IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 20, NO. 1, FEBRUARY 2015 237
Vibration Control of a Nonuniform Wind Turbine
Tower via Disturbance Observer
Wei He, Member, IEEE, and Shuzhi Sam Ge, Fellow, IEEE
Abstract—In this paper, the vibration control problem is stud-
ied for a wind turbine tower subjected to random wind loads. The
tower is modeled as a nonuniform Euler–Bernoulli beam system
with distributed parameters by using the Hamilton’s principle. The
control force is applied at the top boundary of the tower to sup-
press the vibrations of the tower. Disturbance observer is designed
to attenuate the disturbance at the top of the tower. The stability
of the whole system is rigorously proved via the Lyapunov analy-
sis and the satisfactory control performance is guaranteed under
the proper choice of the design parameters. Numerical results are
provided to illustrate that the designed controller is effective in
dissipating the vibrations of the tower.
Index Terms—Distributed parameter system, disturbance
observer, modeling, vibration control.
I. INTRODUCTION
W
ITH the increased focus on the development of renew-
able energy, the control problem for the wind turbine
has gained increasing attention. Wind power, as an alternative
to fossil fuels, is plentiful, renewable, widely distributed, clean,
produces no greenhouse gas emissions during operation, and
uses little land [1]. A wind turbine can extract energy from the
wind power by converting the kinetic energy in the wind to
mechanical energy, and finally to electrical energy. The basic
components of a wind turbine include the blades, hub, low- and
high-speed shaft, gearbox, generator, nacelle, and tower [2].
Based on the linear and nonlinear ordinary differential equa-
tion (ODE) model, a number of research focuses on the control
of the wind turbine by changing the pinch angle and changing
the electrical characteristics of the generator. The proportional-
Manuscript received December 10, 2013; revised February 12, 2014; ac-
cepted March 17, 2014. Date of publication April 14, 2014; date of current
version October 3, 2014. Recommended by Technical Editor Z. Xiong. This
work was supported by the National Natural Science Foundation of China
under Grant 61203057, in part by the Fundamental Research Funds for the
China Central Universities of UESTC under Grant ZYGX2012J087 and Grant
ZYGX2013Z003, in part by the National Basic Research Program of China
(973 Program) under Grant 2014CB744206, and in part by the Foundation of
Key Laboratory of Autonomous Systems and Networked Control, Ministry of
Education, China, under Grant 2013A03.
W. He is with the School of Automation Engineering, University of Elec-
tronic Science and Technology of China, Chengdu 611731, China (e-mail:
hewei.ac@gmail.com).
S. S. Ge is with the Department of Electrical and Computer Engineering, Na-
tional University of Singapore, Singapore 117576, and also with the Robotics
Institute, School of Computer Science and Engineering, University of Elec-
tronic Science and Technology of China, Chengdu 611813, China (e-mail:
samge@nus.edu.sg).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMECH.2014.2313876
integral-derivative approach was used to control several large
wind turbines in the 1970s and 1980s. Later, modern control
technics including the linear quadratic regulator design, switch-
ing control, adaptive control, etc. are developed for wind tur-
bines. The remarkable work on vibration isolation for a wind
turbine is documented in [3], where a nonlinear vibration iso-
lator is designed for decreasing the structural response of the
turbine under wind and seismic loading. In industry, a commer-
cial vibration control system developed by ContiTech has been
applied for minimizing environmental noise of the wind turbine.
However, studies for control of flexible towers are limited.
In modern engineering, wind turbines are usually located
at areas where winds are stronger and more constant, such as
offshore and high altitude sites. However, due to the transport
and price restriction, flexible towers are widely designed to
make wind energy more competitive and cost-effective. Since
the tower becomes lighter and more flexible, the external loads
such as the cyclical (that is repetitive) turbulence will cause the
mechanical vibrations of the tower. The large vibrations lead
to the fluctuating forces stressed on the tower which will result
in the fatigue failure. Therefore, the control system should be
designed to mitigate the effects of external loads and suppress
vibrations of the flexible tower.
Boundary control schemes have been widely used in various
distributed parameter systems [4]–[7]. In [8], a class of nonlin-
ear partial differential equation (PDE) processes is controlled by
using boundary iterative learning control method with transfor-
mation to an output regulation problem in the spatial domain.
In [9], a flexible spacecraft described by a cantilever flexible
beam is stabilized by using adaptive output feedback sliding-
mode control techniques. However,thecontroldesigns in [8], [9]
are based on the convention from the PDEs into ODEs by using
spatial discretization. Due to the high dimensionality of the orig-
inal model, the model discretization will lead to the spillover
instability [10], [11], which should be avoided in the control de-
sign. In order to avoid the spillover problem, more attention has
been given on the control of original distributed parameter sys-
tem without any model discretization. In [12], a robust adaptive
boundary control scheme is investigated to control an axially
moving string with nonlinear behavior. In [13], a linear gantry
crane model with a flexible string-type cable is studied by de-
veloping a boundary controller and experiment is implemented
to verify the control performance. In [14], a three-dimensional
marine riser system modeled by PDEs is stabilized by using
boundary control techniques with hydraulic actuators at the top
end. In all these papers, the effects of unknown spatiotemporally
varying distributed loads and varying system parameters have
been neglected.
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