Riccardo Fratini and Riccardo Santini and Jacopo Serafini and Massimo Gennaretti and Stefano Panzieri
A Spatial Repetitive Controller Applied to an Aeroelastic Model for Wind Turbines
1689 - 1697
2016
10
9
International Journal of Computer and Systems Engineering
https://publications.waset.org/pdf/10005484
https://publications.waset.org/vol/117
World Academy of Science, Engineering and Technology
This paper presents a nonlinear differential model,
for a threebladed horizontal axis wind turbine (HAWT) suited
for control applications. It is based on a 8dofs, lumped
parameters structural dynamics coupled with a quasisteady sectional
aerodynamics. In particular, using the EulerLagrange Equation
(Energetic Variation approach), the authors derive, and successively
validate, such model. For the derivation of the aerodynamic model,
the Greenbergs theory, an extension of the theory proposed by
Theodorsen to the case of thin airfoils undergoing pulsating flows,
is used. Specifically, in this work, the authors restricted that theory
under the hypothesis of low perturbation reduced frequency k,
which causes the lift deficiency function C(k) to be real and equal
to 1. Furthermore, the expressions of the aerodynamic loads are
obtained using the quasisteady strip theory (Hodges and Ormiston),
as a function of the chordwise and normal components of relative
velocity between flow and airfoil Ut, Up, their derivatives, and
section angular velocity &epsilon;. For the validation of the proposed model,
the authors carried out open and closedloop simulations of a 5
MW HAWT, characterized by radius R 61.5 m and by mean chord
c 3 m, with a nominal angular velocity &Omega;n 1.266radsec.
The first analysis performed is the steady state solution, where
a uniform wind Vw 11.4 ms is considered and a collective
pitch angle &theta; 0.88 is imposed. During this step, the authors
noticed that the proposed model is intrinsically periodic due to
the effect of the wind and of the gravitational force. In order
to reject this periodic trend in the model dynamics, the authors
propose a collective repetitive control algorithm coupled with a PD
controller. In particular, when the reference command to be tracked
andor the disturbance to be rejected are periodic signals with a
fixed period, the repetitive control strategies can be applied due to
their high precision, simple implementation and little performance
dependency on system parameters. The functional scheme of a
repetitive controller is quite simple and, given a periodic reference
command, is composed of a control block Crc(s) usually added
to an existing feedback control system. The control block contains
and a free timedelay system e&tau;s in a positive feedback loop, and a
lowpass filter q(s). It should be noticed that, while the time delay
term reduces the stability margin, on the other hand the low pass
filter is added to ensure stability. It is worth noting that, in this
work, the authors propose a phase shifting for the controller and
the delay system has been modified as e(&minus;(T&minus;&gamma;k)), where T is the
period of the signal and &gamma;k is a phase shifting of k samples of the
same periodic signal. It should be noticed that, the phase shifting
technique is particularly useful in nonminimum phase systems, such
as flexible structures. In fact, using the phase shifting, the iterative
algorithm could reach the convergence also at high frequencies.
Notice that, in our case study, the shifting of k samples depends
both on the rotor angular velocity &Omega; and on the rotor azimuth
angle &Psi; we refer to this controller as a spatial repetitive controller.
The collective repetitive controller has also been coupled with a C(s) PD(s), in order to dampen oscillations of the blades.
The performance of the spatial repetitive controller is compared
with an industrial PI controller. In particular, starting from wind
speed velocity Vw 11.4 ms the controller is asked to maintain the
nominal angular velocity &Omega;n 1.266rads after an instantaneous
increase of wind speed (Vw 15 ms). Then, a purely periodic
external disturbance is introduced in order to stress the capabilities
of the repetitive controller. The results of the simulations show that,
contrary to a simple PI controller, the spatial repetitivePD controller
has the capability to reject both external disturbances and periodic
trend in the model dynamics. Finally, the nominal value of the
angular velocity is reached, in accordance with results obtained with
commercial software for a turbine of the same type.
Open Science Index 117, 2016