Modelling the Dynamics of an Arc-shaped Kite for Control Law Design

233 Pages·2010·13.97 MB·English

Modelling the Dynamics of an
Arc-shaped Kite for Control Law Design
Design of a Rigid Body Model for Real-Time Simulation using
a Multi-Body Reference
S.G.C. de Groot, BSc.
May 6, 2010

Modelling the Dynamics of an
Arc-shaped Kite for Control Law
Design
Design of a Rigid Body Model for Real-Time Simulation using a
Multi-Body Reference
Master of Science Thesis
For obtaining the degree of Master of Science in Aerospace
Engineering at Delft University of Technology
S.G.C. de Groot, BSc.
May 6, 2010
Faculty of Aerospace Engineering Delft University of Technology
·
Delft University of Technology
Copyright c S.G.C. de Groot, BSc.
(cid:13)
All rights reserved.
Delft University Of Technology
Department Of
Aerospace for Sustainable Engineering and Technology
The undersigned hereby certify that they have read and recommend to the Faculty of Aerospace
Engineering for acceptance a thesis entitled “Modelling the Dynamics of an Arc-shaped
Kite for Control Law Design” by S.G.C. de Groot, BSc. in partial fulfillment of the
requirements for the degree of Master of Science.
Dated: May 6, 2010
Readers:
Prof. Dr. W.J. Ockels
Dr. Ir. A.L. Schwab
Dr.-Ing. R. Schmehl
Ir. J. Breukels

Summary
The need and interest for sustainable energy solutions is rising. A new branch in this field is
high altitude wind power (HAWP). One novel concept is the Laddermill under development at
the ASSET institute (TU Delft). The Laddermill uses kites to reel a tether from a drum which
drives a generator. One of the key factors for success is the ability to control kites automatically.
Currently successful test have been conducted with leading edge inflatable or arc-shaped kites.
Arc-shaped kites are extensively used and developed in the field of kite surfing. Due to their high
traction and control capabilities arc-shaped kites are the choice for the Laddermill prototypes.
A literature review is conducted to obtain an overview of the current status of technology re-
garding arc-shaped kite modelling and control. For automatic control of kites several advanced
control techniques exist like model predictive control and nonlinear dynamic inversion. Different
kite models exist with specific applications. An example is the complex Multi-Body Kite model
designedinMsc. Adams. Itisconcludedthatfastmodelsarerequiredforonlineimplementation.
A formal methodology is developed to reduce the Multi-Body Arc-shaped Kite model to a Rigid
BodyArc-shapedKitemodel. Inmoregeneralterms: anyflyingobjectmodelledwithmulti-bodies
can be reduced to a set of rigid body states.
The numerous states of the Multi-Body model designed in Adams are reduced to a set of states
describing the motion as a rigid body. For every body, flexible and rigid, holds that the inertial
linearandrotationalaccelerationfollowNewton’ssecondlaw: thesumofexternalforcesisequalto
thetimederivativeofthelinearmomentumandthesumofexternalmomentsisequaltothetime
derivative of the angular momentum. On this principle the state reduction is applied and verified
for the Multi-Body model. The acceleration, velocity and displacement components are obtained
on the basis of conservation of linear momentum. The inertia tensor and angular momentum are
derived with a particle based method. It is proven that the particle based method makes up a
very good approximation to derive the rotational quantities.
The Rigid Body model is developed to describe the dynamic motion of an arc-shaped kite. It
is attempted to reduce the aerodynamics and structural deformation of the Multi-Body Kite
modeltoaparametricaerodynamicmodelandaquasi-staticstructuralmodel. Toaccomplishthe
reduction of the the Multi-Body Kite model to a Rigid Body Kite model it is required that the
aerodynamics and the structural properties can be formulated by a set of rigid body states. The
rigid body states are defined by the state reduction process. Due to the tight interaction between
the flight condition and kite shape the aerodynamic model and structural model are variant with
the flight condition.
TheaerodynamicmodelisformulatedonthebasisofTaylorexpansionsandwrittenindimension-
less form. This results in a linear decomposition of the dependency of each state. The effective
ModellingtheDynamicsofanArc-shapedKiteforControlLawDesign
vi Summary
contribution of each aerodynamic state is given by respective dimensionless aerodynamic deriva-
tives. The aerodynamic derivatives are obtained with the parameter identification technique.
Flight test simulations are performed to identify the aerodynamic model.
The structural model is constituted on a quasi-static basis by formulating functions describing
the initial conditions of the flight test simulations. Functions are formulated for the inertia tensor
properties, meanwing chord, wingspan, projected surfaceareaandthetetherattachment points.
Test simulations are performed to validate the Rigid Body model with respect to the Multi-Body
model. The validation proves that the proposed methodology for model reduction is a qualitative
manner for model reduction of the Multi-Body Kite model and for multi-body model reduction
of flying objects in general. It results in kite models almost ten times faster than real-time,
whereas simulating the Multi-Body Kite model in Adams takes more than ten times real-time.
The development of an arc-shaped kite model which is appropriate for controller design has come
toadetailedlevel. Controltechniqueswhichrequirefastandaccuratemodelslikemodelpredictive
control and nonlinear dynamic inversion can be designed on the basis of this modelling approach.
Forfutureworkitisrecommendedtoinvestigateonadvancedmodelidentificationtechniquesand
to perform a structural modal analysis.
ModellingtheDynamicsofanArc-shapedKiteforControlLawDesign
Acknowledgements
The accomplishment of the master thesis is an exciting, hard work, but above all, a very educa-
tional experience. It forms the final assignment for obtaining the Master’s Degree in Aerospace
Engineering at the Delft University of Technology. It is a pleasure and an honor to express my
gratitude to all individuals who have assisted me during this project.
I would like to thank Prof. Dr. Wubbo J. Ockels for his remarks and useful advice. Furthermore
I would like to thank my first supervisor Jeroen Breukels for his inspiring ideas, professional
guidance and close involvement. I am sincerely grateful to my other supervisors Roland Schmehl
and Arend Schwab.
Otherpersonshavemadegreatcontributionstobringthisthesistoaqualitativeend. Iwouldlike
to thank Chris Verheul for his teaching and support of the multi-body application software Msc.
Adams. I would like to thank Barend Lubbers for his guidance and critical remarks on model
identification.
Grateful thanks goes to the Laddermill group within ASSET. I want to show my appreciation to
Nana Saaneh, Aart de Wachter, Rolf van der Vlugt, Edwin Terink, John van den Heuvel, Roland
Verheul, Lyssandre Rammos, Jorn Baayen and Thomas Frenkel.
Last but not least I want to thank my family, friends and my parents in special for their loving
encouragement and support.
ModellingtheDynamicsofanArc-shapedKiteforControlLawDesign
viii Acknowledgements
ModellingtheDynamicsofanArc-shapedKiteforControlLawDesign