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1
DISTURBANCE OBSERVER BASED CONTROL DESIGN FOR WIND TURBINE
SPEED REGUALTION
Yuan Yuan
Department of Mechanical
Engineering
University of Connecticut
Storrs, CT, United States
Xu Chen
Department of Mechanical
Engineering
University of Connecticut
Storrs, CT, United States
Jiong Tang
Department of Mechanical
Engineering
University of Connecticut
Storrs, CT, United States
ABSTRACT
Disturbance observer based (DOB) control has been
implemented in high precision motion control to reject
unknown or time-varying disturbances. In this research, a DOB
control scheme is applied to wind turbines to reject the
unknown low frequency disturbances which significantly
influence the dynamics of wind turbines. A better speed
regulation has been achieved as the wind turbine is operated at
time-varying and turbulent wind field while maintaining the
constant output power. The disturbance observer combined with
a compensator is further designed to deal with the model
mismatch between nominal model and actual turbine. With this
proposed algorithm tested on both linearized and nonlinear
National Renewable Energy laboratory (NREL) offshore 5-MW
baseline wind turbine, the DOB controller is proved to achieve
improved power and speed regulation in Region 3 (above-rated
wind speeds) compared with a baseline gain scheduling
proportional integral differential (PID) collective controller.
1. INTRODUCTION
Wind energy represents one of the promising clean energy
sources featuring low cost and sustainability. The modern wind
turbines usually adopt large and flexible structure to enhance
the energy capacity. However, long-term maintenance will be
thus challenging and expensive. The highly turbulent operating
wind field is another important issue which leads to varied
dynamics and thus possible component damage. Wind turbine
operating region can be divided into 3 regions by the wind
speed. In Region 1, a brake is implemented and the wind
turbine will not start until the wind speed is large enough. In
Region 2 (below-rated), the maximum power from wind will be
captured by utilizing a generator torque controller with the
blade pitch angle to be held at an optimum constant value.
When wind speed is large in Region 3 (above-rated), the major
task is to maintain the health status of wind turbine to prevent
excessive loads on the turbine [1].
In the above-rated region, a pitch controller is usually
adopted to keep the rotor speed constant and avoid the
excessive load. The current control theory used for wind
turbines include proportional integral differential (PID) control,
disturbance accommodating control (DAC), linear quadratic
regulator (LQR) and feedforward control. A collective gain
scheduled PID controller developed by NREL is widely
adopted to regulate generator speed and simultaneously deal
with the aerodynamic sensitivity change of different wind speed
[2]. It is worth noting that the disturbance may not be perfectly
cancelled in the gain scheduled PID controller. The speed
regulation can also be achieved by add damping to the
corresponding mode implemented by LQR in full state
feedback control when the nonlinear model can be linearized
under selected operating points [3]. Given the sensitivity of the
linearized model to operating points and unpredictable nature
of wind speed, a disturbance accommodating controller is
developed to reject disturbance and mitigate loads by
measuring wind speed with additional state estimators [4].
However, the accuracy of this estimator is not always
guaranteed. 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 [5].
In fact, the system dynamics of wind turbine is highly
affected by complicated and unpredictable wind field in
practice. Therefore a robust and intelligent control system can
tackle the time-varying external wind disturbances is needed to
maintain the constant generator speed and power in Region 3.
The disturbance observer (DOB) based control concept is
widely implemented in high precision motion control to reject
disturbances with unknown and/or time-varying spectra [6].
The fundamental idea of DOB control is to conduct model-
based estimation and cancellation of disturbance using an inner
feedback control loop. It is worth noting that in the field of
wind turbine control, the concept of disturbance observer has
been recently explored in suppressing the vibration of the tower
from the random wind loads [7] and in obtaining maximum
power point tracking (MPPT) with speed funnel control [8]. As
such, the potential effectiveness of DOB control is promising,
since it may achieve disturbance rejection without requiring
real-time sensor such as LIDAR. Moreover, in DAC,
disturbance compensation is achieved by minimizing the norm
of disturbance function . B is input matrix, is
disturbance gain, is disturbance gain and is disturbance
input matrix, refer to [3]. This result is limited if the
disturbance rejection function is not full rank. In comparison,
with the presence of the disturbance observer, wind disturbance
2
is directly rejected by an inner loop disturbance estimation,
which leads to better speed regulation.
In this paper, we extend the study presented in [9] which
shows good results in linearized model but limited performance
in nonlinear turbine in practice. The DOB scheme is augmented
with a collective PID controller to asymptotically reject the
time-varying unknown disturbances. In addition, an extra
compensator is introduced to deal with the mismatch between
the linearized model and the nonlinear turbine. Section 2 briefly
discusses a 5-MW wind turbine model. Disturbance based
observer control is formulated in Sec. 3. Results and
discussions are presented in Sec.4 and the concluding remarks
are shown in Sec. 5.
2. MODEL DESCRIPTION
In this research, we employ National Renewable Energy
laboratory (NREL) offshore 5-MW turbine that is widely used
in control studies. This wind turbine is a three-bladed upwind
variable-speed variable blade-pitch-to-feather-controlled
horizontal axis turbine [2]. The rotor diameter is 126 m and hub
height is 90 m. The cut-in wind speed is 3 m/s, 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 contains blades, a
low speed shaft, a gearbox, a high speed shaft, and a generator.
The aerodynamic power captured by the rotor is given as
23
1,
2
wind p
P R C v
(1)
where is the air density, is the rotor radius, and the power
coefficient is a nonlinear function of tip speed ratio , and
the pitch angle .
rR
v
(2)
where v is the wind speed, is the rotor speed.
The aerodynamic power is the product result from the
aerodynamic torque and the rotor speed. Thus from Equation
(1), the aerodynamic torque applied to the rotor can be
represented as [1]
23
1,
2p
ar
C R v
T
(3)
The power coefficient is a nonlinear function of tip speed
ratio , and the pitch angle , and can be achieved from look-
up table generated by field test data [10].
If we only take the rotor and generator dynamics into
account, and assume the tower, hub, low speed shat are rigid,
we can obtain the equations of motion,
r r a r r ls
g g hs g g em
J T C T
J T C T
(4)
where is the rotor inertia, is the generator inertia, is
the generator speed. and are the low speed shaft torque
and high speed shaft torque, respectively. and are the
rotor external damping and generator external damping,
respectively. is the generator electromagnetic torque.
The gearbox ratio is represented by , and 100% gearbox
efficiency is assumed. We can therefore obtain
g
ls
ghs r
T
nT
(5)
The equation of motion for the simplified two-mass system
is
t r a t r g
J T K T
(6)
where
2
2
t r g g
t r g g
g g em
J J n J
K K n K
T n T
(7)
The equation of motion in Equation (6) can represent
dynamics in all operating regions. Usually the generator speed
can be regulated by aerodynamic torque and
electromagnetic torque . Therefore a torque controller and a
blade pitch control can both regulate the generator speed. In
below-rated region (Region 2), torque controller is often
utilized to adjust the generator speed while blade pitch angle is
held constant to maintain the maximum aerodynamic
coefficient . In above-rated region (Region 3), pitch
controller is often adopted to limit the aerodynamic torque
to avoid extreme loads. The simple model in Equation (6) is
presented to illustrate the theoretical concept how the torque
and pitch controller work. In practice, the actual wind turbine
has more DOFs other than the ones we adopted in Equation (6).
Other unmodeled dynamics will also influence the generator
speed. In this research, we employ the Fatigue, Aerodynamics,
Structures, and Turbulence (FAST) Code developed by NREL
[11] to establish the mathematical model of the wind turbine
involving more DOFs.
The nonlinear aero-elastic equation of motion is
represented in following form [11]:
, , , , , , 0tt
d
M q u q f q q u u
(8)
where is the mass matrix, is the nonlinear forcing
function vector, is the response vector, is the vector of
control inputs, is the vector of wind input disturbances, and
is time. is calculated by AeroDyn using Blade Element
Momentum (BEM) Theory [12]. FAST then numerically
linearizes Equation (8) by perturbing each variable about their
corresponding operating points. After a Taylor series expansion
we can obtain
dd
M q C q K q F u F u
(9)
where is the mass matrix, is the damping matrix, is
the stiffness matrix, is the control input and is the wind
disturbance. Here the reduced-order linearized models are
obtained when the following 5 DOFs are switched on: the first
flapwise blade mode DOF (three blades), the generator DOF
and the drivetrain torsional flexibility DOF.
3
One can further cast the above linearized equation into the
state-space representation,
dd
dd
x Ax B u B u
y Cx D u D u
(10)
where
[ , ]T
x q q
is the state vector, is drive-train
torsional deflection perturbation, is rotor first symmetric
flap displacement perturbation, is generator speed
perturbation, is drive-train torsional velocity perturbation,
is rotor first symmetric flap velocity perturbation. is the
state matrix, is the control input matrix, is the control
input matrix, is the output matrix, is the control input
transmission matrix, is the wind input disturbance
transmission matrix, is the control input (perturbed blade
collective pitch angle), is the disturbance input (perturbed
wind speed), and is the output.
The operating point for linearization in this research is
chosen to be wind speed v = 18 m/s, pitch angle θ=14.92 deg,
and rotor speed ωr=12.1 rpm. We choose v = 18 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). θ=14.92 deg is the corresponding
blade pitch angle that produces the rated power, and
ωr=12.1 rpm is the rated rotor speed.
3. CONTROL DESIGN
In this section we formulate the disturbance observer
(DOB) based controller. We assume the generator speed is the
only available measurement and the controller gives the
collective pitch command. Then a pitch angle saturation, a pitch
rate limiter and a pitch actuator are added to meet the hardware
limits. The pitch actuator is chosen as a first-order model. The
actuator inertia is negligible compared to those of other
structures. The baseline gain scheduling PID controller used
in this research is developed by Jonkman [2].
The gain-scheduling part of PID controller is derived based
on the pitch sensitivity which is expressed as the sensitivity of
the aerodynamic power to the rotor collective blade pitch. The
pitch sensitivity is claimed to vary nearly linearly with the pitch
angle according to the best fit of the scatted points. It is worth
noting that the derived relation is not a strictly linear function.
Thus the disturbance cannot be perfectly cancelled by the gain-
scheduling part. Consequently, we should reduce the effect of
the time-varying wind speed to the output if a better result is
desired. The DOB controller is able to satisfy the need that the
augmentation of the DOB part will not only maintain the
original GSPI closed-loop stability but also further improve the
output performance.
Figure 1 displays the augmentation scheme of the baseline
PID controller for generator speed tracking and the
proposed disturbance observer to reject the time-varying wind
disturbances. In this figure, is the plant model, and
. When is acausal,
is added to make it causal and implementable, where m is the
relative degree of .
The inner loop disturbance observer is an inverse-based
disturbance cancelation scheme. The signal is the time-
varying wind disturbance, which will go through a disturbance
model to affect the input of the plant. is the
pitch angle and is the generator speed. When is
the linearized model, these signals become the perturbed values
corresponding to the operating point. The signal
is a
negative internal feedback of disturbance to cancel out the
influence of .
When
, the inverse-model-
based DOB design provides the advantageous property that
is independent of —the output of . Thus the
design of filter is decoupled and will not influence the
stability of original closed-loop feedback [6].
1
Pz
11
n
Pz
m
z
1
Qz
1
Cz
1
d
Pz
0
dk
dk
yk
ˆ
dk
uk
0
+
-
+
+
+
+
--
-
0
uk
Figure 1 Disturbance observer based control
When disturbance enters the plant input directly, we
can observe from Figure 1,
1 1 1 1
1
1
ˆ
1
n
m
m
d k d k d k Q z P z P z d k u k
Q z z u k
z Q z d k
(11)
For disturbance satisfying , where
is the denominator of the z transform of disturbance source,
disturbance rejection is achieved if [6]
1
11
1
1d
m
d
Az
z Q z K z Az
(12)
where is a polynomial of to assure causality,
is a polynomial in which all in are
replaced by , . The form of depends
on the disturbance form and interested frequency region. To
deal with possible mismatch and uncertainties in practice, the Q
filter need to be carefully selected.
In conventional cases such as vibration mitigation in
precision manufacturing, the disturbance frequency is either
known or adaptively identified. However, for disturbance in
wind turbines, however, it is generally difficult to find or define
its specific frequency contents, since the highly random wind
can contain many frequencies.
To determine . We model the wind disturbance as
the following disturbance wave generator [3, 4],
4
dd
dd
z Fz
uΘz
(13)
We assume that the wind disturbance 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 the
step disturbance, where the amplitude of wind speed changes
from one to another within a relatively short sampling interval.
and are assumed to be known as
0, 1FΘ
(14)
then wind disturbance can be represented as
1D k M k k
(15)
where is the unknown magnitude of wind disturbance.
In the wind turbine, when wind disturbance enters through
a disturbance model
, the output
will be The
objective is to cancel out the influence of the wind disturbance
to the output generator speed and simultaneously keep
the closed-loop system to be stable.
Take the z transform of the step disturbance shown in
Equation (15), and display it as an impulse response.
Similar to Equation (12), Equation (16) is obtained to
asymptotically reject the disturbance based on internal model
principle [13]. More details can refer to [9].
1
1 1 1
1
1
11
mp
p
Kz
z Q z z B z
Mk Bz
(16)
where is chosen to be an FIR filter
, and
1 1 1
1 1 1
1
1
pp
pp
B z z B z
B z z B z
(17 a, b)
.
Arranging Equation (16) in the form of polynomial
Diophantine equation can yield
1 1 1 1
1m
p Q p
B z K z z B z B z
Mk
(18)
where
Thus we can obtain the
Q filter.
Furthermore, the disturbance model should be
carefully selected to perfectly reject the wind disturbances. The
disturbance signal is assumed to be bounded because if
the wind speed exceeds the cut-off wind speed, the turbine is
forced to stop to avoid the excessive structural loads. If
has unstable poles, though is bounded,
will not be bounded after going through , which will
result in divergence of the whole system. Here we carefully
modify the poles to ensure the plant is stable and keep the DC
gain the same as that in unmodified model to maintain the
major dynamics.
The inverse of plant P should be stable when disturbance is
asymptotically rejected perfectly. Nevertheless, 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
1
1
1
p
p
Bz
Pz Az
(19)
where and are the numerator and the
denominator of the plant , respectively.
When implemented in DOB controller, the roots of
polynomial are the characteristic roots of P inverse,
which decide the stability of the
in the control block
in Figure 1. If any of the zeros of is outside or on the
unit circle, the output of closed-loop system will not converge.
In this research, the Zero Phase Error Tracking (ZPET) method
is utilized to keep the system to be stable [14].
4. RESULTS AND DISCUSSION
In this section, simulation results from baseline GSPI and
DOB controllers are demonstrated regarding both linearized
model and nonlinear plant. The linearized model is obtained
from 5 DOFs of the FAST turbine plant to verify the
effectiveness of the DOB controller. We then use both uniform
stepwise constant and uniform random wind disturbance to the
linearized model to test the DOB controller. Furthermore, the
DOB controllers designed from 5 DOFs linearized model are
applied to the NREL offshore 5-MW nonlinear wind turbine.
4.1 DOB controller results implemented in 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 Q filter
formulation, m (the relative degree of
1
Pz
) is 1, and
is
chosen to be 0.9953 which can yield the largest disturbance
rejection bandwidth and simultaneously guarantee the system
convergence. Following the design strategy provided in Section
3, we can compute, based on Equation (18), that
41 2 3
11 2 3 4 5
0.3701 0.
0.003609 0.0009153
764 0.0
3 0.09668 0.6728 - 0.4269 + 0.05
09577 0.008121 0.00123
161
Qz z z z z
z z z
zz
.
For comparison 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 overshoot and fast settling time. Here it
is worth mentioning that we cannot use the GSPI gains in [2]
because that GSPI controller is designed for nonlinear plant.
The stepwise wind disturbance in time domain and the random
disturbance in frequency domain are shown in Figure 2(a) and
2(b). The wind speed increase 5 m/s in every 20 s in Figure 2(a)
and the random disturbance contains rich frequencies in Figure
2(b). The time-domain generator speed error responses of DOB
and PID under stepwise disturbance are shown in Figure 3(a). It
is observed from that DOB has an overshoot of 39 rpm and PID
has a overshoot of 55 rpm. DOB control leads to a reduction of
generator speed error overshoot by 29.09% while maintaining
the same settling time. The frequency-domain response under
random wind disturbance is presented in Figure 3(b). The
5
amplitude spectrum of time-domain results shows obvious
decrease in frequencies below 1 Hz.
4.2 DOB controller implemented in nonlinear wind turbine
under turbulent wind
As shown above, the DOB control with the linearized
model exhibits large reduction in generator speed error under
stepwise and random disturbances. Then we apply this control
method to the nonlinear 5-MW wind turbine. The simulation
runs in FAST and Simulink environment. The simulation time
is 600 seconds with a sampling interval of 0.0125 second. For
the nonlinear plant, all 16 available degrees of freedom are
turned on,
First flapwise blade mode (3 blades)
Second flapwise blade mode (3 blades)
First edgewise blade mode (3 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
(a)
(b)
Figure 2. Wind disturbance implemented in 5-DOF linearized model.
(a) Stepwise wind disturbance in time domain; (b) Random wind
disturbance in frequency domain.
(a)
(b)
Figure 3. Generator speed response of 5-DOF linearized model under
wind disturbances. (a)Time-domain response under stepwise
disturbance; (b) Frequency-domain response under random
disturbance.
Aerodynamic forces and moments are calculated by AeroDyn
[12]. Realistic turbulent wind fields are generated in TurbSim
[15].The turbulence intensity is 14%. The 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.
6
NONLINEAR WIND
TURBINE
(FAST)
BASELINE
GSPI
DOB
r
-
GENERATOR
SPEED
PITCH
COMMAND
PITCH
ACTUATOR
Figure 4. Augmentation of GSPI and DOB controls.
The PID controller in Figure 1 block is chosen to
be the GSPI controller for nonlinear plant. The model mismatch
between the nominal nonlinear plant and the linearized model
in practice will influence the stability of the augmented
feedback system. Therefore the Q filter here should be carefully
adjusted to achieve the stability. From the experiment, the
increase of can increase the stability but decrease the error
reduction level. An extra compensator
is added to
deal with the problem.
The controller is simulated under three different wind files
where the mean speed is 18 m/s, 16 m/s and 20 m/s
respectively. The first 99s of each simulation are ignored for
any performance measures to allow the initial transients to die
out. From generator speed under 18m/s turbulent wind file in
Figure 5(a), it can be seen generator speed stays near the rated
value, 1173.7 rpm. Figure 5(b) is a zoom-in result of generator
speed at steady state between 300 s and 350 s under 18 m/s
turbulent wind file. Less oscillation around the rated value
1173.7 rpm is observed under DOB control. It is can be seen
from Figures 5(a), 5(c), and 5(d), generator speed response
does not have large oscillation and can be kept near 1173.7
rpm, which means DOB controller exhibits excellent robustness
under time-varying wind speed and unmodeled dynamics.
The controller is further examined under 9 wind files with
mean speeds from 14 m/s to 22 m/s to study the robustness.
These wind files cover almost the entire Region 3. To quantify
the overall speed regulation, root mean square (RMS) error of
generator speed under different turbulent wind files is analyzed
to compare the two controllers (Table 1). From Table 1, it can
be clearly observed that the speed RMS error decreases from
5.56% to 16.96% and power RMS error decreases from 8.99%
to 13.44% in 9 wind files. The generator speed and power
regulation is good at a wide wind speed region and exhibits
robustness in nonlinear plant. The effectiveness of disturbance
rejection of DOB is proved.
5. CONCLUSION
In this research an internal model-based disturbance
observer (DOB) design combined with a PID type feedback
controller is formulated for wind turbine speed and power
regulation. The DOB controller utilized the model-based
estimation and cancellation of disturbance using an inner
feedback control loop. The proposed method is applied in 5-
DOF linearized model and the nonlinear 5-MW wind turbine.
Our case studies show that the DOB controller can yield about
14% reduction in generator speed RMS error compared to
baseline PID controller and exhibits excellent robustness under
different turbulent wind field.
(a)
(b)
(c)
7
(d)
Figure 5. Time-domain perfromance comparsion of GSPI and DOB in
different turbulent wind field. (a) 18 m/s turbulent wind filed
performance; (b) 18 m/s turbulent wind filed zoom-in performance;
(c)16 m/s turbulent wind filed performance; (d) 20 m/s turbulent wind
filed performance.
Table 1 performance comparison
Mean
wind
speed
Controller
Speed RMS error
Power RMS error
14
GSPI
0.0545
1.6055
DOB
0.0454 (-16.7%)
1.3897 (-13.44%)
15
GSPI
0.0593
1.8146
DOB
0.0560 (-5.56%)
1.6514 (-8.99%)
16
GSPI
0.0642
1.9511
DOB
0.0570 (-11.21%)
1.7270 (-11.49%)
17
GSPI
0.0699
2.0673
DOB
0.0607 (-13.16%)
1.8424 (-10.88%)
18
GSPI
0.0740
2.2131
DOB
0.0636 (-14.05%)
1.9826 (-10.42%)
19
GSPI
0.0800
2.3388
DOB
0.0684 (-14.5%)
2.1044 (-10.02%)
20
GSPI
0.0862
2.4581
DOB
0.0739 (-14.27%)
2.2276 (-9.38%)
21
GSPI
0.0908
2.4489
DOB
0.0754 (-16.96%)
2.2196 (-9.36%)
22
GSPI
0.0968
2.5393
DOB
0.0806 (-16.74%)
2.3093 (-9.06%)
ACKNOWLEDGMENTS
This research is supported by National Science Foundation
under grant CMMI – 1300236.
REFERENCES
[1] Laks, J.H., Pao, L.Y., and Wright, A.D. 2009, "Control of
wind turbines: Past, present, and future," American Control
Conference, St. Louis, MO, June 10-12,pp. 2096-2103.
[2] Jonkman, J.M., Butterfield, S., Musial, W., and Scott, G.,
2009, “Definition of a 5-MW reference wind turbine for
offshore system development,” Technical Report No.
NREL/TP-500-38060, National Renewable Energy Laboratory,
Golden, CO.
[3] Wright, A.D., 2004, “Modern control design for flexible
wind turbines,” Technical Report No. NREL/TP-500-35816,
National Renewable Energy Laboratory, Golden, CO.
[4] Wright, A.D., and Balas, M.J., 2003, “Design of state-space-
based control algorithms for wind turbine speed regulation,”
Journal of Solar Energy Engineering, V125 (4), pp. 386-395.
[5] Wang, N., Johnson, K.E., and Wright, A.D., 2012, “FX-
RLS-based feedforward control for LIDAR-enabled wind
turbine load mitigation,” IEEE Transactions on Control
Systems Technology, V20 (5), pp. 1212-1222.
[6] Chen, X., and Tomizuka, M., 2015, “Overview and new
results in disturbance observer based adaptive vibration
rejection with application to advanced manufacturing,”
International Journal of Adaptive Control and Signal
Processing, V29 (11), pp. 1459-1474.
[7] He, W., and Ge, S.S., 2015, "Vibration control of a
nonuniform wind turbine tower via disturbance observer,"
IEEE/ASME Transactions on Mechatronics, V20 (1), pp. 237-
244.
[8]Hackl, C.M., 2013, "Funnel control with disturbance
observer for two-mass systems," 52nd IEEE Conference on
Decision and Control, pp. 6244-6249.
[9] Yuan, Y., Chen, X. and Tang, J., 2016, "Disturbance
observer based pitch control of wind turbines for disturbance
rejection," Proceedings of SPIE, Smart Materials and
Nondestructive Evaluation for Energy Systems, Las Vegas, NV,
March 20-24.
[10] Wright, A.D. and Fingersh, L.J., 2008, "Advanced
Control Design for Wind Turbines, Part I: Control Design,
Implementation, and Initial Tests", Technical Report No.
NREL/TP-500-42437, National Renewable Energy Laboratory,
Golden, CO.
[11] Jonkman, J.M., and Buhl Jr., M.L., 2005, “FAST user’s
guide,” Technical Report No. NREL/EL-500-38230, National
Renewable Energy Laboratory, Golden, CO.
[12] Moriarty, P.J., and Hansen, A.C., 2005, “AeroDyn theory
manual,” Technical Report No. NREL/TP-500-36881, National
Renewable Energy Laboratory, Golden, CO.
[13] Francis, B.A., and Wonham, W.M., 1976, “The internal
model principle of control theory,” Automatica, V12 (5),
pp.457-465.
[14] Tomizuka, M., 1987, “Zero phase error tracking algorithm
for digital control,” Journal of Dynamic Systems,
Measurement, and Control, V109 (1), pp. 65-68.
[15] Jonkman, J.M., “TurbSim user's guide: Version 1.50,”
2009, Technical Report No. NREL/TP-500-46198, National
Renewable Energy Laboratory, Golden, CO.
[16] Chen, X., and Tomizuka, M., 2013, “Selective model
inversion and adaptive disturbance observer for time-varying
vibration rejection on an active-suspension benchmark,”
European Journal of Control, V19 (4), pp. 300-312.
[17] Chen, X., Oshima, A., and Tomizuka, M., 2013, “Inverse-
based local loop shaping and iir-filter design for precision
motion control,” Proceedings of the 6th IFAC Symposium on
8
Mechatronic Systems, Hangzhou, China, April 10-12, pp. 490-
497.
[18] Selvam, K., Kanev, S., and van Wingerden, J.W., 2009,
“Feedback–feedforward individual pitch control for wind
turbine load reduction,” International Journal of Robust and
Nonlinear Control, V19 (1), pp.72-91.
[19] Laks, J.H., Pao, L.Y., and Wright, A., 2009, “Combined
feedforward/feedback control of wind turbines to reduce blade
flap bending moments,” Proceedings of 47th AIAA Aerospace
Sciences Meeting including The New Horizons Forum and
Aerospace Exposition, Orlando, FL, January 5-8.
[20] Laks, J.H., Dunne, F., and Pao, L.Y., 2010, “Feasibility
studies on disturbance feedforward techniques to improve load
mitigation performance,” Technical Report No. NREL/SR-
5000-48598, National Renewable Energy Laboratory, Golden,
CO.
[21] Balas, M.J., Magar, K.S.T., and Frost, S.A., 2013,
“Adaptive Disturbance Tracking theory with state estimation
and state feedback for region II control of large wind turbines,”
American Control Conference, Washington, DC, June 17-19,
2013, pp. 2220-2226.
