DEVELOPMENT OF ALTITUDE HOLD AND HEADING...
Transcript of DEVELOPMENT OF ALTITUDE HOLD AND HEADING...
DEVELOPMENT OF ALTITUDE HOLD AND HEADING HOLD
CONTROL SYSTEM FOR SMALL SCALE HELICOPTER
Case Study: Aerobatic Helicopter X-Cell 60
Submitted to the Program Study of Aeronautics and Astronautics Engineering
in partial fulfillment of the requirements for the
Bachelor Degree
By:
Hendra Lesmana
13603022
Advisors:
Prof. Said D. Jenie, Sc.D
DR. Ir. Agus Budiyono, SM-AA, E.A.A
PROGRAM STUDY OF AERONAUTICS AND ASTRONAUTICS ENGINEERING
FACULTY OF MECHANICAL AND AEROSPACE ENGINEERING
BANDUNG INSTITUTE OF TECHNOLOGY
2008
ii
AUTHENTICATION LETTER
DEVELOPMENT OF ALTITUDE HOLD AND HEADING HOLD
CONTROL SYSTEM FOR SMALL SCALE HELICOPTER
Case Study: Aerobatic Helicopter X-Cell 60
By:
Hendra Lesmana
136 03 022
This report had been checked and approved
as partial fulfillment of the requirements for the Bachelor Degree
in Program Study of Aeronautics And Astronautics Engineering
Faculty of Mechanical And Aerospace Engineering
Bandung Institute of Technology
Approved by:
Advisor I Advisor II
Prof. Said D. Jenie, Sc.D DR. Ir. Agus Budiyono, SM-AA, E.A.A
iii
Abstract
Small-scale helicopter has more advances than fixed-wing aircraft because they
have the ability to take-off and land vertically. This flying object can be used for
aerial mapping, movie making, farm fertilization, or military purposes. The
benefits of using small-scale helicopter will become greater if no human is
involved in the operation, or to be operated autonomously. Therefore, this kind of
vehicle has been developed, becoming a very popular vehicle known as
Rotorcraft-based Unmanned Aerial Vehicle (RUAV).
The control system of X-Cell 60 that will be designed in this research is altitude
hold and heading hold system. Method used in this research is classical control
method (gain tuning) by using root locus diagram
Since there is no regulations in Indonesia about RUAV, so the references used in
this research are “Aeronautical Design Standard - Performance Specification
Handling Qualities Requirements For Military Rotorcraft (ADS-33E-PRF)” and
”General Requirements For Helicopter Flying And Ground Qualities (MIL-H-
8501)” which is complied with the control design specification of X-Cell 60.
iv
ACKNOWLEDGEMENTS
Alhamdulillah, praise and my thanks to Allah SWT for all his blessing and grant,
which is always poured to me. Also invocation and greeting for Rasullulah
Muhammad SAW, all of his friends and followers to the last epoch.
Many people have helped to make this report a reality. I can only mention a few
of them here. I would like to thank the persons listed below:
DR. Ir. Agus Budiyono, SM-AA, E.A.A who have given suggestions, advices,
and his tuitions for me.
Prof. Said D. Jenie, ScD who willing to be the First Advisor so this report can
finish at the time.
DR. Ir. M. Giri Suada as my Personal Lecturer at ITB.
DR. Toto Indriyanto and DR. Ridanto Eko Putro for the time to test writer.
LPKM, IOM, Dikti, and ITB Alumni for all scholarship that given to me so writer
can survive at ITB.
All of My Sisters (Ni-na, Owie, and Lidya), with their own style to face the
challenges in life, hopefully we all can be succeed.
Mak uning and family for being my best family while me far away from my mom
and my sisters.
All of my friends as PN 2003 for the pray and support that is given to me,
hopefully our solidarity last forever.
Mas Tata, for discussions and solutions which is helped me to finish this research.
My aircraft design team, The A Team (Sonny, Yanuar, Arzai, and Puji), I hope we
all can be success in our carrier, and our friendship will last forever.
My friends at Cibogo 37A (Shereen, Laras, Oland, Weli, Della, “Ibu and Bapak”
nurul, and baby Nurul) for the support and willingness to be my friends so I have
people to release my stress with.
My friends at Cisitu 28 A, who live with me for almost 3 years.
Syahron Hasbi Nasution, for his report that being reference in the process of
writing this report.
For widhi, I hope my English will get better with your help.
v
My Girlfriend, Siska Kristina Purnamasari, for being the person who always
beside me when I need someone to share with. I hope that our relationship will
never end.
Moreover, the last but the most important persons in my life are my Father and
my Mother who gave a lot to me.
Bandung, February 2008
Hendra Lesmana
vi
Contents
Acceptance Letter ............................................................................................................... ii
Abstract .............................................................................................................................. iii
Acknowledgement ..............................................................................................................iv
Contents ..............................................................................................................................vi
List of Figures ..................................................................................................................... ix
List of Tables .................................................................................................................... xiii
List of Notations ............................................................................................................... xiv
CHAPTER 1 ...................................................................................................................... 1
1.1 Background ....................................................................................................... 1
1.2 Objectives ......................................................................................................... 1
1.3 Assumptions and Research Methods ................................................................ 2
1.4 Outline .............................................................................................................. 2
1.5 Research Stages ................................................................................................ 3
CHAPTER 2 ...................................................................................................................... 4
2.1 Physical Description of X-Cell 60 .................................................................... 4
2.2 Helicopter Dynamics ........................................................................................ 5
2.3 Linear Model of X-Cell 60 ............................................................................... 7
CHAPTER 3 .................................................................................................................... 10
3.1 Introduction ..................................................................................................... 10
3.2 Characteristic Roots ........................................................................................ 10
3.2.1 Longitudinal Mode .................................................................................... 10
3.2.2 Lateral-Directional Mode .......................................................................... 11
3.3 Simulation Results .......................................................................................... 12
3.3.1 Collective Pitch Perturbation .................................................................... 12
3.3.2 Collective Pedal Perturbation .................................................................... 15
3.3.3 Longitudinal Cyclic Perturbation .............................................................. 17
3.3.4 Lateral Cyclic Perturbation ....................................................................... 19
CHAPTER 4 .................................................................................................................... 21
4.1 Introduction ..................................................................................................... 21
4.2 Modeling of Actuator and Sensor ................................................................... 21
vii
4.2.1 Modeling Rules ......................................................................................... 21
4.2.2 Mathematical model of actuator and sensor .............................................. 22
4.3 Automatic Control System Design for Longitudinal Mode. ........................... 23
4.3.1 Control System Design of Pitch Damper .................................................. 23
4.3.1.1 Mathematical Diagram .......................................................................... 23
4.3.1.2 Control System Design ......................................................................... 24
4.3.1.3 Closed Loop Simulation ........................................................................ 27
4.3.2 Control System Design of Pitch Attitude Hold ......................................... 28
4.3.2.1 Mathematical Diagram .......................................................................... 28
4.3.2.2 Control System Design ......................................................................... 29
4.4.2.3 Closed Loop Simulation ........................................................................ 32
4.3.3 Control System Design of Altitude Hold .................................................. 33
4.3.3.1 Mathematical Diagram .......................................................................... 33
4.4.3.2 Control System Design ......................................................................... 34
4.4.3.3 Closed Loop Simulation ........................................................................ 37
4.4 Automatic Control System Design for Lateral-Directional Mode .................. 38
4.4.1 Bank Angle Hold Control System Design ................................................ 38
4.4.1.1 Mathematical Diagram .......................................................................... 38
4.4.1.2 Control System Design ......................................................................... 39
4.4.1.3 Closed Loop System ............................................................................. 42
4.4.2 Heading Hold Control System Design ...................................................... 43
4.4.2.1 Mathematical Diagram .......................................................................... 43
4.4.2.2 Control System Design ......................................................................... 45
4.4.2.3 Closed Loop Simulation ........................................................................ 48
CHAPTER 5 ................................................................................................................... 50
5.1 Introduction ..................................................................................................... 50
5.2 Foundation of Analysis ................................................................................... 50
5.3 Theory of Bandwidth Frequency (ωBW) and Phase Delay (τp) ........................ 50
5.4 Analysis of Longitudinal Control System Simulation .................................... 52
viii
5.4.1 Analysis of Inner Loop I (Pitch Damper System) ..................................... 52
5.4.2 Analysis of Inner Loop II (Pitch Attitude Hold System, PAHS) .............. 54
5.4.3 Analysis of the Outer Loop (Altitude Hold System) .................................. 57
5.4.4 Simulation of Longitudinal Mode Control Movement ............................. 58
5.5 Analysis of Lateral-Directional Control System Simulation .......................... 60
5.5.1 Analysis of Inner Loop (Bank Angle Hold System, BAHS)....................... 60
5.4.2 Analysis of Outer Loop (Heading Angle Hold System, HAHS) ................ 62
5.4.3 Simulation of Lateral-Directional Mode Control Movement ................... 65
CHAPTER 6 .................................................................................................................... 67
6.1 Conclusions ..................................................................................................... 67
6.2 Suggestions ..................................................................................................... 67
REFERENCES ................................................................................................................. 68
APPENDIX A
APPENDIX B
A. Longitudinal Mode
B. Lateral-Directional Mode
APPENDIX C
1 Listing of M-file MATLAB®
1.1 Numerator and Denumerator
1.2 Longitudinal Mode
1.3 Lateral-Directional Mode
2 Control System Toolbox/ MATLAB®
3 Simulink®/ MATLAB
®
ix
List of Figures
Figure 1.1 Research Stages ..................................................................................... 3
Figure 2.1 Bar/Hiller control rotor (flybar) ............................................................. 4
Figure 2.2 Helicopter subsystem ............................................................................. 6
Figure 2.3 Flapping Angle ...................................................................................... 7
Figure 3.1 Position of Longitudinal characteristic roots ....................................... 10
Figure 3.2 Position of Lateral-Directional characteristic roots ............................. 11
Figure 3.3 Doublet perturbation for collective pitch ............................................. 12
Figure 3.4 Longitudinal response of collective pitch perturbation ....................... 13
Figure 3.5 Lateral-Directional response of collective pitch perturbation ............. 14
Figure 3.6 Doublet perturbation for collective pedal ............................................ 15
Figure 3.7 Longitudinal response of collective pedal perturbation....................... 15
Figure 3.8 Lateral-Directional response of collective pedal perturbation............. 16
Figure 3.9 Doublet perturbation for Longitudinal Cyclic ..................................... 17
Figure 3.10 Longitudinal response of longitudinal cyclic perturbation ................ 17
Figure 3.11 Lateral-Directional response of longitudinal cyclic perturbation ...... 18
Figure 3.12 Doublet perturbation for lateral cyclic perturbation .......................... 19
Figure 3.13 Longitudinal response of lateral cyclic perturbation ......................... 19
Figure 3.14 Lateral-Directional response of lateral cyclic perturbation ............... 20
Figure 4.1 Mathematical diagram of pitch damper system .................................... 23
Figure 4.2 Root locus for Inner loop pitch damper with Kct < 0 ............................ 24
Figure 4.3 Root locus for Inner loop pitch damper with Kct < 0 (zoomed
around origin) ........................................................................................ 25
Figure 4.4 Root locus for Inner loop pitch damper with Kct > 0 ............................ 25
Figure 4.5 Root locus for Inner loop pitch damper with Kct > 0 (zoomed
around origin) ........................................................................................ 26
Figure 4.6 Step Response of pitch damper closed loop system ............................. 27
x
Figure 4.7 Impulse Response of pitch damper closed loop system ....................... 27
Figure 4.8 Mathematical diagram of pitch attitude hold ........................................ 28
Figure 4.9 Root locus for Inner loop pitch attitude hold with Kθq < 0 ................... 29
Figure 4.10 Root locus for Inner loop pitch attitude hold with Kθq < 0
(zoomed around arrow point) ................................................................ 29
Figure 4.11 Root locus for Inner loop pitch attitude hold with Kθq < 0
(zoomed around origin) ......................................................................... 30
Figure 4.12 Root locus for Inner loop pitch attitude hold with Kθq > 0 ................. 30
Figure 4.13 Root locus for Inner loop pitch attitude hold with Kθq > 0
(zoomed around origin) ......................................................................... 31
Figure 4.14 Step Response for pitch attitude hold closed loop system .................. 32
Figure 4.15 Impulse Response for pitch attitude hold closed loop system ............ 32
Figure 4.16 Mathematical Diagram of Altitude Hold ............................................ 33
Figure 4.17 Root locus for Altitude hold system with Khθq < 0 ............................. 34
Figure 4.18 Root locus for Altitude hold with Khθq < 0 (zoomed around arrow
point) ...................................................................................................... 34
Figure 4.19 Root locus for Altitude hold system with Khθq < 0 (zoomed
around origin) ........................................................................................ 35
Figure 4.20 Root locus for Altitude hold system with Khθq > 0 ............................. 35
Figure 4.21 Root locus for Altitude hold system with Khθq > 0 (zoomed
around origin) ........................................................................................ 36
Figure 4.22 Step Response of altitude hold closed loop system ............................ 37
Figure 4.23 Impulse Response of altitude hold closed loop system ...................... 37
Figure 4.24 Mathematical Diagram of Bank Angle Hold System ......................... 38
Figure 4.25 Root locus of Bank Angle hold system with Kamp < 0 ....................... 39
Figure 4.26 Root locus of Bank Angle hold system with Kamp < 0 (zoomed
around arrow point) ............................................................................... 40
Figure 4.27 Root locus of Bank Angle hold system with Kamp < 0 (zoomed
around origin) ........................................................................................ 40
Figure 4.28 Root locus of Bank Angle hold System with Kamp > 0 ....................... 41
Figure 4.29 Root locus of Bank Angle hold System with Kamp > 0 (zoomed
around origin) ........................................................................................ 41
xi
Figure 4.30 Step Response for Bank Angle hold closed loop system ................... 42
Figure 4.31 Impulse Response for Bank Angle hold closed loop system .............. 43
Figure 4.32 Mathematical diagram of heading hold system .................................. 43
Figure 4.33 Root locus of heading hold system with *
ampK < 0 ............................... 45
Figure 4.34 Root locus for heading hold system with *
ampK < 0 (zoomed around
arrow point) ........................................................................................... 46
Figure 4.35 Root locus for heading hold system with *
ampK < 0 (zoomed around
origin) .................................................................................................... 46
Figure 4.36 Root locus of heading hold system with *
ampK > 0 ............................... 47
Figure 4.37 Root locus of heading hold system with *
ampK > 0 (zoomed around
origin) .................................................................................................... 47
Figure 4.38 Step Response for Heading Angle hold closed loop system .............. 48
Figure 4.39 Impulse Response for Heading Angle hold closed loop system......... 49
Figure 5.1 Bandwidth and Phase Delay theory ..................................................... 51
Figure 5.2 Illustration of control system response ................................................ 52
Figure 5.3 Comparison between open loop and closed loop simulation of
pitch rate response to doublet input for Pitch Damper System ............ 53
Figure 5.4 Comparison of Closed Loop and Open Loop movement
simulation of Pitch Damper System in Longitudinal mode to the
doublet input ......................................................................................... 53
Figure 5.5 Requirement of pitch angle change to small perturbation ................... 54
Figure 5.6 Bode plot of Pitch Attitude Hold (PAH) system ................................. 54
Figure 5.7 Comparison between open loop and closed loop simulation of
pitch attitude response to doublet input for Pitch Attitude Hold
System .................................................................................................. 55
Figure 5.8 Comparison of Closed Loop and Open Loop movement
simulation of PAHS in Longitudinal mode to the doublet input .......... 56
Figure 5.9 Comparison of altitude responses in the closed loop and open
loop simulation to doublet input for Altitude Hold System ................. 57
xii
Figure 5.10 Comparison of Closed Loop and Open Loop movement
simulation of AHS in Longitudinal mode to the doublet input ............ 57
Figure 5.11 Response Curve of q vs qreference ........................................................ 58
Figure 5.12 Response Curve of θ vs θreference ........................................................ 59
Figure 5.13 Response Curve of h vs hreference ........................................................ 59
Figure 5.14 Requirement of roll attitude change to small perturbation ................ 60
Figure 5.15 Bode Diagram for Bank Angle Hold (BAH) system ......................... 61
Figure 5.16 Comparison of roll angle response in the simulation of open
loop and closed loop to the doublet input for Bank Angle Hold
system ................................................................................................... 61
Figure 5.17 Comparison of Closed Loop and Open Loop movement
simulation of BAHS in Lateral-Directional mode to the doublet
input ...................................................................................................... 62
Figure 5.18 Requirement of yaw attitude change to small perturbation ............... 62
Figure 5.19 Bode Diagram for Heading Angle Hold (HAH) system .................... 63
Figure 5.20 Comparison of heading angle response in the open loop and
closed loop simulation to the doublet input for Heading Angle
Hold system .......................................................................................... 64
Figure 5.21 Comparison of Closed Loop and Open Loop movement
simulation of HAHS in Lateral-Directional mode to the doublet
input ...................................................................................................... 64
Figure 5.22 Response Curve of φ vs φreference ........................................................ 65
Figure 5.23 Response Curve of ψ vs ψreference ....................................................... 65
xiii
List of Tables
Table 2.1 Physical Parameters of the X-Cell 60 ...................................................... 5
Table 3.1 Characteristics of Longitudinal roots ..................................................... 11
Table 3.2 Characteristics of Lateral-Directional roots ........................................... 12
Table 3.3 Longitudinal response characteristics of collective pitch
perturbation ............................................................................................ 13
Table 3.4 Lateral-Directional response characteristics of collective pitch
perturbation ............................................................................................ 14
Table 3.5 Longitudinal response characteristics of collective pedal
perturbation ............................................................................................ 16
Table 3.6 Lateral-Directional response characteristics of collective pedal
perturbation ............................................................................................ 16
Table 3.7 Longitudinal response characteristics of longitudinal cyclic
perturbation ............................................................................................ 18
Table 3.8 Lateral-Directional response characteristics of longitudinal cyclic
perturbation ............................................................................................ 18
Table 3.9 Longitudinal response characteristic of lateral cyclic perturbation ....... 20
Table 3.10 Lateral-Directional response characteristic of lateral cyclic
perturbation ............................................................................................ 20
Table 4.1 Mathematical model of actuator ............................................................ 22
Table 4.2 Closed Loop characteristic roots of Pitch Damper System ................... 26
Tabel 4.3 Closed Loop characteristic roots of Pitch Attitude Hold ....................... 31
Table 4.4 Closed Loop characteristic roots of Altitude Hold System ................... 36
Table 4.5 Closed Loop characteristic roots of Bank Angle Hold system .............. 42
Table 4.6 Closed Loop characteristic roots of Heading Angle Hold System ........ 48
xiv
List of Notations
Symbol Name Unit
(L, M, N) Components of moment about the CG, in body frame Nm
(p, q, r) Angular helicopter body rates, in body frame deg /s
(u, v, w) Velocity components relative to air expressed in body frame m/s
(X, Y, Z) Components of force acting along the (x, y, z) body axes N
(x, y, z) Helicopter body coordinate frame
(φ, θ, ψ) Euler angles deg
a0 Coning angle deg
a1s First harmonic coefficient of longitudinal blade flapping
with respect to shaft (positive for tilt back) deg
A State matrix of State Space Matrix
b1s First harmonic coefficient of lateral blade flapping
with respect to shaft (positive for tilt right) deg
B Control matrix of State Space Matrix
g Gravity constant m/s
G Transfer function
h Vertical distance m
Ixx Rolling moment of inertia kg m2
Iyy Pitching moment of inertia kg m2
Izz Yawing moment of inertia kg m2
l Horizontal distance m
M Helicopter mass kg
N Numerator
Shf Horizontal fin area m
V∞ Velocity vector relative to the atmosphere m/sec
xv
Greek Symbols
βe Sideslip angle deg
δcoll,MR Collective main rotor input deg
δped Pedal input deg
δlat Lateral cyclic input deg
δlong Longitudinal cyclic input deg
Δ Denumerator
e
Turn Rate deg
/s
γe Flight path angle deg
ρ Density of air kg/m3
θ0 Collective main rotor blade pitch deg
ς Damping ratio
τs Time constant sec
τp Phase Delay sec
ωBW Bandwidth frequency rad/sec
ωn Natural frequency rad/sec
Abbreviations
CG Center of gravity
HF Horizontal Fin
MR Main rotor
rpm Rotor rotational speed
TR Tail rotor
TPP Tip path plane
VF Vertical Fin