DEVELOPMENT OF ALTITUDE HOLD AND HEADING …digilib.itb.ac.id/files/disk1/616/jbptitbpp-gdl-hendralesm-30786-1... · DEVELOPMENT OF ALTITUDE HOLD AND HEADING HOLD CONTROL SYSTEM FOR

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




4.3.3 Control System Design of Altitude Hold .................................................. 33




4.4 Automatic Control System Design for Lateral-Directional Mode .................. 38

4.4.1 Bank Angle Hold Control System Design ................................................ 38



4.4.1.3 Closed Loop System ............................................................................. 42

4.4.2 Heading Hold Control System Design ...................................................... 43




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


ampK > 0 ............................... 47


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


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


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


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


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

xvi

Subscripts and Superscripts

act Actuator

coll Collective pitch

e Equilibrium

fus Fuselage

hg Heading Gyro

lat Lateral

latdir; ld Lateral-Directional

long Longitudinal

reff Reference

rg Rate Gyro

vg Vertical Gyro

rpm Rotor rotational speed

DEVELOPMENT OF ALTITUDE HOLD AND HEADING …digilib.itb.ac.id/files/disk1/616/jbptitbpp-gdl-hendralesm-30786-1... · DEVELOPMENT OF ALTITUDE HOLD AND HEADING HOLD CONTROL SYSTEM FOR

Documents