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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.

071006-2 / Vol. 139, JULY 2017 Transactions of the ASME

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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

Journal of Dynamic Systems, Measurement, and Control JULY 2017, Vol. 139 / 071006-3

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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

071006-4 / Vol. 139, JULY 2017 Transactions of the ASME

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

Journal of Dynamic Systems, Measurement, and Control JULY 2017, Vol. 139 / 071006-5

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.

071006-6 / Vol. 139, JULY 2017 Transactions of the ASME

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*

Journal of Dynamic Systems, Measurement, and Control JULY 2017, Vol. 139 / 071006-7

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.

071006-8 / Vol. 139, JULY 2017 Transactions of the ASME

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*

Journal of Dynamic Systems, Measurement, and Control JULY 2017, Vol. 139 / 071006-9

Acknowledgment

This research was supported by National Science Foundation

under Grant CMMI–1300236.

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