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Yuan Yuan
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
X. Chen
Assistant Professor
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
J. Tang
1
Professor
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: jtang@engr.uconn.edu
Disturbance Observer-Based
Pitch Control of Wind Turbines
for Enhanced Speed Regulation
Time-varying unknown wind disturbances influence significantly the dynamics of wind
turbines. In this research, we formulate a disturbance observer (DOB) structure that is
added to a proportional-integral-derivative (PID) feedback controller, aiming at asymp-
totically rejecting disturbances to wind turbines at above-rated wind speeds. Specifically,
our objective is to maintain a constant output power and achieve better generator speed
regulation when a wind turbine is operated under time-varying and turbulent wind condi-
tions. The fundamental idea of DOB control is to conduct internal model-based observa-
tion and cancelation of disturbances directly using an inner feedback control loop. While
the outer-loop PID controller provides the basic capability of suppressing disturbance
effects with guaranteed stability, the inner-loop disturbance observer is designed to yield
further disturbance rejection in the low frequency region. The DOB controller can be
built as an on–off loop, that is, independent of the original control loop, which makes it
easy to be implemented and validated in existing wind turbines. The proposed algorithm
is applied to both linearized and nonlinear National Renewable Energy Laboratory
(NREL) offshore 5-MW baseline wind turbine models. In order to deal with the mismatch
between the linearized model and the nonlinear turbine, an extra compensator is pro-
posed to enhance the robustness of augmented controller. The application of the aug-
mented DOB pitch controller demonstrates enhanced power and speed regulations in the
above-rated region for both linearized and nonlinear plant models.
[DOI: 10.1115/1.4035741]
Keywords: disturbance observer based control, wind turbine, generator speed regula-
tion, disturbance rejection
1 Introduction
Wind energy is one of the most promising renewable energy
sources in the world. To efficiently harvest the wind kinetic
energy, modern wind turbines are designed to have large sizes and
flexible structures. Such system properties, however, also create a
major challenge for long-term durability of wind turbines. In the
meantime, the operating wind field is often highly turbulent,
which gives rise to significant fluctuation of plant dynamics and
hence compromises the turbine performance. Based on the wind
speed, the operation of wind turbines can be divided into three
regions. In region 1, wind turbines do not start up until the wind
speed reaches a threshold value (i.e., the cut-in speed). In region 2
(below-rated), torque control is often applied to capture the maxi-
mum power from wind. In region 3 when wind speed is suffi-
ciently high (above-rated), wind turbines need to operate at rated
speed and provide constant rated power output.
In the above-rated region, pitch control is commonly imple-
mented to avoid the over-speed of rotor. In this process, the highly
nonlinear nature of a wind turbine calls for a robust and intelligent
control system to tackle the time-varying turbulent wind field.
Since the plant model is sensitive to wind speed, a collective
proportional-integral-derivative (PID) controller has been devel-
oped to regulate the generator speed where a gain scheduled part is
added in order to deal with the aerodynamic sensitivity change of
the wind speed (which is treated as the baseline controller for com-
parison in this research) [1]. The optimal power and speed in region
3 under time-varying wind field may then be realized with unknown
model parameters. By linearizing the nonlinear wind turbine model
under selected operating point, a linear turbine model can be
obtained to formulate the state-space feedback control for speed
regulation. As the wind speed is generally unpredictable without
proper sensor, disturbance accommodating control (DAC) has been
adopted to facilitate disturbance rejection and mitigate loads by
estimating wind speed with additional state estimators [2,3]. How-
ever, the estimator accuracy is not usually guaranteed. Since the lin-
earized model is dependent upon the operating point, adaptive
control has been attempted to achieve better speed regulation than
the PID method, as wind turbine model parameters are not precisely
known [4]. With the recent development of light detection and
ranging (LIDAR), feedforward strategy can be adopted to reject the
varying wind disturbance to obtain better rotor speed tracking and
further mitigate structural loads. In Ref. [5], wind velocity is cap-
tured by LIDAR and fed to a filtered-x recursive least square algo-
rithm, which cancels the disturbance effect.
In wind turbines, one of the major challenges for control devel-
opment comes from the time-varying external wind disturbances
[3,5,6]. It is worth noting that in the field of high precision motion
control, the concept of disturbance observer (DOB)-based control
with internal model principle has been recently explored to reject
disturbances with unknown and/or time-varying spectra [7]. For
example, a DOB-based algorithm has been formulated and imple-
mented to a wafer-scanning process in lithography [8]. The funda-
mental idea of DOB control is to conduct an internal disturbance
observation using model inversion and then to achieve disturbance
cancelation by using an inner feedback control loop. As such, the
potential effectiveness of DOB control for wind turbine applica-
tions is promising, since it may reject wind disturbances in speed
regulation without requiring real-time sensor such as LIDAR. In
comparison, the disturbance compensation in DAC [2]is
facilitated by minimizing the norm of disturbance function
ðBGdþBdHÞ.
2
The performance of DAC would thus be limited if
the disturbance rejection function does not have full rank.
1
Corresponding author.
Contributed by the Dynamic Systems Division of ASME for publication in the
JOURNAL OF DYNAMIC SYSTEMS,MEASUREMENT,AND CONTROL. Manuscript received
May 5, 2016; final manuscript received December 29, 2016; published online May 9,
2017. Assoc. Editor: Ryozo Nagamune.
Journal of Dynamic Systems, Measurement, and Control JULY 2017, Vol. 139 / 071006-1
Copyright V
C2017 by ASME
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In this research, we formulate a DOB-based control scheme for
wind turbines, aiming at asymptotically rejecting disturbances at
above-rated wind speeds. Specifically, our objective is to maintain
a constant output power and achieve better generator speed regu-
lation when the wind turbine is operated under time-varying and
turbulent wind conditions. The DOB structure consists of a usual
PID controller augmented with an inner loop feedback. While the
outer-loop PID controller provides the basic capability of sup-
pressing disturbance effects with guaranteed stability, the inner-
loop DOB (i.e., the Qfilter) is designed to yield further disturb-
ance rejection in the low frequency region and at the same time
maintain the original capability of the PID controller in terms of
suppressing disturbance effects in the high frequency region.
Although disturbance rejection through disturbance estimation
with a traditional state estimator is well known [2,3,9], the DOB
structure formulated in this research allows simple and intuitive
tuning of the inner DOB loop gains that are independent of the
outer-loop state feedback or PID gains [10]. The DOB controller
may therefore be built as an on–off loop that is independent of the
original control loop employed in existing wind turbines. This
add-on feature makes it easy to be implemented and validated in
existing wind turbines. In practice, owing to the model mismatch,
applying the DOB that is designed from the linearized model to
the actual, nonlinear system may not lead to desired performance
especially system stability. An extra compensator is then proposed
to enhance the robustness of the augmented controller, which can
not only ensure the stability but also widen the disturbance rejec-
tion bandwidth. The new algorithm is applied to both linearized
and nonlinear National Renewable Energy Laboratory (NREL)
offshore 5-MW baseline wind turbine models.
The rest of this paper is organized as follows: We start with a
brief discussion of the 5-MW wind turbine model in Sec. 2, fol-
lowed by the formulation of the DOB based control in Sec. 3. The
results and discussion are presented in Sec. 4, where DOB will
exhibit better generator speed regulation as well as stability
robustness in a wide region of wind speeds. Concluding remarks
are summarized in Sec. 5.
2 Model Description
In this research, we employ the NREL offshore 5-MW turbine
for control development, which is a benchmark wind turbine
widely used in control studies [1,4,11]. It is a three-bladed upwind
variable-speed variable blade-pitch-to-feather-controlled horizon-
tal axis turbine [1]. The rotor diameter is 126 m, and the hub
height is 90 m. The cut-in wind speed is 3 m/s, the rated wind
speed is 11.4 m/s, and the cut-out wind speed is 25 m/s. The rated
generator speed is 1173.7 rpm.
A variable-speed wind turbine generally consists of blades, a
tower, a nacelle, a hub, drivetrain shafts, a gearbox, and a genera-
tor. The aerodynamic power captured by the rotor is given as [2]
Pwind ¼1
2qpR2Cpk;b
ðÞ
v3(1)
where Ris the rotor radius, and qis the air density. The power
coefficient Cpis a nonlinear function of tip speed ratio kand pitch
angle b, and can be obtained from look-up table generated by field
test data. Here
k¼xR
v(2)
where vis the wind speed, and xis the rotor speed. From Eqs. (1)
and (2), we can observe that the aerodynamic power Pwind
depends on wind speed, rotor speed, and blade pitch angle. Pitch
angle control is therefore the key to adjust the aerodynamic power
captured by rotor to achieve speed regulation. The aerodynamic
torque applied to the rotor can be expressed as [2]
Ta¼pCpk;b
ðÞ
qR2v3
2x(3)
The nonlinear aero-elastic equation of motion for the turbine has
the following form [12]:
Mðq;u;tÞ€
qþfðq;_
q;u;ud;tÞ¼0(4)
where Mis the mass matrix, fis the nonlinear forcing function
vector that contains the stiffness and damping effects, qis the
response vector, uis the vector of control inputs, udis the vector
of wind input disturbance, and tis time. In this research, we use
the fatigue, aerodynamics, structures, and turbulence (FAST) code
developed by NREL [12] to establish the numerical model of the
wind turbine. Without the loss of generality, we let the following
degrees-of-freedom (DOFs) be switched on in FAST: the first
flapwise blade mode DOF (of three blades), the generator DOF,
and the drivetrain torsional flexibility DOF.
Using FAST, we can linearize Eq. (4) by perturbing each vari-
able about its corresponding operating point [2,12]. Following the
usual simplification performed in literature [2,3,11], we eliminate
the generator azimuth state and reduce the flapwise mode of three
blades to one symmetric mode. We then cast the linearized equa-
tion of motion into the state-space representation
_
x¼Ax þBDuþBdDud(5a)
y¼Cx þDDuþDdDud(5b)
where xis a five-dimension state vector, x1is the drive-train tor-
sional deflection perturbation, x2is the rotor first symmetric flap
displacement perturbation, x3is the generator speed perturbation,
x4is the drive-train torsional velocity perturbation, and x5is the
rotor first symmetric flap velocity perturbation. Ais the state
matrix, Bis the control input matrix, Bdis the disturbance input
matrix, Cis the output matrix, Dis the control input transmission
matrix, Ddis the wind input disturbance transmission matrix, Du
is the control input (i.e., the perturbed blade collective pitch
angle), Dudis the disturbance input (i.e., the perturbed wind
speed), and yis the output.
Usually, the generator speed can be regulated by the aerody-
namic torque Ta(Eq. (3)) and the generator torque denoted as Tg.
There are two separate single-input and single-output control
loops which are the torque controller and the blade pitch control-
ler. In the below-rated region, the torque controller is used to gov-
ern the generator speed, while blade pitch angle is held constant
to maintain the maximum aerodynamic coefficient Cp. In the
above-rated region, the pitch controller is used to limit the
aerodynamic torque Tato avoid extreme loads. The operating
point for linearization in this research is chosen to be wind speed
v¼18 m=s, pitch angle h¼14:92 deg, and rotor speed
xr¼12:1 rpm. We choose v¼18 m/s because it is in the middle
between the cut-in speed (11.4 m/s) and the cut-out speed
(25 m/s). h¼14:92 deg is the corresponding blade pitch angle
that produces the rated power, and xr¼12:1 rpm is the rated
rotor speed.
3 Control Design
In this research, we adopt the torque controller designed in Ref.
[1] for the same NREL offshore 5-MW baseline wind turbine.
Here, in this section, we formulate the DOB-based pitch control-
ler. We assume that the generator speed is the only measurement
available, and that the controller gives the collective pitch com-
mand. The pitch actuator dynamics is assumed to be first-order,
since the actuator inertia is negligible compared to those of other
2
Bis the control input matrix, Gdis the disturbance state gain, Bdis the wind
disturbance input matrix, and His the output matrix in disturbance wave generator.
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components. We employ pitch angle saturation and pitch rate lim-
iter to meet the hardware limitations.
3.1 Disturbance Rejection in Disturbance Observer-Based
Control. As mentioned in Sec. 1, in order to deal with the time-
varying turbulent wind condition, Jonkman et al. developed a gain
scheduled PID type control, hereafter referred to as the gain sched-
uled proportional integral (GSPI) control [1]. The gain-scheduling
part is derived based on the pitch sensitivity which is expressed as
the sensitivity of the aerodynamic power to the rotor collective blade
pitch. It is worth noting that the relation between the pitch sensitivity
and the pitch angle, strictly speaking, is not linear. Thus, the disturb-
ance effects may not be perfectly canceled. Here, we propose to
incorporate a disturbance observer structure to a traditional PID con-
troller to fundamentally enhance the disturbance rejection perform-
ance. In this structure, while the outer-loop PID controller provides
the basic capability of suppressing disturbance effects with guaran-
teed stability, an inner-loop disturbance observer (i.e., the Qfilter) is
designed to yield further disturbance rejection in the low frequency
region and at the same time maintain the original capability of the
PID controller in terms of suppressing disturbance effects in the
high frequency region.
The disturbance observer will lead to an inverse-based disturb-
ance rejection scheme, as shown in Fig. 1. Two discrete transfer
functions can be obtained from Eq. (5) to represent the model
from perturbed blade pitch angle to perturbed generator speed
(Pðz1Þ) as well as the model from perturbed wind speed to per-
turbed generator speed (Pdðz1Þ), respectively. The outer-loop
feedback controller is a PID controller Cðz1Þ. The inner-loop
feedback controller, depicted as the collection of blocks connected
through thick arrows in Fig. 1, is the DOB, which is an internal
feedback of the disturbance d0ðkÞ.
We lump all the input disturbances to dðkÞ, and focus on the
signal flow from dðkÞto ^
dðkÞ.IfP1
nðz1Þis the exact model
inversion of plant Pðz1Þ, letting the filter Qðz1Þ¼1 will create
the exact disturbance estimation of dðkÞ, which will result in the
perfect disturbance rejection at the input of the plant. We then
consider the flows of control input uðkÞ. Practically, P1ðz1Þis
acausal. We thus introduce P1
nðz1Þ¼zmP1ðz1Þ.zmis added
to make it causal and implementable (i.e., the degree of numerator
not exceeding the degree of denominator), where mis the relative
degree of Pðz1Þ. We can have P1
nðz1ÞPðz1Þ¼zm, which
means uðkÞwill not influence ^
dðkÞ[7]. Consequently, the raw dis-
turbance estimation drðkÞincludes rich information of dðkÞwith
the introduction of the inverse architecture. Nevertheless, in prac-
tical cases we usually have P1
nðz1ÞPðz1Þzm, and thus,
drðkÞzmdðkÞ. Mismatch exists between drðkÞand dðkÞ,
because drðkÞis a delayed estimate of dðkÞ. In what follows we
demonstrate how this issue can be handled.
Consider the original problem of wind turbine generator speed
tracking. The signal d0ðkÞis the time-varying wind disturbance,
which will go through a disturbance model Pdðz1Þto affect the
input of the plant. rðkÞis the setpoint, uðkÞis the pitch angle, and
yðkÞis the generator speed. When Pðz1Þis the linearized model,
these signals become the perturbed values corresponding to the
operating point. The signal ^
dðkÞis a negative internal feedback of
disturbance to cancel out the influence of dðkÞ. When disturbance
dðkÞenters the plant directly, we can observe, from Fig. 1, that
dðkÞ ^
dðkÞ¼dðkÞQðz1ÞP1
nðz1ÞPðz1ÞðdðkÞþuðkÞÞ
þQðz1ÞzmuðkÞ
½1zmQðz1ÞdðkÞ(6)
Let Adðz1Þand Bdðz1Þbe the denominator and numerator of the
ztransform of disturbance source, respectively. For a disturbance
that satisfies the following condition in the asymptotic sense:
Adðz1ÞdðkÞ¼Bdðz1ÞdðkÞ¼0(7)
we can achieve disturbance rejection if [7]
1zmQz
1
ðÞ
¼Kz
1
ðÞ
Adz1
ðÞ
Adaz1
ðÞ (8)
where Kðz1Þis a polynomial of z1to assure causality, Adðaz1Þ
is a polynomial in which all z1in Adðz1Þare replaced by az1,
a2ð0;1Þ. The form of Adðz1Þdepends on the disturbance form
and the interested frequency region. To deal with the wind dis-
turbance and to ensure the stability of the augmented system
(which is not always guaranteed due to the possible model mis-
match in practice), the Qfilter needs to be carefully selected,
which will be further discussed in details in Sec. 3.3 based on the
stability and robustness criteria.
In certain conventional cases such as vibration mitigation in
precision manufacturing, the disturbance frequency is either
known or can be adaptively identified. For disturbance in wind
turbines, however, it is generally difficult to find or define its spe-
cific frequency contents, since the highly random wind can con-
tain many frequencies. To determine Adðz1Þ, we model the wind
disturbance through the following disturbance wave generator [2]:
_
zd¼Fzd(9a)
ud¼Hzd(9b)
Any waveform governed by a linear ordinary differential equation
can be expressed by this generator. We assume that the wind dis-
turbance is the variance from the wind speed at the operating point
and has a known waveform but unknown amplitude. Specifically,
we can model it as step disturbance. Fand Hare assumed to be
known as
F0(10a)
H1(10b)
If we take the ztransform of the step disturbance and treat the dis-
turbance as the response to an impulse input dðkÞ, we can obtain
d0k
ðÞ
¼Mk
ðÞ
1z1dk
ðÞ (11)
where owing to the time-varying nature, an unknown magnitude
MðkÞis added.
When disturbance enters through a disturbance model Pdðz1Þ
¼Bp;dðz1Þ=Bpðz1Þ, the output will be yðkÞ¼Pdðz1ÞPðz1Þ
d0ðkÞþPðz1ÞuðkÞas shown in Fig. 1, and the disturbance enter-
ing the plant is
dk
ðÞ
¼Pdz1
ðÞ
d0k
ðÞ
¼Mk
ðÞ
1z1
Bp;dz1
ðÞ
Bpz1
ðÞ
dk
ðÞ (12)
Fig. 1 Structure of the DOB-based control
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Thus, we have, asymptotically
1z1
ðÞ
Bpz1
ðÞ
Mk
ðÞ dk
ðÞ
¼Bp;dz1
ðÞ
dk
ðÞ
¼0(13)
Recall Eqs. (7) and (8). Based on the internal model principle
[13], to asymptotically reject the disturbance, the following equa-
tion should be satisfied:
1zmQz
1
ðÞ
¼1z1
ðÞ
Bpz1
ðÞ
Mk
ðÞ (14)
To further ensure the causality and the capability of local loop
shaping, filters Kðz1Þand
Bpðbz1Þare added to the right-hand
side of Eq. (14)
1zmQz
1
ðÞ
¼
Bpz1
ðÞ
Mk
ðÞ
Kz
1
ðÞ
Bpbz1
ðÞ (15)
It is worth noting that Eq. (13) still holds after those two filters are
introduced. Kðz1Þis selected as a finite impulse response (FIR)
filter Kðz1Þ¼k0þk1z1þþknkznk, and
Bpðz1Þ¼ð1z1ÞBpðz1Þ(16a)
Bpðbz1Þ¼ð1bz1ÞBpðbz1Þ(16b)
where b2ð0;1Þ. The design of
Bpðbz1Þis based on the damped
pole-zero pair principle [7,8], which entertains the advantage of
controlled waterbed effect in loop shaping.
Arranging Eq. (15) in the form of polynomial Diophantine
equation can yield
Bpz1
ðÞ
1
Mk
ðÞ
Kz
1
ðÞ
þzmBQz1
ðÞ
¼
Bpbz1
(17)
where Qðz1Þ¼BQðz1Þ=
Bp½bz1. The conditions required to
guarantee that Eq. (17) has a unique solution are [14]:
(1)
Bpðbz1Þis divisible by the greatest common factor of
Bpðz1Þand zm.
(2) The order of BQðz1Þplus mis greater than or equal to the
order of
Bpðz1Þ.
(3) The order of BQðz1Þplus mis equal to the order of
Bpðz1Þplus the order of Kðz1Þ.
Since MðkÞ2R(Ris the set of real numbers) and Kðz1Þis an
FIR filter, to solve Eq. (17) we can assume
1
Mk
ðÞ
Kz
1
ðÞ
¼
k0þ
k1z1þ
knkznk(18)
Also, we can assume
Bpðz1Þ¼1þ
bp1z1þþ
bpkzk(19a)
Bpðbz1Þ¼1þb
bp1z1þþbk
bpkzk(19b)
According to the conditions mentioned previously, a minimum
order solution can be obtained
BQðz1Þ¼bQ0þbQ1z1þþbQðkmÞzðkmÞ(20)
1
Mk
ðÞ
Kz
1
ðÞ
¼
k0(21)
The filter Qðz1Þcan be determined by equating the respective
coefficients of ziin Eq. (17). In addition, it can be observed that
the wind disturbance MðkÞwill only affect Kðz1Þbut not Qðz1Þ.
3.2 Nonminimum Phase Zeros and Unstable Poles. From
Fig. 1,P1
nðz1ÞzmP1ðz1Þ.P1ðz1Þshould be stable, in
order to ensure the stability of the augmented system. Neverthe-
less, in most realistic cases, the inverse model of a wind turbine
may not be stable. Let the transfer function of the plant be
expressed as
Pz
1
ðÞ
¼Bpz1
ðÞ
Apz1
ðÞ (22)
where Bpðz1Þand Apðz1Þare the numerator and the denominator
of Pðz1Þ, respectively. When implemented in DOB controller,
the roots of polynomial Bpðz1Þare the characteristic roots of
P1ðz1Þ. They must be inside the unit circle in the zplane, in
order to be implementable. If any of the zeros of Pðz1Þis outside
of or on the unit circle, the output of the closed-loop system with
DOB controller will oscillate or diverge. In addition, the results
will be highly oscillating if the zeros are on the unit circle or close
to 1. The zero-phase error tracking (ZPET), which is a stable
model-inverse approximation, is adopted to obtain the stable
model inversion P1ðz1Þapproximately when there are nonmini-
mum phase zeros in Pðz1Þand to keep the output converge [15].
It is also worth noting that the disturbance signal d0ðkÞis
assumed to be bounded. The operation of a turbine will be termi-
nated to avoid excessive structural loads, if the wind speed
exceeds the cut-out wind speed. If Pdðz1Þhas unstable poles,
although d0ðkÞis bounded, dðkÞwill not be bounded after d0ðkÞ
goes through Pdðz1Þ. It will result in divergence of the whole
system. Here, we make a slight change of the disturbance dynam-
ics, by moving the unstable poles to the left plane and at the same
time keeping the direct current gain of the modified Pdðz1Þthe
same as that of the original Pdðz1Þ. We can therefore ensure that
the disturbance entering the plant is bounded.
3.3 Stability Analysis and Robustness Analysis. As men-
tioned in Sec. 3.1, the Qfilter (shown in Eq. (8)) needs to be care-
fully selected. In this subsection, we focus on the analyses of the
stability and robustness of the closed-loop system, which provides
the basis for properly selecting Qfilter in practice to asymptoti-
cally reject the disturbance.
3.3.1 Stability Analysis. Figure 2illustrates loop shaping
based on Fig. 1. The equivalent controller of the augmented
scheme from eðkÞto u(k) can be expressed as
Caug z1
ðÞ
¼Cz
1
ðÞ
þP1
nz1
ðÞ
Qz
1
ðÞ
1zmQz
1
ðÞ (23)
The complementary sensitivity function from rðkÞto yðkÞis
T¼Gr!y¼PCaug
1þPCaug
¼PCþP1
nQ
1zmQþPC þPP1
nQ(24)
Fig. 2 Loop shaping of DOB
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In Eq. (24), all z1notations are omitted for brevity. When there
is no plant mismatch between the actual model and the nominal
model, we have P1
nðz1Þ¼zmP1ðz1Þ, and therefore
Gr!y¼PCaug
1þPCaug
¼PC þ1
1þPC ¼1(25)
One can obtain perfect tracking of reference generator speed
when the Qfilter is properly selected. The sensitivity function S
0
of the system with the PID controller only is
S0¼1
1þPC (26)
Also, the current sensitivity function from dðkÞto eðkÞis
S¼1
1þPCaug
¼1zmQ
1þPC þPP1
nzm
Q(27)
In frequency regions where the nominal model has a small mis-
match with the actual model, we have PP1
nzm0. The fre-
quency response of Swill not be significantly influenced by the
spectrum of ðPP1
nzmÞQ, and thus S¼S0ð1zmQÞ. The
sensitivity function performance can be enhanced by the proper
selection of Qfilter. When Qis stable, the stability of Swill be
guaranteed [8]. On the other hand, in frequency regions where a
large mismatch exists between the linearized reduced-order model
and the nonlinear model of the wind turbine, a very small QðejxÞ
has to be selected to maintain Sin the form of 1=ð1þPCÞin order
to suppress the disturbance effects through the original PID con-
troller. As the sensitivity function Sis only determined by the fre-
quency response of ð1zmQÞ, a large cutoff frequency in Qis
desired to reject wider disturbance bandwidth. However, due to
physical limitations in hardware and turbine components, the cut-
off frequency cannot be very large in practice.
3.3.2 Robustness Analysis. A high-fidelity model of wind tur-
bine requires a very large number of DOFs. The aerodynamic
load imposed to the blades is often influenced by the time-varying
wind speed, the asymmetric wind shear effect, the tower shadow
effect, and the varying azimuth position when the rotor rotates.
The dynamics neglected due to order-reduced modeling and the
uncertainties/variations of the plant parameters introduce inevita-
bly model mismatch. From the preceding discussion of stability
analysis, Qshould be carefully selected in frequency regions
where there is a mismatch between the nominal model and the
actual turbine. The conditions to satisfy the robust stability are
discussed in details as follows.
The characteristic polynomial of the closed-loop augmented
scheme is given as
1þPðz1ÞCaugðz1Þ¼0(28)
Let the bounded perturbed model uncertainty from the nominal
plant be Dðz1Þ. The nominal model is an order-reduced linear-
ized model (under uniform constant 18 m/s wind speed with
5DOFs switched on, as presented Sec. 2). The nonlinear turbine
with unmodeled dynamics under time-varying wind speed can be
approximately represented as
Prðz1Þ¼Pðz1Þð1þDðz1ÞÞ (29)
The robust stability condition should be satisfied according to the
small gain theorem [16]
kTðejxÞDðejxÞk1<1(30)
Tis the complementary sensitivity function in Eq. (24). We can
therefore choose the proper cutoff frequency in the Qfilter to
maintain the stability of the augmented feedback system where
there is a model mismatch. In the Qfilter, the cutoff frequency
can be adjusted by selecting different values of b, and the slope of
high frequency response can be further tuned by an extra compen-
sator as will be shown in Sec. 4.
4 Case Analyses and Discussion
In this section, case analyses and comparisons are conducted
for both the linearized model and nonlinear plant. First, a 5DOF
linearized model of the NREL offshore 5-MW wind turbine is
obtained from FAST, and employed to verify preliminarily the
effectiveness of the DOB controller. Both uniform stepwise con-
stant and uniform random wind disturbances are used to examine
the DOB controller. Then, the DOB controller designed based on
the 5DOF linearized model is applied to the nonlinear turbine
model and compared with the GSPI controller developed in Ref.
[1] (which is treated as the baseline for comparison in nonlinear
plant). Based on the robustness analysis presented in Sec. 3.3,we
further introduce a compensator to deal with the model mismatch
to improve the DOB controller.
4.1 Disturbance Observer Controller Implemented to
Linearized Model. To examine the initial design principle and to
gain the preliminary understanding of its effectiveness, we first
apply a DOB controller to the linearized model. For Qfilter for-
mulation, m(the relative degree of Pðz1Þ) is 1, and bis chosen to
be 0.9953 which can yield the largest disturbance rejection band-
width and simultaneously guarantee the system convergence. Fol-
lowing the design strategy provided in Sec. 3.1, we can compute,
based on Eq. (17), that Qðz1Þ¼ð0:003609 0:0009153 z1
0:009577z2þ0:008121z30:00123z4Þ=ð0:3701 0:7643z1
þ0:09668z2þ0:6728z30:4269z4þ0:05161z5Þ. For com-
parison purpose, a conventional PID controller is designed, where
the proportional (0.0018225), integral (0.0040), and derivative
(0.00031894) gains are carefully selected to yield small over-
shoot and fast settling time. Here, it is worth mentioning that we
cannot use the GSPI gains in Ref. [1] because that GSPI controller
is designed for nonlinear plant. The stepwise wind disturbance
and the corresponding time-domain generator speed error
responses of DOB and PID are shown in Figs. 3(a)and 3(b).Itis
observed from Fig. 3(b)that the DOB has an overshoot of 50 rpm
and the PID has an overshoot of 70 rpm. The DOB control leads
to a reduction of generator speed error overshoot by 28.57%,
while maintaining the same settling time. The frequency-domain
reponse under random wind disturbance is presented in Fig. 4.
The amplitude spectrum of time-domain results show decrease in
frequencies below 1 Hz.
4.2 Disturbance Observer Controller Implemented to
Nonlinear Wind Turbine Under Turbulent Wind Field. As
shown above, the DOB control with the linearized model exhibits
promising performance under stepwise and random disturbances.
For the nonlinear plant, the response analysis of the 5-MW bench-
mark wind turbine is carried out by connecting FAST with the
respective controllers in the MATLAB/SIMULINK environment. The
time duration is from 0 to 600 s with an integration step of
0.0125 s. All available 16DOFs are turned on, which include:
first flapwise blade mode (three blades)
second flapwise blade mode (three blades)
first edgewise blade mode (three blades)
drivetrain rotational-flexibility
generator
yaw
first fore–aft tower bending-mode
second fore–aft tower bending-mode
first side-to-side tower bending-mode
second side-to-side tower bending-mode
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Aerodynamic forces and moments are calculated by using
AeroDyn [17]. Realistic turbulent wind fields are generated in
TurbSim using IEC Kaimal spectral model [18]. The turbulence
intensity (the ratio of root-mean-square (RMS) of the turbulent
velocity fluctuations to the mean velocity) is selected as standard
IEC category B, which is 14%. Pitch saturation is added to limit
the pitch angle between 0 and 90 deg. The pitch rate limiter has a
maximum absolute rate of 8 deg/s. The actuator is a first-order
model.
First, we directly apply the augmented controller to the nonlin-
ear model to investigate the effectiveness. The PID controller
Cðz1Þis chosen to be the GSPI controller (treated as the baseline)
for nonlinear plant. It is worth noting that the model mismatch
between the nominal nonlinear turbine and the linearized model in
practice will influence the stability of the augmented feedback
system. Therefore, the Qfilter used in Sec. 4.1 needs to be modi-
fied to have a larger b(0.997) to ensure its convergence. From the
bode diagram of Qunder different bvalues shown in Fig. 5, the
frequency regions which yield Q¼1 for b¼0:97 and b¼0:999,
respectively, are 0.0001–0.3 Hz and 0.0001–0.004 Hz. Conse-
quently, a smaller bgives a wider bandwidth of disturbance rejec-
tion since we can achieve perfect disturbance rejection when
Q¼1. However, a smaller balso leads to a larger magnitude in
high frequency region where model mismatch usually happens.
According to the stability analysis in Sec. 3.3, a very small
QðejxÞis desired to maintain Sin the form of 1=ð1þPCÞin
model-mismatch frequency regions. It can retain the capability of
suppressing disturbance effects of the original GSPI controller
and maintain the stability of the augmented system. The nonlinear
plant is convergent when b0:997. The modification of Qfilter
can be realized by changing bor even by including an extra
compensator (which will be discussed in Sec. 4.3). Here, we first
change bto guarantee the stability of the nonlinear system.
The controller is examined under nine wind files with mean
speeds from 14 m/s to 22 m/s. These wind files cover virtually the
entire region 3. Figure 6shows the zoom-in result of generator
speed at steady-state between 300 s and 350 s under 18 m/s turbu-
lent wind file. It can be seen that the generator speed stays near
the rated value of 1173.7 rpm. Less oscillation around the rated
value 1173.7 rpm under DOB control is observed. To quantify the
overall speed regulation, RMS errors of generator speed under dif-
ferent turbulent wind files are calculated and listed in Table 1.
From Table 1, we can see that the DOB control reduces the RMS
Fig. 3 Wind disturbance and generator speed responses (under 5DOF linearized model): (a)
stepwise wind disturbance and (b) comparison of time-domain responses of DOB and PID
Fig. 4 Frequency-domain generator speed performance com-
parison of DOB and PID under 5DOF-linearized model and ran-
dom wind field
Fig. 5 Bode diagram of Qfilter under different b
Fig. 6 Zoom-in view of generator speed responses. REF refers
to the rated generator speed.
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errors of speed and power for six wind files, but increases the
RMS errors for the other three wind files. Indeed, the modification
of Qfilter to some extent sacrifices the disturbance rejection capa-
bility, as the neglected modes of the plant severely limit the band-
width of Qfilter.
4.3 An Added Compensator Design to Improve QFilter.
As shown in Sec. 4.2, while we can modify the Qfilter in the
DOB controller by tuning bto guarantee the stability of the non-
linear closed-loop system, the performance of generator speed
regulation in the nonlinear plant cannot be guaranteed. Here, we
further study the Qfilter design in order to deal with the model
mismatch between the linearized model and the nonlinear turbine
in practice. We prefer smaller magnitude in high frequency region
and larger cutoff frequency which are hard to be achieved
simultaneously as shown in Fig. 5. To further widen the disturb-
ance rejection region, we propose to add an extra compensator
(i.e., a low-pass filter) with faster roll-off at high frequencies.
Here, a fourth-order filter 1=ð1þssÞ4is added to tune the high
frequency response when b¼0:92 is used in the Qfilter. The
improved controller is referred to as the DOB*.
If PP1
nzm0, Eqs. (26) and (27) yield the current sensi-
tivity function as
SðejxÞ¼S0ðz1Þð1zmQðz1ÞÞz¼ejx(31)
Based on Eq. (31), in Fig. 7, we plot the comparison of frequency
responses of the sensitivity functions of PID, DOB, and DOB*.
Note that Pis selected as the model linearized under constant uni-
form wind speed of 18 m/s. For the sensitivity function formula-
tion of PID, the proportional and integral gains used follow those
derived in Ref. [1]. While a family of curves from the frequency
responses of the sensitivity function corresponding to different
wind speeds can be generated with the added gain scheduled part,
for simplicity, we only pick one representative curve from PID,
DOB, and DOB* where the gain scheduled part is omitted to com-
pare the controller performances since the performances exhibit
similar trend with or without the gain scheduled part. From Fig. 7,
Table 1 Comparisons of generator speed RMS error and power
RMS error by GSPI, DOB, and DOB*
Mean wind speed Controller Speed RMS error Power RMS error
14 GSPI 0.0687 0.9506
DOB 0.0742 (þ8.01%) 1.0470 (þ10.14%)
DOB* 0.0448 (34.79%) 0.6497 (31.65%)
15 GSPI 0.0782 1.1440
DOB 0.0825 (þ5.50%) 1.1933 (þ4.31%)
DOB* 0.0562 (28.13%) 0.7844 (31.43%)
16 GSPI 0.0799 1.2757
DOB 0.0818 (þ2.38%) 1.2387 (2.90%)
DOB* 0.0526 (34.17%) 0.8200 (35.72%)
17 GSPI 0.0836 1.4124
DOB 0.0806 (3.59%) 1.2684 (10.20%)
DOB* 0.0530 (36.60%) 0.8757 (38.00%)
18 GSPI 0.0879 1.5096
DOB 0.0831 (5.46%) 1.3681 (9.37%)
DOB* 0.0535 (39.14%) 0.9042 (40.10%)
19 GSPI 0.0929 1.6652
DOB 0.0878 (5.49%) 1.5072 (9.49%)
DOB* 0.0572 (38.43%) 0.9951 (40.24%)
20 GSPI 0.0987 1.8439
DOB 0.0922 (6.59%) 1.6537 (10.32%)
DOB* 0.0610 (38.20%) 1.0892 (40.93%)
21 GSPI 0.0991 1.9864
DOB 0.0906 (8.58%) 1.7129 (13.77%)
DOB* 0.0621 (37.34%) 1.2351 (37.82%)
22 GSPI 0.1046 2.1170
DOB 0.0946 (9.56%) 1.8125 (14.38%)
DOB* 0.0657 (37.19%) 1.3558 (35.96%)
Fig. 7 Comparison of magnitude responses of sensitivity
functions
Fig. 8 Time-domain performance comparison of DOB, DOB*,
and GSPI: (a) wind speed (18 m/s turbulent field), (b) generator
speed, (c) power, and (d) pitch angle. : GSPI,
: DOB, : DOB*
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for the DOB controller formulated based on Sec. 4.2, we can
observe magnitude reduction from 0.05 Hz to 1 Hz. Meanwhile,
DOB* with an extra compensator yields significant reduction of
magnitude from 0.0006 Hz to 2 Hz. The magnitude response of
DOB* is smaller compared with both DOB and PID, which indi-
cates that the DOB* can improve considerably the disturbance
rejection performance. Figure 8shows the time-domain responses
of wind speed, generator speed, power, and blade pitch angle.
With DOB*, generator speed and power response show less fluc-
tuation as compared with the other two controllers, while the pitch
angle has more fluctuation which means more pitch activity regu-
lating the generator speed. Figure 9gives the frequency response
comparison of the time-domain data under 18 m/s turbulent wind
file, from which we can clearly see the decreased magnitude of
DOB* in 0.01–0.16 Hz.
The performance of the DOB* controller is also tabulated in
Table 1. The results are obtained under the same nine wind files
used in Sec. 4.2. We can observe a decrease in generator speed
RMS error by approximately 35% and a similar decrease in power
RMS error by approximately 35% compared to those of GSPI. To
further facilitate visual comparison of the three controllers, Fig.
10 displays the decreased percentage of generator speed RMS
error, where an obvious drop is observed in DOB* (approximately
35%) compared to GSPI.
Finally, we investigate the influences of DOB* on pitch rate,
average power capture, and loads on blades, tower, and low-speed
shaft. Here, we examine the fatigue damage equivalent load
(DEL) which serves as an important metric for comparing fatigue
loads across the entire spectrum of turbulent wind files. The
equivalent damage is represented by a constant load and calcu-
lated by using MLife [19] based on the rainflow counting algo-
rithm. The RMS pitch rate, average power, low-speed shaft torque
(LSShftTq) DEL, blade root edgewise moment DEL, blade root
flapwise moment DEL, tower base side-to-side moment DEL, and
tower base fore–aft moment DEL under nine wind files are shown
in Fig. 11. We can observe that the RMS pitch rate is generally
increased under DOB* than GSPI, but the controller still works
within the pitch rate limit (8 deg/s). The average power in DOB*
is increased (þ1.18% to þ2.74%) compared to GSPI because of
the reduction of the power RMS error. The low-speed shaft torque
(LSShftTq) DEL values exhibit consistent decrease (3.65% to
11.02%) for nine wind files because the reduction of fluctuation
of rotor speed will directly influence the drive-train torsional load.
The blade root edgewise moment DEL values are nearly
unchanged (0.75% to þ1.17%) for nine wind files. The blade
root flapwise moment DEL values do not change much (0.29%
to þ3.56%) except for the one under 14 m/s. The tower base side-
to-side moment DEL values increase (þ1.57% to þ46.49%) for
some wind files, but decrease (3.85% to 20%) for other wind
files. The tower base fore–aft moment DEL values increase
(þ8.64% to þ34.04%) for all wind files. It is worth emphasizing
that the disturbance observer structure is designed for speed and
power regulation and can indeed enhance those performances. On
the other hand, the effects to the component loads may be mixed,
which is consistent with the results obtained by similar studies
[20,21].
5 Conclusion and Future Work
In this research, an internal model-based DOB design combined
with a PID type feedback controller is formulated for wind turbine
generator speed regulation under time-varying unknown wind dis-
turbance. The key idea is to conduct an internal disturbance obser-
vation using model inversion and to achieve disturbance
cancelation using an inner feedback control loop. The proposed
approach is implemented to both the linearized reduced-order
model and the nonlinear NREL offshore 5-MW baseline wind tur-
bine model. The DOB controller shows decreased overshoot for
the linearized model. To improve the control robustness as it is
applied to the nonlinear turbine with inevitable model mismatch
between the linearized reduced-order model and actual model
Fig. 9 Frequency-domain performance comparison of DOB,
DOB*, and GSPI, under 18 m/s turbulent wind file: (a) overall
performance and (b) zoom-in view at low-frequency region
Fig. 10 Generator speed error performance comparison of
DOB, DOB*, and GSPI. The generator speed errors of DOB and
DOB* are normalized with respect to the error of GSPI.
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especially in high frequency regions, design criterion for the Qfil-
ter involved is formulated. Furthermore, an extra compensator
is introduced to enhance the generator speed regulation. Our
case studies indicate that the eventual control strategy,
referred to as the DOB* control, can yield approximately
35% reduction in generator speed RMS error and approxi-
mately 35% reduction in power RMS error as compared with
the PID controller. Since the component loads are not
explicitly treated as control objective, the loads on certain
components have mixed results.
Future work may include investigating the rejection of periodic
wind disturbance which can help to achieve load mitigation on
blades and tower in the controller design. Individual pitch control
can be explored to mitigate asymmetric blade loads. Online sys-
tem identification can be used to derive the turbine model to
design an adaptive Qfilter.
Fig. 11 Comparisons of RMS pitch rate (a), average power (b), low-speed shaft torque
moment DEL (c), blade root edgewise moment DEL (d), blade root flapwise moment DEL
(e), tower base side-to-side moment DEL (f), and tower base fore–aft moment DEL, and
(g) of GSPI and DOB*. : GSPI, : DOB*
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Acknowledgment
This research was supported by National Science Foundation
under Grant CMMI–1300236.
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