Anderson, David (1999) Active control of turbulence-induced

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Anderson, David (1999) Active control of turbulence-induced helicopter
vibration. PhD thesis.

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ACTIVE
CONTROL
OF
TURBULENCE-INDUCED
HELICOPTER
VIBRATION
DAVID ANDERSON
Thesis Faculty Engineering, University Glasgow, for
to the
submitted of of
Degree Doctor Philosophy. All
the of of aspects of the work contained
herein in indicated.
are original content except where
This is based between October 1994
thesis
on research conducted and
October 1997 Department Aerospace Engineering.
the
at of
University Glasgow.
of
-a
David Anderson', March 1999.
© David Anderson, 1999.
Abstract
Helicopter
induced by ha\
vibration
signatures severe atmospheric turbulence e
been
differ
shown to from The
considerably
nominal, still air vibration. perturbations of
the transmission frequency have
implications for design
significant the of passive and
devices,
active
vibration
alleviation
which are generally tuned to the nominal vibration
frequency.
This
investigates
thesis in
the
the
existence of phenomena several realistic
atmospheric turbulence Computational Fluid Dynamic
environments, generated using
(CFD)
high-fidelity
engineering
software and assimilated within a rotorcraft simulation,
RASCAL. The RASCAL
is blade
simulation modified to calculate element sampling of
the high frequency In final
thorough,
gust, enabling the
analyses of rotor response. a
integration-based inverse GENISA is
modification, a numerical, simulation algorithm,
incorporated is henceforth HISAT. Several
the to
and augmented simulation referred as
implementation issues from because
arise the symbiosis, principally of the modelling of
lead-lag However, for increasing
the
technique
variable rotorspeed and motion. a novel
is
tested
numerical stability margins proposed and successfully.
higher harmonic 'HHC'
Two
active vibration control schemes, control and
`worst-case'
individual blade control 'IBC', are then evaluated against a sharp-edged
demonstrates lack
field. The higher harmonic
a worrying of robustness,
controller
gust
levels. Several intuitive
begins to to the vibration modifications
contribute
and actually
disturbance is A
but
estimation successful. new
only
to the algorithm are proposed
is derived implemented MATLAB
blade
and using
motion
of coupled
model
simulation
Following bandwidth
IBC
design problems, a
is compensator.
to a simple
and used
improves
Hý the
is theory which controller performance.
using
proposed
redesign
is to
using artificial neural networks
Disturbance attempted
prediction/estimation
the
limited Overall, the aims and objectives of research are met.
success.
Anderson. D.
4ctiý Control Turbulence /,, doted Helicopter l
e of
ihraii ':
Acknowledgements
I'd like
to express my deepest thanks to Dr Stewart Houston for his
exceptional
guidance,
support and supervision throughout the course of this
for his
research and also in
motivation and encouragement getting me to write this
dissertation. I would also like to thank Dr Douglas Thomson for fielding
my
inverse
for having
endless questions on simulation and the restraint to not throw
his Special
me out of office! mention must also go to Dr Steve Rutherford, Dave
Ewing Garry Leacock for
and participating in those incredibly beneficial
brainstorming
if did little
Dr Chris
sessions, even we get a side-tracked at times.
O'Neill deserves
for his Monday
also thanks
many
morning motivation classes, as
do Dr John Maclean Dr Nick Brignall from Marconi. There
and
are many others
Aerospace Department beyond
the in helping
within and who contributed to
make
know
this
possible, you who you are, many thanks.
Many Centre for Systems Control
thanks to the
must also go and at the
University Glasgow for
DERA
of providing me with the research grant and to
Bedford for My
to these two
volunteering additional sponsorship. gratitude
bodies for financial intellectual be
their
and contributions cannot understated.
I'd like Charles Rae Anderson, for loving
to thank their
and my parents,
for belief day
throughout times their that
support some painful and unending one
be I doubted judgement.
this thesis would submitted, even though at times their
I'd like beautiful beloved Theresa,
Most
to thank
of all, my and wife who
do
has throughout to
stoically supported me my academic career and continues so
day. She has been faith throughout the downs,
to this my rock of all of ups and
failures I've The love I
this
experienced with work. and gratitude
and
successes
feel for her be in dedicating this to
cannot expressed mere words, so perhaps work
for linguistic inadequacy.
in
her
will some small way make up my
David Anderson March, 1999.
-
I 11
Anderson
D
Control Turbulence Helicopter
Active tir
of
-Induced
Contents
ABSTRACT
ACKNOWLEDGEMENTS
CONTENTS
NOMENCLATURE
CHAPTER I
ACTIVE CONTROL OF TURBULENCE-INDUCED HELICOPTER VIBRATION. 1
1.1 INTRODUCTION.
1.2 REVIEW VIBRATION ALLEVIATION CONTROL LITERATURE 3
OF AND
1.2.1 The Creation Transmission Helicopter Vibration. 4
and of
1.2.2 Passive 10
vibration alleviation.
1.2.3 Active 13
vibration control.
1.3 AIMS RESEARCH 16
OF THE
1.4 THE STRUCTURE THESIS 17
OF THIS
1.5 SUMMARY CHAPTER I. 20
OF
CHAPTER II
SIMULATION MODEL. 21
A DESCRIPTION OF THE RASCAL HELICOPTER
21
2.1 INTRODUCTION RASCAL.
TO
23
2.2 RIGID-BODY
DYNAMICS.
25
2.3 ROTOR FORCES MOMENTS.
AND
25
2.3.1 Introduction.
26
2.3.2 Blade Element Theory.
27
2.3.3 Blade Element Velocity.
30
Blade Acceleration.
2.3.4
31
Blade Aerodynamics.
2.3.5
36
Total Forces Moments.
2.3.6 and
37
EQUATIONS MOTION.
BLADE OF
2.4
Multiblade Co-ordinate Transformation. 39
2 4.1
.
Iv
Anderson
D.
Active Control Turbulence Induced Helicopter
l'ih'(cid:30)
of
2.5
ROTOR
WAKE
MODEL.
4(1
2.5.1
Static
Inflow Models.
41
2.5.2
Dynamic
Inflow
models.
.1
2.5.2.1
Perturbation
model.
42
2.5.2.2
Peters
HaQuang
model.
44
2.6
FUSELAGE
AERODYNAMICS.
45
2.6.1
Polynomial
expansion.
45
2.6.1.1
Absolute forces
and moments.
45
2.6.1.2
Aerodynamic
coefficient expansion. 4(-
2.6.2 Tabular
approach.
47
2.6.2.1 Forces
and moments.
47
2.6.2.2 Coefficient
abstraction. 48
2.7 FIN AERODYNAMICS
48
2.8 TAILPLANE AERODYNAMICS
49
2.9 ENGINE TRANSMISSION MODEL
AND
50
2.10 ATMOSPHERE MODEL.
51
2.11 CHAPTER SUMMARY DISCUSSION.
AND 53
CHAPTER III
INTEGRATION OF A GUST MODULE WITHIN RASCAL.
54
3.1 WHAT IS ATMOSPHERIC TURBULENCE? 54
3.2 TRANSFORMATION
OF THE GUST VELOCITIES TO BLADE AXES. 57
3.2.1 Blade
57
element position.
3.2.2 Gust in blade 60
velocity axes.
3.2.3 Non-rotating 61
components.
3.3 THE 62
RESPONSE OF A SINGLE MAIN AND TAILROTOR HELICOPTER TO A SHARP-EDGED GUST.
3.4 ANALYSIS GUST VIBRATION SIGNATURE. 63
OF THE
3.4.1 Time Domain Calculation Phase Shift. 64
the
of
3.5 CHAPTER 67
SUMMARY AND DISCUSSION.
CHAPTER IV
THE DEVELOPMENT OF ADVANCED TURBULENT ENVIRONMENTS. 68
4.1 ATMOSPHERIC TURBULENCE MODELLING. 68
4.2 TECHNIQUES LIMITATIONS OF EXISTING TURBULENCE MODELS. 69
AND
4.2.1 Modelling Atmosphere Using Discrete 69
the
gusts.
4.2.2 Continuous PSD 71
turbulence models methods.
-
Gust (SDG) Method.
4.2.3 Statistical Discrete
-, 4
1'
Anderson
D. Active Control Turbulence-Induced Helicopter l'ihrntu(,,:
of
4.2.4 Limitations Statistical Turbulence 76
of models.
4.3 GENERATING
TURBULENT ENv'IRON%, USING CFD.
A IENT
,1
4.3.1
Merging Rotorcraft Simulation. 77
with a
4.3.2 Bilinear Interpolation. 7S
4.4 EXAMPLES CFD GENERATED OBSTRUCTION-INDUCED TURBULENCE. 79
OF
4.4.1 Flow block. 80
tower
around a
4.4.2 Flow
80
over a cliff.
4.4.3 Flow
81
across a valley.
4.4.4 Flow 81
around an offshore oil platform.
4.5 ANALYSIS OF THE RESPONSE TO LONGITUDINAL AND LATERAL/DIRECTIONAL TURBULENCE. S-'
4.5.1 Uncontrolled flight block 82
tower
past a
4.5.2 Uncontrolled flight 83
top.
over a cliff
CHAPTER DISCUSSION. 85
4.6 SUMMARY AND
CHAPTER V
86
THE INVERSE SIMULATION OF RASCAL
86
5.1 CONTINUING DEVELOPMENT OF HISAT.
87
5.1.1 Advantages Inverse Simulation.
of
88
5.1.2 Methods Inverse Simulation.
of
90
5.1.3 Inverse Simulation by Differentiation.
91
5.1.4 Inverse Simulation in the Forward Sense using Integration.
92
GENISA ALGORITHM.
5.2 DESCRIPTION OF THE
95
System Jacobian.
5.2.1 Estimation
the
of
96
METHOD FLIGHT PATH GENERATION.
5.3 POLYNOMIAL OF
96
5.3.1 Boundary Value Polynomials.
97
5.4 SIMPLE EXAMPLE MAINTAINING TRIM.
-
98
Simulation Time Histories.
5.4.1 Analysis
of
99
interval
to
5.4.2 The importance of the control application stability.
100
5.4.3 Other
numerical sensitivities.
100
NEWTON STEP.
5.5 ENHANCEMENT OF THE
101
Newton Step Using the Bisection Algorithm.
5.5.1 Enhancement the
of
Preserving Trim. 102
Modified Newton'Step Technique to
5.5.2 Applying the
103
Flight Path Accelerations.
Tracking
5.5.3
103
OSCILLATIONS.
CONSTRAINT
5.6
THROUGH ATMOSPHERIC
INVERSE SIMULATION
HELICOPTER
5.7
106
HISAT.
TURBULENCE
-
106
Manoeuvre.
5.7.1 Precision Flare-to-Hover
109
CHAPTER SUMMARY.
5.8
VI
Anderson
D.
At Control Turbulcncc-Induced
Hcli(opler
tit Vibration
e of
_
CHAPTER
VI
STRATEGIES
FOR
IMPLEMENTING
ACTIVE VIBRATION CONTROL.
110
6.1
ACTIVE
VIBRATION CONTROL TECHNIQUES.
110
6.2
HIGHER
HARMONIC
CONTROL.
111
6.3
HARMONIC
ANALYSIS VIBRATION
OF DATA.
113
6.3.1
Fourier
Analysis.
11
6.3.2
Trapezoidal
Approximation
Fourier Integral.
to the
115
6.3.3
High filter
pass algorithm.
116
6.4 THE DESIGN
OF AN OPTIMAL MULTICYCLIC CONTROLLER.
117
6.4.1 Optimal
control methods.
118
6.4.2 Calculation
Sensitivity Matrix.
the
of
119
6.5 PERFORMANCE
HHC
OF THE ALGORITHM.
120
6.5.1 Baseline Performance
the Variational HHC Algorithm.
of 120
6.5.2 Attenuation Step-Gust-Induced
Vibration.
of 121
6.5.3 Stochastic Model (Kalman Filter Implementation).
122
6.5.3 Multi-Harmonic
control. 12 3
6.6 DISTURBANCE FEED-FORWARD HIGHER HARMONIC CONTROL.
125
6.6.1 Description Controller.
the 125
of
6.6.2 Performance Controller.
the 126
of
6.7 INDIVIDUAL B CONTROL.
LADE 127
6.7.1 Defining IBC Strategy.
the 127
6.8 DERIVATION BLADE EQUATIONS MOTION.
OF THE OF 128
6.8.1 Inertial Terms.
128
6.8.2 Aerodynamic Terms.
131
6.8.3 SIMULINK Model Coupled Flap-Lag Motion. 132
of
6.9 IBC CONTROLLER DESIGN FOR DISTURBANCE REJECTION. 133
6.10 CONTROLLER ASSESSMENT UNDER OPERATIONAL CONDITIONS. 135
6.11 CHAPTER SUMMARY. 137
CHAPTER VII
VIBRATION CONTROL LAW DESIGN USING ADVANCED CONTROL
ACTIVE
1
TECHNIQUES. 138
7.1 REVIEW OF HHC & IBC CONTROLLERS. 138
7.2 MODERN OPTIMAL CONTROL LAW DESIGN TECHNIQUES. 1 39
7.2.1 State-Space Optimal Control Methods. 1 39
7.2.2 H, Synthesis. 141
7.3 INDIVIDUAL BLADE CONTROL VIA MIXED-SENSITIVITY H, SYNTHESIS. 142
7.3.1 Closed-Loop Peiforinance Parameters. 142
vii
Anderson
D-Acti, Control Turbulence-Induced He!,,
c of ý1 'ý rlý i', ý;; ý -*ý
7.3.2
H.
1
norm.
7.3.3
Weighting functions Mixed Sensitivit\v Algorithm.
144
the
and
7.3.4
Plant
Augmentation H, Small Gain Problem.
the 145
and
_
7.3.5
iteration.
y- 1_40
7.4 INDIVIDUAL
BLADE CONTROL MIXED-SENSITIVITY H7 SYNTHESIS.
VIA 141,
7.4.1
Design 1: Sensitivity-Only Weighting.
147
7.4.2
Design 2: Sensitivity Complementary Sensitivity Weighting.
14S
and
7.5 DHHC DISTURBANCE ESTIMATION: NEURAL NETWORKS.
150
-
7.5.1 What
Neural Networks?
150
are
7.5.2 Neuron Models.
151
7.5.3 Training the Network The Backpropogation Algorithm. 152
-
7.5.4 Improving Convergence by Adding Momentum Term. 15 3
a
7.6 DESIGN AND TRAINING OF A NEURAL NETWORK FOR GUST PARAMETER PREDICTION. 154
7.6.1 Network Architecture. 154
7.6.2 Network Performance. 154
7.7 CHAPTER SUMMARY. 157
CHAPTER VIII.
CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK. 158
158
8.1 REVIEW RESEARCH AIMS.
OF THE
159
8.2 DEVELOPMENT HIS AT.
OF
161
8.3 ACTIVE VIBRATION CONTROL.
163
8.4 RECOMMENDATIONS FOR FUTURE WORK.
164-167
1
APPENDIX
168-171
II
APPENDIX
172
III
APPENDIX
173-174
IV
APPENDIX
175-261
& TABLES
FIGURES
262-271
REFERENCES
viii
Aildcr%oll
h.
Active Coittiol Ti
Helicopter
of rhiilý red
,, -Ilid
Nomenclature
Notes
:
i. Where
has both
a vector subscript and superscript, the subscript denotes the
location
and the superscript the axis set.
ii. Unless
in SI
explicitly stated, all quantities are given standard units.
iii. In duplication,
the event of the the be from
meaning of symbol will apparent the
the text.
context of
iv. i, j denote i`l` j`1
the
subscripts combined row and column of the attached matrix
General
descriptive
translational
a acceleration vector
hinge in blade
translational the
ahg acceleration of axes
blade in blade
translational
aeie11 acceleration of a element axes
A11, A Fourier blade loading, disc
coefficient of general area
A, A,
system state matrix, constraint oscillation equation state matrix
intermittency for SDG local
the
parameter model, speed of sound
a
lift
curve slope
ao
b intensity for the SDG
parameter model.
be, distance from the hub to a nominal blade element on blade 1.
rl
length
blade
element chord
c
integral
C Fourier
cosine
lift drag
CI, Cd blade
and coefficients
element
CT, CL, CM thrust, rolling and pitching moment coefficients
non-dimensionalised
dynamic
dp
pressure
disturbance
harmonic the the turn
d (tk+l) coefficients of over next rotor
vector of
fractional hinge blade
offset, root cut-out
e, eR
E[.. ]
operator
expectation
(tk) time tk
tracking error vector at
e
force from N blades, frequency (/re\, )
F/Tee hub
F, total all
shear
forces in body
Lex:
vector of all external axes
1-v