</))>
43323;20
   2  2 3       <)#>   
.324*4&,
3        2            7       
<)#>2
BDE  3     4 <)=>      
;    3    .  .     3      
3=P*,6 4
<)->4&233.223
3  33 6
32223236222
3 <->  %    3  3   2    3  
36
;  2  2   2
A3243
3 323  3  4&
2
2   : 2  
3%
8;
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 2 
322 8
73232<#@>
 37
3 :2
 3 3    C = 2   
22.32:2
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32323:.
2 *I,   8
233:;
  *
,.  2 2
7          3       4        3

.78%
2 22 23
2
;332I
 #2237 =
          -  
; /
2. Wind Turbine Modeling
2.1 General equations of motion
%3273 6
/$=J I;K3 <#+>32;32'
;632632G3;63
237.%;32
22326
  3 22 3 
8227
%  3  
  3         
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4 3   A % 2 *A% , 
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; 282 3LA *
,6;
3.8 <=#> 2023
3  3    3 LA    LA      
3LA.LA%30
322
2322
       A    2     2  ;  2.  3      
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      3 2 <@ #@>  4  2   3 
3 <#@==>3 
4;32
 3        ;    A%  
63
d d
d d
 
 
x Ax Bu B u
y Cx Du D u
*/,
3x2yu
d
u
2
2 )  
2 #  
2 =  
 
2 )  
2 #  
2 =  
 
2 )  2 
2 # 
 
 
 
 
 
 
 
 
 
 
 
x
y 2 
2 =  2 
 
 
 
 
 
 
*",
2 )  
2 #  
2 =  
; 2. 3 
; 3 
 3 
d
 
 
 
 
 
 
 
 
 
 
u
u
*@,
4 3 2    23.   8     
  3  2         6 
 4 2.          8 
6   G 3    2.     3   
8<#$>4333
22
;2.3
2.2 Multi-blade coordinate (MBC) transformation
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B43 L
33
3348*/,2A% 322
6 <=->4
23233
                3      3     .2    *I,
                       .  
*363,
3  3    I          .
 2 <=/>  C   3   I  3 2   
  23  ;  2      ;          2
2<=">;326
I<=->
2626
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   
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   
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 
 
*+,
 
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  
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  
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T
   
   
 
 
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   
 
   
 
   
 
 
   
 
   
 
   
 
*$,
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%    * 3 ,  A%   ; .
 .2 ;   .        2
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2 2 2 2 2 2 2
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2.6%32B4
326332
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2.3 Open-loop transfer functions
% ##I B4 6
;332 72
564
33233 ;
2 G3 3
2 ; :
)+H)-H)"H#!H
##HA)A#
    .  8    23              3

-100
0
100 tilt
0
180
360
-100
0
100
10 010 2
-720
0
720
yaw
10 010 2
Uncertain model
Nominal model
Bode Diagram
Frequency (Hz)
A)833
23*)+H3,3
*)-H)"H#!H##H3,
A )3 833
:32
               8        ;  
2)+H 3A% :3)-H)"
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H#! H##H 382A% 
3332B4
*)+H,3323
8 22.
3
-50
0
50
100
ud avg
-720
0
720
1440
-100
0
100
10 0
-720
0
720
ud tilt
10 0
ud yaw
10 0
Uncertain model
Nominal model
Bode Diagram
Frequency (Hz)
A#823
23*)+H3,
3*)-H)"H#!H##H3,
A#382*;
2, 3  : 2 2 ; 
23*

d
u
3
d
u
,@!I+!I;3*

d
u
,
       #! I  =! I 3     
 2 2    2 2  
37
3. Robust Individual Control Formulation
6  3 2       
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    nP 8 *3 P    8     
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 % 3 2     20   2 6 
 3  3 3      <-> 3 3  2 
0  
 2 02; :
 3   27 5CB .2 3 2    
L3    23 3   
38
3.1 Baseline controllers
4       3
22.
*E &4,<#$>E &43;2
    2  2    :     3  3
2283023
      2    &4.2   
3..2 <)=>
: 72
3%3&4
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   ! 
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)P    4 3  3  8   # P =P  -P 8
3    3.8   4  3        3
2   6  I   3    4 
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2
3.2 Proposed control structure for individual pitch control
% ;67   
3243
      3             2  ;    
         A = 3 3   
273
       L                    3
            2  2; 
     4       2   
     3    6   I    
     3  27  
I3

G3
H

H

3..32323
34223
  3      0    8        8      
A226
;
H
2
r
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M
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A=27
3.3 Structured singular value (µ)-synthesis
4      3        ;        *9,.  
22;3A=

μ
.3222
  2           3
7   3       M. 
8
3A-:
2222G
3              2           2    
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332.<=@>
&2*C&,3A63
2w2238=P*
6,3206 S
      8     4            3  6
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W
    
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W W I
3
p
W
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l
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   .
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 =P *!"G;,80#P-PR8
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  
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  G 8 2 -P   
223
3 3 
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23 2   
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       2   
23:
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W W I
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u
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3
32323223 
82
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A/383
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3
2  2         6
  2         <=@>     
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         2      
..2
3320 3
3   2   ; 
  3  2         A "  4  2
238.33
 .        =P 8    3  
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A@.8333
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!)@+-C C&
  3     A @   2     3
        3      4                     
   L    2                8  
.383
      3  8   :    = P 8      .    
2                 .  .      2

4. Results and Performance Comparison
                      
362H 7
 5CBA%  <=#>   
27322 <#$>2
322 <-!>3)!.
I323323
26
  2 . *E &4, <#$> &4.2
 <)=>2243
2&4.22
E &4 
E &43</>
4.1 Nominal performance around the operating point
:      6               :    
323)+H3)-J2
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*,*2,
*,*,
A+.E &4&4.2
2*,:*)+H23,N*2,E
N*,&N*,I)3
A+*,323A+*2,S+*,3.
2)2)3:
2)  22# 2= 
AA +*2,322&4.2
2        62              
  D  C      
&4.22!!+#=
!!@-=    !!@/-                    3
 2    2   
        % 3  A +*,    2  
   8      3   5  
38 C 
        &4.2            2    
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8*B,3
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4.2 Robust performance
62333
 :3.
2)2)3)-H23
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 !!/$+!!/-"!!/-@   )+H 23
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C &4.2
          2        3    A  $*,  
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4.3 Load mitigation and fatigue alleviation
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    &  2 3  4
2& 2+@"$J+@+$J
2
4  3   2       &    =P 8
2 =P 8  223   =-

A 3 6  2    3 3     
)+H:.3)-H)"H)+H#!H
##H8*B,A))3
C= 3
2 3B 2 3 B3 2. 
B32.BA)) %
          2   I    &4            2
23B 
3 #!J    3     2  3  B  2
 2 2    3        2 /J  
32.B66223
      3 2 .  B   2 =J.)!J 2  
   L    2     ;
233

*,*2,
#-
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/@"
/@@
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/+!
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/+#
/+=
/+-
/+/
/+"
/+@
/++
/+$
/$!
/$)
/$#
/$=
/$-
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
*,*,
A))23B*,23B*2,
32.B*,32.B*,
&42 ' '&4
 'C2
5. Conclusion
          3  2      3        2
%  7     3        3
22C=
3%322
223  .2  *I, 
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Acknowledgment
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References
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... 5 To damp periodic loads in rotor blades caused by unsymmetrical wind fields and gravitational force, independent pitch control (IPC) is required. 6 Stochastic nature of wind is considered as a disturbance to a WT system. Consequently, there is need to reduce its effect on the performance of the turbine. ...
... 14 Robust controllers based on μ-synthesis using DK-iteration procedure have been proposed in previous studies. 6,[15][16][17] In Mirzaei et al, 15 parametric uncertainties in the drive-train are considered in designing a robust controller for better regulation of generated power and rotor speed. However, its impact on the turbine's component loads is not studied. ...
... A robust μ-synthesis approach based on IPC is proposed in earlier research, 6,16 for reducing periodic blade F-W loads. In both cases, a CPC controller is designed as a separate loop for generator speed regulation. ...
Article
Full-text available
Over the past few decades, global demand for renewable energy has been rising steadily. To meet this demand, there has been an exponential growth in size of wind turbines (WTs) to capture more energy from wind. Consequent increase in weight and flexibility of WT components has led to increased structural loading, affecting reliability of these wind energy conversion systems. Spatio‐temporal variation of rotor effective wind field acts as a disturbance to a WT system, hence, necessitating controllers that can cancel this disturbance. Additionally, assumptions made in extracting linear models for controller design lead to modeling errors resulting from changing operating conditions. Previous attempts have proposed robust controllers incorporating wind disturbance models. However, these controllers have been evaluated on smaller WTs, which experience lower structural loading than larger ones. Additionally, a majority these controllers are based on collective pitch control (CPC), hence do not address loading in the blades. To address these challenges, this contribution proposes an independent pitch‐based robust disturbance accommodating controller (IPC‐RDAC) for reducing structural loads and regulating generator speed in utility‐scale WTs. The proposed controller is designed using μ$$ \mu $$‐synthesis approach and is evaluated on the 5 MW National Renewable Energy Laboratory (NREL) reference WT. Its performance is evaluated against a gain‐scheduled proportional integral (GSPI)‐based reference open‐source controller (ROSCO) and a CPC‐based RDAC (CPC‐RDAC) controller, developed previously by the authors. Simulation results for various wind conditions show that the proposed controller offers improved performance in blade and tower load mitigation, as well a generator speed regulation.
... To develop a robust control strategy in which the performance of the IPC system with multiple inputs and outputs is designed by using H∞ norms in reference [69]. This is a proposed robust control method to reduce the effect of periodic loads under all wind conditions in region 3. Thus, the influence of wind disturbances on the blade flap loads is reduced. ...
... The block diagram of CPC and IPC[69]. ...
Article
Full-text available
Renewable energy sources are becoming increasingly popular, especially wind power. According to many criteria, the Wind Energy Conversion System (WECS) can be categorized into various types. As part of their application, in the small and standalone Horizontal Axis Wind Turbine (HAWT), most of the generators utilized in these technologies are Permanent Magnet Synchronous Generators (PMSGs) because of their low weight and high efficiency regarding their cost. This study compares and presents the advantages and limitations of various Wind Turbine (WT) types. In addition, a comparison between the PMSG and doubly fed induction generator has been presented. On the other hand, this paper reviews and analyzed the main control strategies applied in WECS. Based on the available studies in the literature, maximum power point tracking control strategies are widely used to harvest the maximum power from wind energy. This control is divided into indirect power control and direct power control. While the pitch angle control strategies can be classified as traditional collective pitch angle control and individual pitch angle control, which is applied to adjust the rotation speed of WT blades. Nevertheless, machine-side converter and grid-side converter control strategies are among the widely used methods for improving power quality. The conventional control strategies reveal many drawbacks and challenges. However, to reduce and even overcome this issue, combining conventional with robust and intelligent controllers may be a good solution.
... Modern nonlinear control theory can be used in the pitch control system, which considers more additional variables and parameters. The disturbance accommodating control (DAC) [17,18], robust control strategies [19,20], adaptive control [18,21], and model prediction control (MPC) [22,23] methods can adjust the pitch angle to reduce the loads considering constraint parameters such as generator rotation speed and mechanical power. Artificial intelligence control strategies can handle the strong nonlinearity situation resulting from the external environment and the mechanical system. ...
... In this paper, the virtual work generated by the inertial forces of blades, hub and nacelle are mainly considered, which is expressed in Eq. (18). The generalized earthquake loads s are given in Eq. (19). ...
Article
Modern wind turbines are becoming taller and more slender to gather wind energy more efficiently and are increasingly installed in complex environments. Consequently, the new generations of wind turbines are prone to vibration-related problems, making the development of vibration control strategies important. Various pitch angle control methods and dynamic vibration absorbers (DVAs) have been proposed recently to reduce the aerodynamic forces and structural responses of wind turbines. However, these approaches are often implemented independently, limiting the effectiveness of the overall control strategy. In this paper, pitch angle control and DVAs are integrated to improve the performance of wind turbines in a complex environment. Firstly, a simplified eight degree-of-freedoms (DOFs) model of the wind turbine is developed using Lagrange's Equation, and the wind turbine is linearized at specific operating points. The NREL 5MW wind turbine is taken as a benchmark model with strategies based on a proportional-integral (PI) pitch controller. Secondly, the pitch angle of each blade is adjusted by the combination of disturbance accommodating control (DAC) and linear quadratic gaussian (LQG) controller considering the wind speed disturbances. Additionally, the tuned mass damper with inerter (TMDI) is adopted to further suppress the structural vibrations. Thirdly, the passive and active methods of TMDl integrated with the pitch controller are investigated. Lastly, the effectiveness of the integrated control strategies is assessed when the wind turbines are subjected to earthquake and wind loads. The results indicate that combining active pitch control and TMDI can improve the power generation performance of wind turbines by reducing structural responses and damage-equivalent loads, and can also improve the power generation performance more effectively than when they are used separately.
... Vertical wind shear, tower shadow, and gravitational forces, which mainly affects large WTs cause periodic 1P and 3P excitations of the rotor blades and the tower and fixed structure of the WT, respectively [7]. These periodic excitations can be reduced by using independent pitch control (IPC) [8]. In this work, IPC is proposed for reducing WT blade loads. ...
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As the size of wind turbines (WTs) increases, an additional increase in the structural load on the WT components is to be expected. This will have an impact on operational safety in terms of damage and service life. Spatial and temporal fluctuations in wind speed are responsible for the fatigue load during power generation. To minimize the effects of varying stresses, advanced control systems that incorporate appropriate models of the disturbances are proposed. These controllers are usually developed based on reduced-order models of nonlinear WTs so that they can minimize uncertainties such as modeling errors. Although robust controllers are able to deal with uncertainties, they are still only developed for design situations. Therefore, their performance can deteriorate significantly under very uncertain operating conditions. Adaptive controllers, on the other hand, are designed to consider multiple operating points in the design. However, most of these methods do not consider the optimization of different objectives in the design for structural load reduction or speed control of WTs. In this paper, a novel adaptive robust observer-based control strategy for structural load reduction and rotor speed regulation of commercial WTs operating at higher wind speed is proposed. To achieve this, a robust disturbance accommodating controller (RDAC) is combined with an adaptive pitch controller (aIPC). This adapts to changing operating points. The proposed control method is tested on a 1.5 MW reference WT (RWT) developed by the National Renewable Energy Laboratory (NREL). The simulation results show that, compared with the state of the art presented on a gain-scheduled proportional integral (GSPI) and RDAC controllers, the proposed control method reduces the structural load on the rotor blades by 10.7 % and 9.2 %, respectively, and on the tower by 36.2 % and 8.4 %, respectively. It therefore makes a key contribution to mitigating the structural dynamic loads on the WT by reducing the load on several WT components. This is achieved without any significant impact on the rotor speed and power control or the generated power under changing operating conditions.
... With the deepening of wind power research, it has been found that the complex load changes of wind turbines caused by wind fluctuations and turbulence characteristics will adversely affect the output power quality and service life of wind turbines (Yuan et al., 2020). Currently, a wind turbine usually uses pitch control to reduce the load on the blades and ensure a smooth output of power. ...
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In recent years, wind turbines are becoming larger, which will exacerbate the complexity of loads Complex load change affect the output power quality and wind turbine service life so that must be studied. Pitch control is usually used to reduce wind turbine load. In this paper, based on the Light Detection and Ranging (LiDAR) technology and incremental feedforward control theory, an incremental feedforward collective pitch controller is proposed. The controller can be directly superimposed on the traditional collective pitch controller so that the incremental pitch angle can fully compensate wind influence. The effectiveness of the controller is verified by multi-software platform joint simulation and hardware-in-the-loop experiment. The results show that the controller can effectively reduce the wind turbine power and load fluctuation when the variation trend of wind speed in the rotor plane estimate by LiDAR data is the same as the actual wind speed.
... Meanwhile, the complex motion of wind turbines has higher requirements for the structural load, and how to reduce structural cost and maintenance cost is also the main research content. At present, many control methods (Tang et al., 2022;Sarkar et al., 2020;Yuan et al., 2020;Zhang and Plestan, 2021) can reduce the blade load/fatigue and stabilize the platform, but based on the fixed design layout, these control methods have limited ability to reduce the cost. Therefore, novel layout design is the most fundamental solution to reduce the cost, and this section investigates its practical significance according to the corresponding wind energy conversion capacity and rough blade cost estimation of three design methods. ...
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This article provides a survey of recently emerged methods for wind turbine control. Multivariate control approaches to the optimization of power capture and the reduction of loads in components under time-varying turbulent wind fields have been under extensive investigation in recent years. We divide the related research activities into three categories: modeling and dynamics of wind turbines, active control of wind turbines, and passive control of wind turbines. Regarding turbine dynamics, we discuss the physical fundamentals and present the aeroelastic analysis tools. Regarding active control, we review pitch control, torque control, and yaw control strategies encompassing mathematical formulations as well as their applications toward different objectives. Our survey mostly focuses on blade pitch control, which is considered one of the key elements in facilitating load reduction while maintaining power capture performance. Regarding passive control, we review techniques such as tuned mass dampers, smart rotors, and microtabs. Possible future directions are suggested.
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We transform the National Renewable Energy Laboratory (NREL) 5-MW geared equipped monopile wind turbine model into a hydrostatic wind turbine (HWT) by replacing its drivetrain with a hydrostatic transmission (HST) drivetrain. Then, we design an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> loop-shaping torque controller (to regulate the motor displacement) and a linear parameter varying (LPV) blade pitch controller for the HWT. To enhance the performances of the pitch control system during the transition region around the rated wind speed, we add an antiwindup (AW) compensator to the LPV controller, which would otherwise have had undesirable system responses due to pitch saturation. The LPV AW pitch controller uses the steady rotor effective wind speed as the scheduling parameter, which is estimated by the light detection and ranging preview. The simulations based on the transformed NREL 5-MW HWT model show that our torque controller achieves a very good tracking behavior, while our pitch controller (no matter with or without AW) gets much improved overall performances over a gain-scheduled PI pitch controller.
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