We present a helicopter flight dynamics nonlinear model for a flybarless, articulated, pitch–lag–flap (P–L–F) main rotor (MR) with rigid blades, particularly suited for small-scale unmanned aerial vehicles (UAVs). The model incorporates the MR, tail rotor (TR), fuselage, and tails. This model is further applicable for high bandwidth control specifications and is valid for a range of flight conditions, including the vortex-ring-state (VRS) and autorotation. Additionally, the paper reviews all assumptions made in deriving the model, i.e., structural, aerodynamics, and dynamical simplifications. Simulation results show that this nonlinear model is in good agreement with an equivalent flightlab model, for both static (trim) and dynamic conditions.

References

References
1.
Kendoul
,
F.
,
2012
, “
A Survey of Advances in Guidance, Navigation and Control of Unmanned Rotorcraft Systems
,”
J. Field Rob.
,
29
(
2
), pp.
315
378
.
2.
Cai
,
G.
,
Dias
,
J.
, and
Seneviratne
,
L.
,
2014
, “
A Survey of Small-Scale Unmanned Aerial Vehicles: Recent Advances and Future Development Trends
,”
Unmanned Syst.
,
2
(
2
), pp. 175–199.
3.
Weilenmann
,
M. F.
, and
Geering
,
H. P.
,
1994
, “
Test Bench for Rotorcraft Hover Control
,”
AIAA J. Guid., Control, Dyn.
,
17
(
4
), pp.
729
736
.
4.
Bendotti
,
P.
, and
Morris
,
J. C.
,
1995
, “
Robust Hover Control for a Model Helicopter
,”
American Control Conference
, Seattle, WA, June 21–23. pp.
682
687
.
5.
Conway
,
A.
,
1995
, “
Autonomous Control of an Unstable Helicopter Using Carrier Phase GPS Only
,”
Ph.D. thesis
, Stanford University, Stanford, CA.
6.
Johnson
,
E. N.
, and
DeBitetto
,
P. A.
,
1997
, “
Modeling and Simulation for Small Autonomous Helicopter Development
,”
AIAA
Paper No. 97-3511.
7.
Grady
,
N. B.
,
Frye
,
M. T.
, and
Qian
,
C.
,
2006
, “
The Instrumentation and Flight Testing of a Rotorcraft Vehicle for Undergraduate Flight Control Research
,”
AIAA
Paper No. 2006-6739.
8.
Cai
,
G.
,
Chen
,
B. M.
,
Peng
,
K.
,
Dong
,
M.
, and
Lee
,
T. H.
,
2006
, “
Modeling and Control System Design for a UAV Helicopter
,”
Mediterranean Conference on Control and Automation
, Ancona, June 28–30, pp. 1–6.
9.
Velez
,
C. M.
,
Agudelo
,
A.
, and
Alvarez
,
J.
,
2006
, “
Modeling, Simulation and Rapid Prototyping of an Unmanned Mini-Helicopter
,”
AIAA
Paper No. 2006-6737.
10.
Zhao
,
L.
, and
Murthy
,
V. R.
,
2009
, “
Optimal Controller for an Autonomous Helicopter in Hovering and Forward Flight
,”
AIAA
Paper No. 2009-57.
11.
Khaligh
,
S. P.
,
Fahimi
,
F.
, and
Saffarian
,
M.
,
2009
, “
Comprehensive Aerodynamic Modeling of a Small Autonomous Helicopter Rotor at All Flight Regimes
,”
AIAA
Paper No. 2009-6140.
12.
Kim
,
S. K.
, and
Tilbury
,
T. M.
,
1998
, “
Mathematical Modeling and Experimental Identification of a Model Helicopter
,”
AIAA
Paper No. 98-4357.
13.
Munzinger
,
C.
,
1998
, “
Development of a Real-Time Flight Simulator for an Experimental Model Helicopter
,” M.S. thesis, Georgia Institute of Technology, Atlanta, GA.
14.
Shim
,
D. H.
,
2000
, “
Hierarchical Control System Synthesis for Rotorcraft-Based Unmanned Aerial Vehicles
,” Ph.D. thesis, University of California, Berkeley, CA.
15.
Civita
,
M. L.
,
2002
, “
Integrated Modeling and Robust Control for Full-Envelope Flight of Robotic Helicopters
,” Ph.D. thesis, Carnegie Mellon University, Pittsburgh, PA.
16.
Cunha
,
R.
, and
Silvestre
,
C.
,
2003
, “
Dynamic Modeling and Stability Analysis of Model-Scale Helicopters With Bell-Hiller Stabilizing Bar
,”
AIAA
Paper No. 2003-5349.
17.
Tanner
,
O.
,
2003
, “
Modeling, Identification, and Control of Autonomous Helicopters
,”
Ph.D. thesis
, ETH Zurich, Zurich, Switzerland.
18.
Sudiyanto
,
T.
,
Budiyono
,
A.
, and
Sutarto
,
H. Y.
,
2005
, “
Hardware in-the-Loop Simulation for Control System Designs of Model Helicopter
,”
Aerospace Indonesia Meeting
,
Bandung, Indonesia
, pp. 1–9.
19.
Hald
,
U. B.
,
Hesselbaek
,
M. V.
, and
Siegumfeldt
,
M.
,
2006
, “
Nonlinear Modeling and Optimal Control of a Miniature Autonomous Helicopter
,”
M.S. thesis
, Aalborg University, Aalborg, Denmark.
20.
Bhandari
,
S.
, and
Colgren
,
R.
,
2006
, “
6-DOF Dynamic Model for a Raptor 50 UAV Helicopter Including Stabilizer Bar Dynamics
,”
AIAA
Paper No. 2006-6738.
21.
Cai
,
G.
,
Chen
,
B. M.
,
Lee
,
T. H.
, and
Lum
,
K. Y.
,
2012
, “
Comprehensive Nonlinear Modeling of a Miniature Unmanned Helicopter
,”
J. Am. Helicopter Soc.
,
57
(
1
), pp.
1
13
.
22.
Andersen
,
T. L.
,
Lauritzen
,
D. F.
,
Madsen
,
J. T.
,
Sorensen
,
M. M.
, and
Mertz
,
B. A.
,
2008
, “
Autonomous Inverted Hover of a Small Scale Helicopter
,” Aalborg University, Aalborg, Denmark,
Technical Report No. 08gr834
.
23.
Bagnell
,
J.
, and
Schneider
,
J.
,
2001
, “
Autonomous Helicopter Control Using Reinforcement Learning Policy Search Methods
,”
International Conference on Robotics and Automation
(
ICRA
), Seoul, South Korea, May 21-26, pp. 1615–1620.
24.
Buskey
,
G.
,
Roberts
,
O.
,
Corke
,
P.
,
Ridley
,
P.
, and
Wyeth
,
G.
,
2003
, “
Sensing and Control for a Small-Size Helicopter
,”
Experimental Robotics VIII
,
Springer
,
Berlin
, pp.
476
486
.
25.
Ng
,
A. Y.
,
Kim
,
H. J.
,
Jordan
,
M.
, and
Sastry
,
S.
,
2004
, “
Autonomous Helicopter Flight Via Reinforcement Learning
,” Neural Information Processing Systems (
NIPS
).
26.
Engel
,
J. M.
,
2005
, “
Reinforcement Learning Applied to UAV Helicopter Control
,”
M.S. thesis
, Delft University of Technology, Delft, The Netherlands.
27.
Amidi
,
O.
,
1996
, “
An Autonomous Vision-Guided Helicopter
,”
Ph.D. thesis
, Carnegie Mellon University, Pittsburgh, PA.
28.
Shakernia
,
O.
,
Sharp
,
C. S.
,
Vidal
,
R.
,
Shim
,
D. H.
,
Ma
,
Y.
, and
Sastry
,
S.
,
2002
, “
Multiple View Motion Estimation and Control for Landing an Unmanned Aerial Vehicle
,”
International Conference on Robotics and Automation
, Washington, DC, pp. 2793–2798.
29.
Roberts
,
J. M.
,
Corke
,
P. I.
, and
Buskey
,
G.
,
2002
, “
Low-Cost Flight Control System for a Small Autonomous Helicopter
,”
Australian Conference on Robotics and Automation
, Auckland, New Zealand, Nov. 27–29, pp. 71–76.
30.
Saripalli
,
S.
,
Montgomery
,
J. F.
, and
Sukhatme
,
G. S.
,
2003
, “
Visually-Guided Landing of an Autonomous Aerial Vehicle
,”
IEEE Trans. Rob. Autom.
,
19
(
3
), pp.
371
381
.
31.
Barabanov
,
A. E.
,
Vazhinsky
,
N. Y.
, and
Romaev
,
D. V.
,
2007
, “
Full Autopilot for Small Electrical Helicopter
,” 33rd European Rotorcraft Forum, Kazan, Russia, Sept. 11–13.
32.
Gavrilets
,
V.
,
Mettler
,
B.
, and
Feron
,
E.
,
2001
, “
Nonlinear Model for a Small-Size Acrobatic Helicopter
,”
AIAA
Paper No. 2001-4333.
33.
Mettler
,
B.
,
2003
,
Identification Modelling and Characteristics of Miniature Rotorcraft
,
Kluwer Academic Publishers
,
Norwell, MA
.
34.
Marconi
,
L.
, and
Naldi
,
R.
,
2006
, “
Robust Nonlinear Control for a Miniature Helicopter for Aerobatic Maneuvers
,”
32nd European Rotorcraft Forum
, Maastricht, The Netherlands, Sept. 12–14.
35.
Ng
,
A. Y.
,
Coates
,
A.
,
Diel
,
M.
,
Ganapathi
,
V.
,
Schulte
,
J.
,
Tse
,
B.
,
Berger
,
E.
, and
Liang
,
E.
,
2004
, “
Autonomous Inverted Helicopter Flight Via Reinforcement Learning
,”
9th International Symposium on Experimental Robotics
, Singapore, June 18–21.
36.
Abbeel
,
P.
,
Coates
,
A.
,
Quigley
,
M.
, and
Ng
,
A. Y.
,
2007
, “An Application of Reinforcement Learning to Aerobatic Helicopter Flight,” Neural Information Processing Systems (NIPS).
37.
Abbeel
,
P.
,
Coates
,
A.
,
Hunter
,
T.
, and
Ng
,
A. Y.
,
2008
, “
Autonomous Autorotation of an RC Helicopter
,”
11th International Symposium on Experimental Robotics (ISER)
, Athens, Greece, July 13–16.
38.
Taamallah
,
S.
,
2010
, “
A Qualitative Introduction to the Vortex-Ring-State, Autorotation, and Optimal Autorotation
,” 36th European Rotorcraft Forum, Paris, Sept. 7–9.
39.
Santamara
,
D.
,
Viguria
,
A.
,
Bejar
,
M.
,
Kondak
,
K.
, and
Ollero
,
A.
,
2013
, “
Towards Autonomous Autorotation Landing for Small Size Unmanned Helicopters
,”
J. Intell. Rob. Syst.
,
69
(
1–4
), pp.
171
180
.
40.
Taamallah
,
S.
,
2011
, “
Small-Scale Helicopter Blade Flap-Lag Equations of Motion for a Flybarless Pitch-Lag-Flap Main Rotor
,”
AIAA
Paper No. 2011-6279.
41.
Taamallah
,
S.
,
2011
, “
Flight Dynamics Modeling for a Small-Scale Flybarless Helicopter UAV
,”
AIAA
Paper No. 2011-6448.
42.
Taamallah
,
S.
,
2012
, “
Optimal Autorotation With Obstacle Avoidance for a Small-Scale Flybarless Helicopter UAV
,”
AIAA
Paper No. 2012-4834.
43.
Taamallah
,
S.
,
Bombois
,
X.
, and
van den Hof
,
P. M. J.
,
2012
, “
Optimal Control for Power-Off Landing of a Small-Scale Helicopter a Pseudospectral Approach
,”
American Control Conference
, Montreal, Canada, June 27–29, pp. 914–919.
44.
Taamallah
,
S.
,
2013
, “
Flatness Based Trajectory Generation for a Helicopter UAV
,”
AIAA
Paper No. 2013-4765.
45.
Taamallah
,
S.
,
2015
, “
Small-Scale Helicopter Automatic Autorotation: Modeling, Guidance, and Control
,”
Ph.D. thesis
, Delft University of Technology, Delft, The Netherlands.
46.
Boiffier
,
J. L.
,
1998
,
The Dynamics of Flight the Equations
,
Wiley
,
Chichester, UK
.
47.
Blake
,
B. B.
, and
Lunn
,
K.
,
1980
, “
Helicopter Stability and Control Test Methodology
,”
AIAA
Paper No. 80-1610.
48.
Tischler
,
M. B.
, and
Remple
,
R.
,
2006
,
Aircraft and Rotorcraft System Identification
,
American Institute of Aeronautics & Astronautics (AIAA)
,
Reston, VA
.
49.
Padfield
,
G. D.
,
1996
,
Helicopter Flight Dynamics
,
Blackwell Science Ltd.
,
Oxford, UK
.
50.
Brackbill
,
C. R.
,
2000
, “
Helicopter Rotor Aeroelastic Analysis Using a Refined Elastomeric Damper Model
,” Ph.D. thesis, Pennsylvania State University, State College, PA.
51.
Seckel
,
E.
, and
Curtiss
,
H. C.
,
1962
, “
Aerodynamic Characteristics of Helicopter Rotors
,” Department of Aerospace and Mechanical Engineering, Princeton University, Princeton, NJ, Technical Report No. 659.
52.
Chen
,
R. T. N.
,
1979
, “
A Simplified Rotor System Mathematical Model for Piloted Flight Dynamics Simulation
,” NASA Ames Research Center, Mountain View, CA,
Technical Report No. NTM 78575
.
53.
Chen
,
R. T. N.
,
1980
, “
Effects of Primary Rotor Parameters on Flapping Dynamics
,” NASA Ames Research Center, Mountain View, CA,
Technical Report No. NTP 1431
.
54.
Gessow
,
A.
, and
Myers
,
G. C.
,
1999
,
Aerodynamics of the Helicopter
,
College Park Press
, College Park, MD.
55.
Shevell
,
R. S.
,
1989
,
Fundamentals of Flight
,
Prentice Hall
,
Upper Saddle River, NJ
.
56.
Anderson
,
J. D.
,
2001
,
Fundamentals of Aerodynamics
,
3rd ed.
,
McGraw-Hill Higher Education
, New York.
57.
Prouty
,
R. W.
,
1995
,
Helicopter Performance, Stability, and Control
,
Krieger Publishing Company
,
Malabar, FL
.
58.
Chen
,
R. T. N.
,
Lebacqz
,
J. V.
,
Aiken
,
E. W.
, and
Tischler
,
M. B.
,
1988
, “
Helicopter Mathematical Models and Control Law Development for Handling Qualities Research
,” NASA Ames Research Center, Mountain View, CA,
Technical Report No. NCR 2495
.
59.
Chen
,
R. T. N.
,
1987
, “
Flap-Lag Equations of Motion of Rigid, Articulated Rotor Blades With Three Hinge Sequences
,” NASA Ames Research Center, Mountain View, CA, Technical Report No. NTM 100023.
60.
Ellis
,
C. W.
,
1953
, “
Effects of Rotor Dynamics on Helicopter Automatic Control System Requirements
,”
Aeronaut. Eng. Rev.
, 12(7).
61.
Miller
,
D. G.
, and
White
,
F.
,
1987
, “
A Treatment of the Impact of Rotor-Fuselage Coupling on Helicopter Handling Qualities
,” American Helicopter Society, Alexandria, VA.
62.
Curtiss
,
H. C.
,
1986
, “
Stability and Control Modeling
,” 12th European Rotorcraft Forum, Garmesch-Partenkirchen, Germany, Sept. 22–25.
63.
Tischler
,
M. B.
,
1991
, “
System Identification Requirements for High Bandwidth Rotorcraft Flight Control System Design
,” Rotorcraft System Identification, Paper No. AGARD LS-178.
64.
Wells
,
D. A.
,
1967
,
Lagrangian Dynamics
,
McGraw-Hill
, New York.
65.
Taamallah
,
S.
,
2011
, “
A Flight Dynamics Helicopter UAV Model for a Single Pitch-Lag-Flap Main Rotor: Modeling and Simulations
,” National Aerospace Laboratory (NLR), Bengaluru, India, Technical Report No. NLR-TP-2010-286-PT-1.
66.
Johnson
,
W.
,
1994
,
Helicopter Theory
,
Dover Publications
, New York.
67.
ART
,
2006
, flightlab Theory Manual, Vols. 1 and 2,
Advanced Rotorcraft Technology
Inc., Sunnyvale, CA.
68.
Leishman
,
G. J.
,
2000
,
Principles of Helicopter Aerodynamics
,
Cambridge University Press
,
Cambridge, UK.
69.
Chen
,
R. T. N.
, and
Hindson
,
W. S.
,
1986
, “
Influence of High-Order Dynamics on Helicopter Flight Control System Bandwidth
,”
AIAA J. Guid., Control, Dyn.
,
9
(
2
), pp.
190
197
.
70.
Takahashi
,
M. D.
,
1990
, “
A Flight-Dynamic Helicopter Mathematical Model With a Single Flap-Lag-Torsion Main Rotor
,” NASA Ames Research Center, Mountain View, CA,
Technical Report No. TM 102267
.
71.
Kahaner
,
D.
,
Moler
,
C.
, and
Nash
,
S.
,
1989
,
Numerical Methods and Software
,
Prentice-Hall
, Englewood Cliffs,
NJ
.
72.
Stoer
,
J.
, and
Bulirsch
,
R.
,
2002
,
Introduction to Numerical Analysis
,
Springer-Verlag
, New York.
73.
Chen
,
R. T. N.
,
1989
, “
A Survey of Nonuniform Inflow Models for Rotorcraft Flight Dynamics and Control Applications
,” NASA Ames Research Center, Mountain View, CA,
Technical Report No. NTM 102219
.
74.
Kothmann
,
B. D.
,
Lu
,
Y.
,
DeBrun
,
E.
, and
Horn
,
J.
,
2004
, “
Perspectives on Rotorcraft Aerodynamic Modeling for Flight Dynamics Applications
,”
4th Decennial Specialists Conference on Aeromechanics
.
75.
Kunz
,
D. L.
,
2005
, “
Comprehensive Rotorcraft Analysis: Past, Present, and Future
,”
AIAA
Paper No. 2005-2244.
76.
van Hoydonck
,
W. R. M.
,
Haverdings
,
H.
, and
Pavel
,
M. D.
,
2009
, “
A Review of Rotorcraft Wake Modeling Methods for Flight Dynamics Applications
,” 35th European Rotorcraft Forum, Hamburg, Germany, Sept. 22–25.
77.
Pitt
,
D. M.
, and
Peters
,
D. A.
,
1980
, “
Theoretical Prediction of Dynamic-Inflow Derivatives
,” 6th European Rotorcraft Forum, Bristol, UK, Sept. 16–19.
78.
Gaonkar
,
G. H.
, and
Peters
,
D. A.
,
1986
, “
Effectiveness of Current Dynamic-Inflow Models in Hover and Forward Flight
,”
J. Am. Helicopter Soc.
,
31
(
2
), pp.
47
57
.
79.
Peters
,
D. A.
, and
HaQuang
,
N.
,
1988
, “
Technical Notes-Dynamic Inflow for Practical Applications
,”
J. Am. Helicopter Soc.
, pp.
64
68
.
80.
Gaonkar
,
G. H.
, and
Peters
,
D. A.
,
1988
, “
Review of Dynamic Inflow Modeling for Rotorcraft Flight Dynamics
,”
Vertica
, 12, pp.
213
242
.
81.
Peters
,
D. A.
,
Boyd
,
D. D.
, and
He
,
C. J.
,
1989
, “
Finite-State Induced-Flow Model for Rotors in Hover and Forward Flight
,”
J. Am. Helicopter Soc.
,
34
(
4
), pp.
5
17
.
82.
Peters
,
D. A.
, and
He
,
C. J.
,
1991
, “
Correlation of Measured Induced Velocities With a Finite-State Wake Model
,”
J. Am. Helicopter Soc.
,
36
(
3
), pp.
59
70
.
83.
Peters
,
D. A.
, and
He
,
C. J.
,
1995
, “
Finite State Induced Flow Models—Part II: Three-Dimensional Rotor Disk
,”
AIAA J. Aircr.
,
32
(
2
), pp.
323
333
.
84.
Hamers
,
M.
, and
Basset
,
P. M.
,
2000
, “
Application of the Finite State Unsteady Wake Model in Helicopter Flight Dynamic Simulation
,” 26th European Rotorcraft Forum, The Hague, The Netherlands, Sept. 26–29.
85.
Peters
,
D. A.
, and
He
,
C.
,
2006
, “
Technical Note: Modification of Mass-Flow Parameter to Allow Smooth Transition Between Helicopter and Windmill States
,”
J. Am. Helicopter Soc.
,
51
(
3
), pp.
275
278
.
86.
Jimenez
,
J.
,
Desopper
,
A.
,
Taghizad
,
A.
, and
Binet
,
L.
,
2001
, “
Induced Velocity Model in Steep Descent and Vortex Ring State Prediction
,” 27th European Rotorcraft Forum, Moscow, Sept. 11–14.
87.
Keller
,
J. D.
,
1996
, “
An Investigation of Helicopter Dynamic Coupling Using an Analytical Model
,”
J. Am. Helicopter Soc.
,
41
(
4
), p.
322330
.
88.
Curtiss
,
H. C.
,
1999
, “
Aerodynamic Models and the Off-Axis Response
,” American Helicopter Society, Alexandria, VA.
89.
Arnold
,
U. T. P.
,
Keller
,
J. D.
,
Curtiss
,
H. C.
, and
Reichert
,
G.
,
1998
, “
The Effect of Inflow Models on the Predicted Response of Helicopters
,”
J. Am. Helicopter Soc.
,
43
(
1
), pp.
25
36
.
90.
Hamers
,
M.
, and
von Grunhagen
,
W.
,
1997
, “
Nonlinear Helicopter Model Validation Applied to Realtime Simulations
,” American Helicopter Society, Alexandria, VA.
91.
Benoit
,
B.
,
Dequin
,
A. M.
,
Kampa
,
K.
,
von Grunhagen
,
W.
,
Basset
,
P. M.
, and
Gimonet
,
B.
,
2000
, “
Host a General Helicopter Simulation Tool for Germany and France
,” American Helicopter Society, Alexandria, VA.
92.
Pitt
,
D. M.
, and
Peters
,
D. A.
,
1981
, “
Theoretical Prediction of Dynamic-Inflow Derivatives
,”
Vertica
,
5
, pp.
21
34
.
93.
Bailey
,
F. J.
,
1941
, “
A Simplified Theoretical Method of Determining the Characteristics of a Lifting Rotor in Forward Flight
,” National Advisory Committee for Aeronautics, Washington, DC, NACA, Technical Report No. 716.
94.
Houck
,
J. A.
,
Moore
,
F. L.
,
Howlett
,
J. J.
,
Pollock
,
K. S.
, and
Browne
,
M. M.
,
1977
, “
Rotor Systems Research Aircraft Simulation Mathematical Model
,” NASA Langley Research Center, Hampton, VA, Technical Report No. NTM 78629.
95.
Voorsluijs
,
G. M.
,
2002
, “
A Modular Generic Helicopter Model
,” M.S. thesis, Delft University of Technology, Delft, The Netherlands.
96.
Fletcher
,
T. M.
, and
Brown
,
R. E.
,
2006
, “
Main Rotor-Tail Rotor Wake Interaction and Its Implications for Helicopter Directional Control
,” 32nd European Rotorcraft Forum, Maastricht, The Netherlands, Sept. 12–14.
97.
Fletcher
,
T. M.
, and
Brown
,
R. E.
,
2008
, “
Main Rotor-Tail Rotor Interaction and Its Implications for Helicopter Directional Control
,”
J. Am. Helicopter Soc.
,
53
(
2
), pp.
125
138
.
98.
Pavel
,
M. D.
,
2001
, “
On the Necessary Degrees of Freedom for Helicopter and Wind Turbine Low-Frequency Mode-Modelling
,” Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.
99.
Talbot
,
P. D.
,
Tinling
,
B. E.
,
Decker
,
W. A.
, and
Chen
,
R. T. N.
,
1982
, “
A Mathematical Model of a Single Main Rotor Helicopter for Piloted Simulation
,” NASA Ames Research Center, Mountain View, CA, NASA,
Technical Report No. NTM 84281
.
100.
Jewel
,
J. W.
, and
Heyson
,
H. H.
,
1959
, “
Charts of Induced Velocities Near a Lifting Rotor
,” NASA Langley Research Center, Hampton, VA,
NASA Technical Report No. 4-15-59LY
.
101.
Baskin
,
V. E.
,
Vildgrube
,
L. S.
,
Vozhdayev
,
Y. S.
, and
Maykapar
,
C. I.
,
1976
, “
Theory of the Lifting Airscrew
,” NASA, Washington, DC, Technical Translation No. TT-F-823.
102.
Zhao
,
X.
, and
Curtiss
,
H. C.
,
1988
, “
A Study of Helicopter Stability and Control Including Blade Dynamics
,” NASA Ames Research Center, Mountain View, CA,
Technical Report No. TR 1823T
.
103.
Advanced Rotorcraft Technology, 2008, “
ART
,” Advanced Rotorcraft Technology Inc., Sunnyvale, CA, http://www.flightlab.com/
104.
Peters
,
D. A.
,
Chouchane
,
M.
, and
Fulton
,
M.
,
1990
, “
Helicopter Trim With Flap-Lag-Torsion and Stall by an Optimized Controller
,”
AIAA J. Guid. Control Dyn.
,
13
(
5
), pp.
824
834
.
105.
Peters
,
D. A.
, and
Barwey
,
D.
,
1996
, “
A General Theory of Rotorcraft Trim
,”
Math. Probl. Eng.
,
2
(
1
), pp.
1
34
.
106.
Achar
,
N. S.
, and
Gaonkar
,
G. H.
,
1993
, “
Helicopter Trim Analysis by Shooting and Finite Element Methods With Optimally Damped Newton Iterations
,”
AIAA J.
,
31
(
2
), pp.
225
234
.
107.
van den Hof
,
P. M. J.
, and
Schrama
,
R. J. P.
,
1995
, “
Identification and Control-Closed-Loop Issues
,”
Automatica
,
31
(
12
), pp.
1751
1770
.
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