DESIGN, DEVELOPMENT AND CONTROL OF ATWIN ROTOR SYSTEM

A Thesis Submitted tothe Graduate School of Engineering and Sciences of

Izmir Institute of Technologyin Partial Fulfillment of the Requirements for the Degree of

MASTER OF SCIENCE

in Electronics and Communication Engineering

byFırat DOGAN

July 2014IZMIR

We approve the thesis of Fırat DOGAN

Examining Committee Members:

Prof. Dr. Serhan OZDEMIRDepartment of Mechanical EngineeringIzmir Institute of Technology

Assist. Prof. Dr. Barbaros OZDEMIRELDepartment of Electrical and Electronics EngineeringIzmir Institute of Technology

Assoc. Prof. Dr. Enver TATLICIOGLUDepartment of Electrical and Electronics EngineeringIzmir Institute of Technology

10 July 2014

Assoc. Prof. Dr. Enver TATLICIOGLUSupervisor, Department of Electrical and Electronics EngineeringIzmir Institute of Technology

Prof. Dr. M. Salih DINLEYICI Prof. Dr. R. Tugrul SENGERHead of the Department of Dean of the Graduate School ofElectrical and Electronics Engineering Engineering and Sciences

ACKNOWLEDGMENTS

I would like to express my sincere gratitude to my thesis advisor Assoc. Prof.

Dr. Enver Tatlıcıoglu for his support, encouragement and enthusiasm throughout this

thesis. His constructive criticism, constant motivation and guidance led me to give my

best. He has been supportive since I began to study in his laboratory as an undergraduate.

I consider it an honor to be his student.

I gratefully acknowledge the contributions of Assist. Prof. Dr. Alper Bayrak.

I admire his enthusiasm and knowledge on both software and hardware issues. I see

him as an expert in giving suggestions and guiding to solutions for any kind of problem

throughout this thesis.

I would like to thank Assist. Prof. Dr. Barbaros Ozdemirel. His undergraduate

lessons and valuable tips helped me during the thesis.

I would like to thank Assist. Prof. Dr. M. I. Can Dede. He inspired me on robotics

and control by giving me the opportunity to work on a hexapod project in undergraduate

program. This inspiration continued throughout this thesis.

I would like to thank my family for their unconditional support and endless love

during my whole life. They always gave me support during my studies.

I would like to thank Aylin Bayram for her moral support and motivation. Her

encouragement helped me to have continuous inspiration throughout this thesis.

ABSTRACT

DESIGN, DEVELOPMENT AND CONTROL OF A TWIN ROTORSYSTEM

Twin rotor multi-input multi-output system (TRMS) is a laboratory setup resem-

bling the dynamics of a helicopter. It is a complicated nonlinear system with high cou-

pling effects between the propellers. In the literature, there is no commonly agreed dy-

namic model for these systems mainly due to the difficulties in modelling aerodynamic

effects. As a result, numerical simulations of controllers performed on currently available

dynamic models do not agree with experimental results obtained from a real system. The

main motivations behind this thesis are to develop a TRMS in our laboratory and then

apply different control algorithms on it.

Firstly, the mechanical system is described briefly. The mechanical components

are explained and the computer aided design model is given. The electronic system is then

presented in detail. In the electronic system, hardware parts of the TRMS (mainboard,

encoder reader circuits, and motor controller circuits) and the embedded algorithms are

developed. The development of the user interface that is used both to observe the TRMS

and to communicate with it, is then explained. Development of a mathematical model

of the TRMS is described where its physical parameters are given. Finally, the perfor-

mance of the TRMS is verified by conducting experiments for proportional, integral and

derivative type controllers. The analysis of the experiments are discussed and compared

in average maximum steady-state error, average root-mean-square error, error standard

deviation, average root-mean-square control input and control input standard deviation.

iv

OZET

CIFT ROTORLU SISTEMIN TASARIMI, GELISTIRILMESI VEDENETLENMESI

Cift rotorlu coklu girisli coklu cıkıslı sistem, bir helikopterin dinamiklerini temsil

eden bir laboratuvar duzenegidir. Pervaneleri arasında baglantılı etki olan ve dogrusal

olmayan karmasık bir sistemdir. Aerodinamik etkilerin modellenmesindeki zorluklar

sebebiyle, bu tur sistemlerin literaturde ortak kabul edilen bir dinamik modeli bulun-

mamaktadır. Bunun sonucu olarak, denetleyicilerin su an var olan dinamik modeller

uzerindeki sayısal benzetimleri gercek bir sistem uzerinden elde edilen deneysel sonuclar

ile ortusmemektedir. Bu tezin arkasındaki ana motivasyon, kendi cift rotorlu sistemimizin

gelistirilmesi ve uzerinde farklı denetleyici algoritmalarının uygulanmasıdır.

Mekanik sistem kısaca acıklandı. Mekanik bilesenler acıklandı ve bilgisayar destekli

tasarım modeli verildi. Elektronik sistem detayları ile sunuldu. Sistemin donanımsal

kısımları (ana devre, kodlayıcı okuyucu devreleri ve motor denetleyici devreleri) ve gomulu

algoritmaları gelistirildi. Daha sonra hem cift rotorlu sistemi gozlemlemek hem de onunla

haberlesmek icin gelistirilen kullanıcı ara yuzu acıklandı. Cift rotorlu sistemin matematik

modelinin gelistirilmesi acıklandı ve fiziksel parametreleri verildi. Son olarak, cift rotorlu

sistemin performansı oransal, integral ve turev iceren cesitli denetleyicilerin uygulandıgı

deneyler ile dogrulandı. Deneylerin analizleri tartısıldı ve ortalama maksimum sabit du-

rum hatası, hatanın karekok ortalaması, hatanın standart sapması, denetleyici girisinin

karekok ortalaması ve denetleyici girisinin standart sapması karsılastırıldı.

v

TABLE OF CONTENTS

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

LIST OF ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

CHAPTER 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

CHAPTER 2. TRMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1. Mechanical System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2. Electronic System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1. Mainboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1.1. Main Processor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.1.2. RS232 to/from UART Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.2. Encoder Reader and Position & Velocity Transmitter Circuit . . 13

2.2.2.1. Optical Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.2.2. Encoder Reader Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.2.3. Position & Velocity Transmitter Circuit . . . . . . . . . . . . . . . . . . . 18

2.2.3. Motor Controller Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.3.1. MCU Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.3.2. Motor Driver Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2.3.3. Isolation Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

CHAPTER 3. COMPUTER SOFTWARE DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1. LabVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2. User Interface Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

CHAPTER 4. MATHEMATICAL MODELLING OF TRMS . . . . . . . . . . . . . . . . . . . . . . . . 33

vi

CHAPTER 5. CONTROL OF TRMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1. Proportional (P) Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.2. Proportional - Integral (PI) Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.3. Proportional - Derivative (PD) Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.4. Proportional - Integral - Derivative (PID) Control . . . . . . . . . . . . . . . . . . . 43

5.5. Analysis of the Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

CHAPTER 6. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

vii

LIST OF FIGURES

Figure Page

Figure 1.1. TRMS by Feedback Instruments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Figure 1.2. 2 DOF helicopter by Quanser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Figure 1.3. 3 DOF helicopter by Quanser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Figure 1.4. The TRMS built in Universita Politecnica Delle Marche, Ancona, Italy. 5

Figure 1.5. The CAD model of the TRMS developed in our laboratory. . . . . . . . . . . . . . 6

Figure 1.6. The TRMS developed in our laboratory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Figure 2.1. Inside of the base box. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Figure 2.2. The block diagram of the TRMS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Figure 2.3. Mainboard. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Figure 2.4. Port configurations of the MCU on Mainboard. . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Figure 2.5. The flow diagram of the algorithm embedded in the MCU on Main-

board. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Figure 2.6. Encoder reader and position & velocity transmitter circuit. . . . . . . . . . . . . . . 14

Figure 2.7. The optical encoder on the pitch axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Figure 2.8. The optical encoder on the yaw axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Figure 2.9. Clockwise and counterclockwise rotations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Figure 2.10. XOR values of the channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Figure 2.11. Port configurations of the MCU labelled as IC2 in Figure 2.6. . . . . . . . . . . . 20

Figure 2.12. The flow diagram of the algorithm embedded in IC2 in Figure 2.6. . . . . . 21

Figure 2.13. Port configurations of the MCU labelled as IC1 in Figure 2.6. . . . . . . . . . . . 22

Figure 2.14. The flow diagram of the algorithm embedded in IC1 in Figure 2.6. . . . . . 23

Figure 2.15. Port configurations of the MCU on motor driver circuit. . . . . . . . . . . . . . . . . . 24

Figure 2.16. The flow diagram of the algorithm of the motor driver circuit. . . . . . . . . . . . 25

Figure 2.17. PWM signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Figure 2.18. Motor controller circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Figure 3.1. View of the user interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Figure 3.2. User interface of adjusting serial port parameters, termination character

and the timeout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Figure 3.3. User interface of setting controller gains and desired angular position

values, and observing tracking errors and quantized input voltage val-

ues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Figure 3.4. User interface of configuration of data bytes received from the TRMS. . 32viii

Figure 3.5. Graphic view of pitch and yaw tracking errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Figure 5.1. [P control] angular position on pitch and yaw axes, respectively. . . . . . . . . 38

Figure 5.2. [P control] tracking error on pitch and yaw axes, respectively. . . . . . . . . . . . 39

Figure 5.3. [P control] control input on pitch and yaw axes, respectively. . . . . . . . . . . . . 40

Figure 5.4. [PI control] angular position on pitch and yaw axes, respectively. . . . . . . . 41

Figure 5.5. [PI control] tracking error on pitch and yaw axes, respectively. . . . . . . . . . . 42

Figure 5.6. [PI control] control input on pitch and yaw axes, respectively. . . . . . . . . . . . 43

Figure 5.7. [PD control] angular position on pitch and yaw axes, respectively. . . . . . . 44

Figure 5.8. [PD control] tracking error on pitch and yaw axes, respectively. . . . . . . . . . 45

Figure 5.9. [PD control] control input on pitch and yaw axes, respectively. . . . . . . . . . . 46

Figure 5.10. [PID control] angular position on pitch and yaw axes, respectively. . . . . . 47

Figure 5.11. [PID control] tracking error on pitch and yaw axes, respectively. . . . . . . . . 47

Figure 5.12. [PID control] control input on pitch and yaw axes, respectively. . . . . . . . . . 48

ix

LIST OF TABLES

Table Page

Table 2.1. Mechanical parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Table 2.2. Specifications of the encoder WDG 58C 1024-ABN-R30-K3-F29-070 . 15

Table 2.3. Optical encoder output table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Table 2.4. Maximum angular velocities for pitch and tail rotor in both directions . . 19

Table 2.5. Received data packet for the main motor controller . . . . . . . . . . . . . . . . . . . . . . 23

Table 2.6. Received data packet for the tail motor controller . . . . . . . . . . . . . . . . . . . . . . . . 24

Table 4.1. System parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Table 4.2. Calculated parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Table 5.1. Independent effects of the gains of PID control . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Table 5.2. Analysis of the errors for different controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Table 5.3. Analysis of the control inputs for different controllers . . . . . . . . . . . . . . . . . . . . 48

x

LIST OF SYMBOLS

φresolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The resolution of the optical encoder

ω(t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The angular velocity

T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The sampling interval

N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The number of pulse count per rotation

n . . . . . . . . . . . . . . . . . . . . . . . . . .The number of the pulses counted in one sampling interval

PR2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Register which keeps the period

Tosc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Oscillator period

Fosc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Oscillator frequency

FPWM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PWM frequency

CCPR1L . . . . . . . . . . . . . . . . . . . . . . . . Register which keeps the low byte of the duty cycle

CCP1CON . . . . . . . . . . . . . . .Register which keeps the 9th and 10th bits of the duty cycle

VS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The maximum supply voltage

IP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The peak load current

dV/dt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The limited rise time of the output voltage

θv (t) . . . . . . . . . . . . . . . . . . . . . . . . . . . The angular position of the beam in the vertical plane

θv (t) . . . . . . . . . . . . . . . . . . . . . . . . . . . The angular velocity of the beam in the vertical plane

θv (t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The acceleration of the beam in the vertical plane

θh (t) . . . . . . . . . . . . . . . . . . . . . . . . The angular position of the beam in the horizontal plane

θh (t) . . . . . . . . . . . . . . . . . . . . . . . . The angular velocity of the beam in the horizontal plane

θh (t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . The acceleration of the beam in the horizontal plane

J . The sum of the moment of inertia of the counter balance beam and the free-free beam

τh (t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The controller input for horizontal plane

τv (t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The controller input for vertical plane

θ (t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The angular position vector

M (θ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The inertia matrix

N(θ, θ)

. . . . . . . . . . . . . The other dynamic effects such as coriolis and centrifugal forces

τ (t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The control input vector

J1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The moment of inertia of the free-free beam

J2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The moment of inertia of the counter balance beam

J3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The moment of inertia of the pivoted beam

g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The gravitational acceleration

h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The length of the pivoted beam

m1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The total mass of the free-free beamxi

m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The total mass of the counter balance beam

l1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The center of gravity of the free-free beam

l2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The center of gravity of the counter balance beam

mt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The mass of the tail beam

mtr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The mass of the tail rotor

mts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The mass of the tail shield

mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The mass of the main beam

mmr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The mass of the main rotor

mms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The mass of the main shield

lm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The length of main part of the free-free beam

rms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The radius of the main shield

rts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The radius of the tail shield

mb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The mass of the counter balance beam

lb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The length of the counter-weight beam

mcb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The mass of the counter-weight

lcb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The length between the counter-weight and the joint

mh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The mass of the pivoted beam

θ(t0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The initial angular position

θd(t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The desired angular position

KP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The constant diagonal proportional gain matrix

KI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The constant diagonal integral gain matrix

KD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The constant diagonal derivative gain matrix

Ti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The integral time constant

Td . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The derivative time constant

xii

LIST OF ABBREVIATIONS

SISO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single Input Single Output

MIMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multi Input Multi Output

TRMS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Twin Rotor MIMO System

CAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computer Aided Design

DOF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Degree of Freedom

FPGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Field Programmable Gate Array

VHSIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Very High Speed Integrated Circuit

VHDL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VHSIC Hardware Description Language

GA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Genetic Algorithm

DC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Direct Current

P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Proportional

I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integral

D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Derivative

UART . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Universal Asynchronous Receiver/Transmitter

MCU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Microcontroller Unit

PIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Peripheral Interface Controller

IC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integrated Circuit

PCB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Printed Circuit Board

CW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Clockwise

CCW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Counterclockwise

ISR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interrupt Service Routine

LSbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Least Significant Bits

PWM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pulse Width Modulation

MSbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Most Significant Bits

VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Virtual Instrument

SSE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Steady-State Error

SD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Standard Deviation

RMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Root-Mean-Square

xiii

CHAPTER 1

INTRODUCTION

Twin rotor multi input multi output system (TRMS) is a laboratory set up resem-

bling a helicopter which is designed for conducting control experiments. In a typical

TRMS, there are two rotors, two optical encoders and a controller circuit. Two rotors

have rotation axes orthogonal to each other. The system moves on yaw and pitch axes

with the thrust produced by the propellers mounted on the rotors. The pitch movement

is up or down movement of the nose of a helicopter relative to the tail. The yaw move-

ment is side to side movement of the nose of a helicopter. The position of the TRMS is

adjusted by the main rotor and the tail rotor with the help of the feedback provided by

the optical encoders. The overall system is nonlinear and complex with a high coupling

effect between the propellers.

There are some commercial products developed by companies. The company

Feedback Instruments Limited1 has produced a TRMS for educational purposes and mostly

for control experiments. Figure 1.1 shows TRMS by Feedback Instruments. Quanser

Inc.2, which manufactures robotic and mechatronic systems, has also developed heli-

copter systems. Figure 1.2 shows the 2 degree of freedom (DOF) helicopter and Figure

1.3 shows the 3 DOF helicopter by Quanser.

There is some past research on modification of commercially available TRMS.

Juang and Liu (2008) employed Xilinx Spartan II SP200 Field Programmable Gate Array

(FPGA) for real time control to construct a hardware-in-the-loop system through coding

VHSIC hardware description language (VHDL). While Yu et al. (2010) utilized Altera

Cyclone II FPGA for real time control to construct a hardware-in-the-loop system through

embedding C and VHDL codes on this FPGA.

Design and development of TRMS have been studied in the university laboratories

as well Verzilli (2007). Corradini et al. (2011) used NI-PCI6024e, produced by National

Instruments which allows data exchange between a PC and the TRMS, and they setup the

TRMS by building an interface board to filter and to adapt sensor signals, and building

1Feedback Instruments Limited, Crowborough, UK. http://www.feedback-instruments.com/

2Quanser Inc., Ontario, Canada. http://www.quanser.com/

1

Figure 1.1. TRMS by Feedback Instruments.

a power board to drive the motors with suitable voltages. Their TRMS can be seen in

Figure 1.4.

There has been some previous research in dynamic modelling of TRMSs. La-

grangian and Newtonian approaches were utilized in the physics-based methods. Shih

et al. (2008) utilized Lagrangian approach to derive a mathematical model for the TRMS

and analyzed some of the characteristics of the proposed model such as equilibrium po-

sition, propeller thrust and gravity compensation. Rahideh and Shaheed (2007) presented

two dynamic models for the TRMS by utilizing Newtonian and Lagrangian approaches

and modelled the interface circuit, DC motors, and propulsive forces due to these motors.

Artificial intelligence-based empirical approaches such as genetic algorithms (GA) and

neural networks were also utilized to develop dynamic models for the TRMS. These ap-

proaches are usually utilized by adding a term to the analytical model to reflect the effects

that were not considered when obtaining the analytical model. In Rahideh and Shaheed

(2008), the Newtonian method was used to develop the dynamic equations of the 2 DOF

system. Some of the parameters of the system were obtained and other parameters were

estimated by using physical properties of the system. After that, GA optimization ap-

proach was utilized to improve the accuracy of the estimated parameters. In Rahideh

et al. (2008), analytical approaches in conjunction with neural networks based empiri-2

Figure 1.2. 2 DOF helicopter by Quanser.

cal approaches were used to derive dynamic models for a one DOF TRMS. A black-box

system identification technique is utilized to derive dynamic model of two DOF TRMS

Ahmad et al. (2000).

The focus of the other past research is on designing control algorithms for TRMSs.

Classical control techniques such as combinations of proportional (P), integral (I), deriva-

tive (D) controllers were commonly used to control TRMSs. Liu et al. (2006) proposed

to improve the performance of classical controllers by using a fuzzy controller. Shih et al.

(2008) proposed a PD controller and a fuzzy PID controller for set-point stabilization

control. In addition, robust controllers were studied to deal with modelling uncertain-

ties, unmeasured disturbances and unmodelled effects in the system. Karimi and Motlagh

(2006) proposed a robust controller based on a feedback linearization scheme to overcome

model uncertainties and disturbances. Lu and Wen (2007) presented a robust controller

by decoupling the MIMO system into two independent single input single output (SISO)

systems and cross-coupling effects were treated as disturbance and/or parametric uncer-

tainty. Bayrak et al. (2010) developed a robust controller, based on the restriction that

the TRMS dynamic model is unknown, by fusing a continuous nonlinear feedback com-

ponent with a nonlinear neural network feedforward term. Su et al. (2002) developed a

3

Figure 1.3. 3 DOF helicopter by Quanser.

robust control scheme for a class of cascade connected uncertain nonlinear systems which

was applied to TRMSs.

In this thesis, design, development and control of a TRMS in an academic set-

ting were studied. In Figures 1.5 and 1.6, the computer aided design (CAD) model and

the developed twin rotor system in our laboratory are presented, respectively. As a me-

chanical system, a TRMS setup which was previously developed in our laboratory was

used. Hardware parts, mainboard, encoder reader circuits and motor controller circuits

were designed. Embedded software parts were developed as well. Afterwards, a dy-

namical model was derived for the TRMS. Several measurements were done to obtain

the physical parameters and the limitations (i.e., maximum and minimum operating con-

ditions) of the TRMS. A computer software was developed on LabVIEW Development

Environment in order to monitor the TRMS and to communicate with it online. Pro-

portional (P), proportional-integral (PI), proportional-derivative (PD) and proportional-

integral-derivative (PID) controllers were applied and their performances were observed

on the developed TRMS.

The organization of the rest of this thesis is as follows. Chapter 2 explains the me-

chanical and electronic systems of the TRMS. Chapter 3 gives information about the com-

puter program written on LabVIEW Development Environment to monitor the TRMS and4

Figure 1.4. The TRMS built in Universita Politecnica Delle Marche, Ancona, Italy.

to communicate with it. Chapter 4 presents the Lagrangian based dynamic model. Chap-

ter 5 presents the P, PI, PD and PID controllers with their experimental results. Chapter

6 presents the conclusion of this thesis and highlights some possible future research av-

enues.

5

Figure 1.5. The CAD model of the TRMS developed in our laboratory.

Figure 1.6. The TRMS developed in our laboratory.

6

CHAPTER 2

TRMS

In this chapter, the mechanical system design and the electronic system design are

presented. The electronic system design are explained in three subsections as mainboard,

encoder reader and motor controller circuit.

2.1. Mechanical System Design

The mechanical part of the system includes two rotors on a beam with a counter

balance as shown in Figure 1.6. The main rotor produces vertical thrust and rotates the

beam around the pitch axis. The other rotor, called as the tail rotor, is mounted on the

opposite side of the beam, perpendicular to the main rotor, to obtain movement on the

yaw axis. This beam is placed on the top of a shaft which is seated on two co–axial

bearings. Aluminum is preferred in construction of the beam, counter balance and shaft

due to its high strength to weight ratio. The system is then placed on top of an steel base

box for mechanical stability. The electronic units are placed inside the base box as can be

seen in Figure 2.1. The parameters of the system are given in Table 2.1.

Table 2.1. Mechanical parameters

Parameter Valuelength of beam 655 mmlength of counter balance beam 306 mmdistance between pivot and main rotor 327.5 mmdistance between pivot and tail rotor 327.5 mmmass of the counter balance beam 65 grmass of the beam 400 grmass of main rotor 450 grmass of tail rotor 435 grraidus of the main rotor propeller 156 mmradius of the tail rotor propeller 77 mm

7

Figure 2.1. Inside of the base box.

2.2. Electronic System Design

The electronic system consists of: i) a mainboard, ii) two encoder readers, and iii)

two motor driver modules that are described in detail in the following sections.

Mainly, encoder readers acquire the square wave signals coming from the optical

encoders. They calculate the quantized number of the angular position and transmits them

via parallel data lines. Position and velocity transmitter circuits calculate the angular

velocity and send the angular position and angular velocity data to the main circuit via

Universal Asynchronous Receiver/Transmitter (UART). Main circuit collects the angular

positions and the angular velocities of the system, and sends the data to the computer via

RS232. The computer calculates the control inputs which are the required voltage values

for the two motors, and sends the data to the motor controller circuits. Motor controller

circuit drives the motors according to the required voltage values.

As can be seen in the block diagram in Figure 2.2, all modules use the same serial

bus to communicate with each other and with the computer. The communication is at

57600 baud rate. The motor driver circuits are accessible to the mainboard processor

through the shared serial bus structure. This design allows execution of the controller

algorithm on the mainboard processor instead of the external computer. In that case, the

experimental setup may become a standalone control system where the computer is used

only for monitoring the system behavior.8

ENCODER READER

OPTICAL ENCODER

SPEED AND POSITION TRANSMITTER

MAIN CIRCUIT

ENCODER READER

OPTICAL ENCODER

SPEED AND POSITION TRANSMITTER

MOTOR CONTROLLER

MOTOR CONTROLLER

TAIL ROTOR

MAIN ROTOR

UART

UART

PWM

PWM

PARALLEL

PARALLEL

UART

UART

RS232

Figure 2.2. The block diagram of the TRMS.

2.2.1. Mainboard

Mainboard consists of a microcontroller unit (MCU), a 5V regulator and a serial

line driver-receiver (MAX232) as shown in Figure 2.3. The mainboard is connected to

all the other circuits (i.e., encoder reader circuits, motor controller circuits) through the

shared serial bus. The primary duty of the mainboard is to supervise the whole system,

and it is responsible for arrangement of when to request angular position and angular

velocity values of the TRMS from the encoder reader circuit, and when to take required

voltage values from the computer.

The mainboard has two jumpers for selection. JP1 jumper is for programming

purposes and gives option to connect motor data line to receiver port of the mainboard

processor labelled as IC1. In this way, mainboard processor can listen the communication

between the computer and the motor driver circuit. During the course of the development

of the TRMS, different algorithms were tried, and in order to handle a reliable commu-

nication, we decided to use the jumper as closed, which means IC1 listens the data line

between the computer and the motor driver circuit. In this way, the mainboard processor

knows whether the computer completed its process or not.

9

Figu

re2.

3.M

ainb

oard

.

10

The controller algorithm runs on the computer but it can also be embedded into

the mainboard processor. The second jumper, labelled as JP2, is for design changes that

require an option to connect the motor driver circuit to the mainboard processor instead

of the computer. If JP2 is connecting pin 3 to pin 2, the computer drives the motors. If it

is connecting pin 1 to pin 2, the mainboard processor drives the motors. In this way, the

whole system will turn into a standalone system independent from the computer.

2.2.1.1. Main Processor

PIC16F877 MCU manufactured by Microchip1 is used as the main processor. The

port configurations of the MCU are given in Figure 2.4. MCU reads angular position and

PIC16F877

USART

PORTC

RC4-REQUEST2

RC5-REQUEST1

RA6-TX

RA7-RX

PORTD

RD0-LED

Figure 2.4. Port configurations of the MCU on Mainboard.

angular velocity data from the two encoder readers and sends these data to the computer.

To read the data from encoder readers successively, the MCU uses encoder reader request

pins, namely REQUEST1 and REQUEST2 pins in Figure 2.3. When an encoder request

pin is activated, the related encoder reader begins to send latest angular position and

angular velocity values to the mainboard via the serial bus. When the reading process from

1Microchip Technology Inc, Chandler, Arizona, USA. https://www.microchip.com/

11

both encoder readers are completed, MCU sends these data to the computer as a combined

data packet. The flow diagram of the above algorithm embedded in the mainboard MCU

is summarized in Figure 2.5.

Activate encoder reader 1 request line

BEGIN

Is transmition from encoder reader 1

complete?

Activate encoder reader 2 request line

Send encoder readings to the computer

Is transmition from encoder reader 2

complete?

Is data transmission from computer

complete?

YES

YES

YES

NO

NO

NO

Figure 2.5. The flow diagram of the algorithm embedded in the MCU on Mainboard.

12

2.2.1.2. RS232 to/from UART Circuit

RS232 to/from UART circuit is designed with MAX232 manufactured by Maxim2.

MAX232 has two drivers and two receivers inside. Each receiver converts TIA/EIA-232-

F inputs to 5V TTL/CMOS levels, and each driver converts TTL/CMOS input levels into

TIA/EIA-232-F levels.

MAX232 has a maximum data rate of 120kbps. First, the communication between

the circuit and the computer were setup to operate at 115200 baud rate. However, in the

experiments, it was observed that some of the data can be corrupted while the communi-

cation continues. The communication speed was close to the maximum data rate of the

MAX232 IC. Also, the maximum data rate is expected to be reduced due to the tolerances

of the capacitors. Thus, the communication rate is adjusted to 57600 baud rate.

2.2.2. Encoder Reader and Position & Velocity Transmitter Circuit

Encoder reader and position & velocity transmitter circuits are designed in one

printed circuit board (PCB). The circuit is designed as in Figure 2.6 consisting of two

MCUs and an XOR gate. The overall system has two of these circuits for the two axes as

can be seen in Figure 2.2. In the following subsections, the design will be described in

three parts; optical encoder, encoder reader circuit and velocity calculator circuit.

2.2.2.1. Optical Encoder

An optical rotary encoder is a device which converts angular position into a se-

quence of digital pulses. Optical encoders basically have a circular disk which contains a

set of radial lines between the photo-emitter and the photo-detector pairs. As the disk ro-

tates, the light between the photo-emitter and the photo-detector pair is interrupted by the

radial lines. As a result of this, it produces digital pulses. There are two different types;

absolute encoders and incremental encoders. Absolute encoders give data byte or word as

output which corresponds to an absolute angular position. Incremental encoders produce

digital pulses as the shaft rotates, and allow measurement of relative angular position only.

2Maxim Integrated, San Jose, California, USA. http://www.maximintegrated.com/13

Figu

re2.

6.E

ncod

erre

ader

and

posi

tion

&ve

loci

tytr

ansm

itter

circ

uit.

14

The TRMS has two optical encoders to detect the angular position on yaw and

pitch axes. The pitch axis encoder is directly coupled to the pivot of the horizontal beam

as shown in Figure 2.7. The yaw axis encoder is mounted next to the main vertical shaft.

The coupling between the encoder and the shaft is obtained through a belt as shown in

Figure 2.8.

Figure 2.7. The optical encoder on the pitch axis.

In this work, an incremental encoder WDG 58C from Wachendorff Automation3

company is used with the specifications given in Table 2.2.

Table 2.2. Specifications of the encoder WDG 58C 1024-ABN-R30-K3-F29-070

Power Supply 5VDC-30VDCLight Source IR LEDResolution 1024 pprOutput Current max 40mAOutput Circuit TTLOutput Frequency max 200KHz at 5V and 7m cable length

3Wachendorff Automation GmbH & Co KG, Geisenheim, Germany. http://www.wachendorff-automation.com/

15

Figure 2.8. The optical encoder on the yaw axis.

The incremental optical encoder consists of two photo-emitter and photo-detector

pairs. It has two output signal lines named A and B, which corresponds to the two photo-

detectors. By reading the logical voltage states of these lines, angular position, rotation

direction and angular velocity can be measured. As the pulse trains of the channels are out

of phase with each other, the rotation direction is determined with this timing difference

between the signals. The angular velocity is determined by measuring the frequency of

the signals while the angular position is determined by the number of pulses. The graphs

in Figure 2.9 explain the working principle of the optical encoder.

The resolution of the optical encoder is calculated as

φresolution =2π

N. (2.1)

Considering that the optical encoder is capable of producing 1024 pulses per rotation

(ppr), each pulse corresponds to 360/1024 = 0.352. The angular velocity ω(t) in

radian/sec can be calculated as

ω(t) =2πn

NT(radian/sec) (2.2)

where T is the sampling interval, N is the number of pulse count per rotation, and n is

the number of the pulses counted in one sampling interval.

The individual outputs of the encoders used in this system generate 1024 square

wave cycles per revolution. The number of quadrature steps is 4096 per revolution as de-

scribed in Figure 2.10. When the two outputs are combined, a precision of 0.088 degrees16

0 1 2 3 4 5 6 70

2

4

6

8

Time

Vol

tage

Clockwise Rotation − A leads B

Channel A

0 1 2 3 4 5 6 70

2

4

6

8

Time

Vol

tage

Channel B

0 1 2 3 4 5 6 70

2

4

6

8

Time

Vol

tage

Counterclockwise Rotation − B leads A

Channel A

0 1 2 3 4 5 6 70

2

4

6

8

Time

Vol

tage

Channel B

Figure 2.9. Clockwise and counterclockwise rotations.

per step is obtained. Thus, an XOR IC is added to the design and the MCU can count

4096 steps for 360 with the help of the XOR data. In this method, considering that both

the current state and the previous state are used to determine the rotation direction, the

optical encoder output table can be written as in Table 2.3.

2.2.2.2. Encoder Reader Circuit

The MCU labelled as IC2 is responsible for reading the square wave signals com-

ing from the optical encoder. Its main duty is to read the signals, calculate the quantized

angular position values of the axis and write them to output ports as parallel data lines.

The port configurations of IC2 are given in Figure 2.11. The flow diagram of the algorithm

embedded in IC2 is given in Figure 2.12.

As an MCU, PIC16F883 manufactured by Microchip company is used. It is a 28

pin flash-based, 8 bit CMOS MCU. PIC is set up with an external oscillator running at

20MHz with PortB change interrupts enabled. The processor reads the optical encoder

outputs and increases or decreases the angular position count after every encoder inter-

rupt. The interrupt service routine (ISR) compares the current encoder outputs with the

values before the interrupt that were recorded in the previous ISR call. A two-byte counter

is used to count the encoder pulses. The angular position counts are stored as 16–bit inte-

gers where the 12 least significant bits (LSbs) vary between 0 and 4095 in each encoder17

0 1 2 3 4 5 6 70

5

Time

Vol

tage

Clockwise Rotation − A leads B

Channel A

0 1 2 3 4 5 6 70

5

Time

Vol

tage

Channel B

0 1 2 3 4 5 6 70

5

Time

Vol

tage

XOR(A,B)

Figure 2.10. XOR values of the channels.

rotation. The counter is started at 32768 to avoid the zero crossing of the counter register.

The main routine is responsible for writing the quantized angular position data to output

ports.

The MCU should handle the encoder interrupts at the maximum possible transition

rate. In the TRMS, maximum angular velocity that can be achieved is measured as shown

in Table 2.4.

Since the maximum velocity is 1.7498 rad/sec at the maximum possible transition

rate, considering that the encoder resolution is 4096 counts/rev, the required interrupt ser-

vice time is calculated as 876.65 µ sec. The MCU is capable of serving encoder interrupts

once every 20 µ sec. In this case, the processor is always capable of serving the encoder

interrupts on–time. Main routine of the IC2 MCU sends the angular position value to the

IC1. The whole main routine takes 20.8 µ sec. Considering one total cycle, it takes 40.8

µ sec, which means that the processor is capable of processing every step of the optical

encoder.

18

Table 2.3. Optical encoder output table

State A B XOR DirectionCurrent : 1 0 1 CWPrevious: 1 1 0Current : 0 1 1 CCWPrevious: 1 1 0Current : 0 1 1 CWPrevious: 0 0 0Current : 1 0 1 CCWPrevious: 0 0 0Current : 1 1 0 CWPrevious: 0 1 1Current : 0 0 0 CCWPrevious: 0 1 1Current : 0 0 0 CWPrevious: 1 0 1Current : 1 1 0 CCWPrevious: 1 0 1

Table 2.4. Maximum angular velocities for pitch and tail rotor in both directions

Pitch Up 1.7498 rad/secPitch Down -1.6500 rad/sec

Tail CW 1.0365 rad/secTail CCW -0.9987 rad/sec

2.2.2.3. Position & Velocity Transmitter Circuit

The MCU labelled as IC1 is responsible for calculating angular velocity and for

sending angular position and angular velocity values when the main circuit requests them.

The port configurations of ICI are given in Figure 2.13. The flow diagram of the algorithm

embedded in IC1 is given in Figures 2.14.

As an MCU PIC16F883 is used. PIC is setup with an external oscillator running

at 20 MHz, a UART at 57600 baudrate, an 8-bit timer configured with 1:256 prescaler for

maximum period. The MCU always reads the parallel data lines and updates the angular

position registers. When the timer0 interrupt occurs, which is once every 13.1 ms, it

calculates the angular velocity.

19

PIC16F876

TIMER1

PORTA

RA0-COUNTER,0

RA1-COUNTER,1

RA2-COUNTER,2

RA3-COUNTER,3

PORTC

RA4-COUNTER,4

RA5-COUNTER,5

RC0-COUNTER,6

RC1-COUNTER,7

RC2-COUNTER,8

RC3-COUNTER,9

RC4-COUNTER,10

RC5-COUNTER,11

RC6-COUNTER,12

RC7-COUNTER,13

PORTB

RB1-SIGNAL A

RB7-SIGNAL XOR

RB6-COUNTER,14

RB7-COUNTER,15

Figure 2.11. Port configurations of the MCU labelled as IC2 in Figure 2.6.

The MCU keeps the angular position and angular velocity values ready for trans-

mission. When the request line connected to the mainboard is set low, it sends the angular

position and angular velocity data packet via UART. Request line is pulled high with a

10KΩ pull–up resistor in order to work as active low.

The software was written in C language. In order to speed up the execution of

data transmission, some functions related to data reading algorithm were replaced with

assembly codes. In this way, the reading process which takes 87.8 µ sec was decreased to

27.8 µ sec.

2.2.3. Motor Controller Circuit

Motor controller circuit is designed as in Figure 2.18 consisting of an MCU, an

H-Bridge and an optocoupler. The TRMS has two of these circuits for the two motors as

can be seen in the Figure 2.2.

In the following subsections, the motor controller design will be described in three

parts; MCU circuit, motor driver circuit and circuit isolation.20

Increase ordecrease the counter

according to the signal

BEGIN

Does interrupt occur?

YES

NO

Write counter value to the output ports

Figure 2.12. The flow diagram of the algorithm embedded in IC2 in Figure 2.6.

2.2.3.1. MCU Circuit

The MCU labelled as IC1 in Figure 2.18 is responsible for communicating with

the computer or the mainboard. Both computer and main circuit can send commands to

the MCU. In this study, the control algorithms are developed on the computer, and thus

the computer sends the commands. The port configurations of IC1 are given in Figure

2.15, and the flow diagram of the algorithm embedded in IC1 is given in Figure 2.16.

Motor driver modules produce PWM signals according to the duty cycle settings

sent from the computer to drive the DC motors. As shown in Figure 2.17, in PWM

technique, the average value of the signal is adjusted by changing the on–off times of the

signal. The ratio of “on” duration and period of the signal is named as duty cycle and is

expressed in percentage.

As an MCU, PIC16F628 is used. PIC is setup as UART at 57600 baud rate,

Capture/Compare/PWM (CCP) module with adjusted in PWM mode, timer2 with 1:1

prescale value. CCP module uses timer2 when setup in PWM mode, differently from the

capture and compare mode which uses timer1. In PWM mode, the CCP1 pin produces a

PWM output up to 10-bit resolution. There are 3 registers which determine the period and

21

PIC16F876

TIMER1

PORTA

RA0-COUNTER,7

RA1-COUNTER,6

RA2-COUNTER,5

RA3-COUNTER,4

PORTB

RA4-COUNTER,3

RA5-COUNTER,2

RB0-COUNTER,15

RB1-COUNTER,14

RB2-COUNTER,13

RB3-COUNTER,12

RB4-COUNTER,11

RB5-COUNTER,10

RB6-COUNTER,9

RB7-COUNTER,8

PORTC

RC0-COUNTER,1

RC1-COUNTER,0

RC6-TX

RC7-REQUEST

USART

Figure 2.13. Port configurations of the MCU labelled as IC1 in Figure 2.6.

the duty cycle of the PWM signal. Specifically, PR2 register keeps the period, CCPR1L

register keeps the low byte of the duty cycle, and CCP1CON register keeps the 9th and

10th bits of the duty cycle. It should be recalled that the duty cycle is 10 bits of data.

The period of the PWM signal is calculated as

PWM period = [(PR2) + 1]× 4× Tosc × (TMR2 prescale) (2.3)

where PR2 is the value of the timer2 period register PR2, Tosc is the oscillator pe-

riod of the external clock as the MCU was setup with external crystal oscillator, and

TMR2 prescale is the value of the timer2 prescale register. Considering the MCU work-

ing at 20MHz, in order to achieve 20KHz PWM signal, PR2 register is calculated as

0xF9.

The duty cycle of the PWM signal is calculated as

Duty cycle = (CCPR1L : CCP1CON < 5 : 4 >)× Tosc × (TMR2Prescale) (2.4)

where CCPR1L : CCP1CON < 5 : 4 > is the value of the 10 bits as a combination

of the eight most significant bits (MSbs) in CCPR1L register and the two least significant

bits as the forth and the fifth bits of the CCP1CON register.22

Send position and velocity valuesto mainboard.

BEGIN

Is request line activated?

Read ports

YES

NO

Figure 2.14. The flow diagram of the algorithm embedded in IC1 in Figure 2.6.

As can be seen from Equation 2.4, the duty cycle is determined by writing the

registers CCPR1L and CCP1CON < 5 : 4 >. The value to be written is determined

by the computer, and is received via UART. The communication line of the two motor

controller circuits is a shared serial bus. Both of the two MCUs for the two axes read

the same data packets. However, the data packets differ with the prefix bytes and the end

byte. The data packet for the main and tail motor controllers are defined as in Tables 2.5

and 2.6, respectively.

Table 2.5. Received data packet for the main motor controller

Prefix Prefix Duty Cycle High Byte Duty Cycle Low Byte End Byte0xF1 0x01 0x.. 0x.. 0xF1

Maximum PWM resolution in bits for a given PWM frequency is determined by

the oscillator frequency, PWM frequency and the prescaler of the timer2 module. It is

23

PIC16F628

USART

RB1-RX

PORTB

RB3-PWM Signal

PWM

Figure 2.15. Port configurations of the MCU on motor driver circuit.

Table 2.6. Received data packet for the tail motor controller

Prefix Prefix Duty Cycle High Byte Duty Cycle Low Byte End Byte0xF2 0x02 0x.. 0x.. 0xF2

calculated as

PWM Resolution =log(

FOSC

FPWM×TMR2 Prescaler

)log2

bits (2.5)

where FOSC is the oscillator frequency, and TMR Prescaler is the value of the timer2

prescale register.

Considering that the PWM frequency is 20KHz, FOSC is 20MHz and TMR2

Prescaler is 1, the maximum PWM resolution is calculated as 9.966 bits. 9.966 bits of

resolution is equal to 29.966 = 1000.15 steps for PWM duty cycle adjustment. Thus, the

duty cycle value is sent as 0 to 1000 in decimal.

2.2.3.2. Motor Driver Circuit

The motor driver circuits utilize PWM to obtain high power efficiency, and conse-

quently, to minimize the cooling requirement of the driver components. Thus, the driver

MCU generates the PWM waveform for the H–bridge operation. The H–bridge used in

the motor driver circuits is L6203 manufactured by STMicroelectronics4. The transistors

4STMicroelectronics, Geneva, Switzerland. http://www.st.com/24

Write new values to PWM registers

BEGIN

Do new PWM values receive?

YES

NO

Figure 2.16. The flow diagram of the algorithm of the motor driver circuit.

in L6203 have an intrinsic diode between their source and drain that can operate as a fast

freewheeling diode. They protect the H–bridge during the on–off switching of the H–

bridge transistors. The H–bridge L6203 has a 24V supply voltage and drives the motors

with PWM control signal transferred via the optocoupler. A snubber network made by

the series of a resistor labelled R13 and a capacitor labelled C2 is mounted at the motor

terminals to filter the noise generated as the collector of the DC motor switches through

the armature windings. BYW98 diodes, D1 and D2, are connected between power output

pins and ground. The following formulas are used to calculate the snubber values SGS

Thomson Microelectronics (1997)

R ∼= VS/IP (2.6)

C = IP/(dV/dt) (2.7)

where VS is the maximum supply voltage, IP is the peak load current, and dV/dt is the

limited rise time of the output voltage. Considering that the supply voltage is 24V and the

maximum motor current is 21.5A, R13 is calculated as 1.12Ω. When dV/dt is 200V/µ sec

with reference to the L6203 datasheet, C2 is calculated as 108nF. Two bypass capacitors

(C5 and C10) are used on the motor driver circuit to stabilize the DC power supply voltage

at the H-bridge input. The bypass capacitor C10 is an electrolytic capacitor, and C5 is a25

0 1 2 3 4 5 6

x 104

−2

−1

0

1

2

3

4

5

Time ( µs )

Am

plitu

de (

V )

PWM signal

τ

T

Figure 2.17. PWM signal.

ceramic capacitor. The electrolytic capacitor can respond to H-bridge current demands up

to 100kHz, and the ceramic capacitor can be effective up to several MHz.

The heat caused by L6203 was dissipated with an additional heatsink which was

also supported with a fan.

2.2.3.3. Isolation Circuit

The switching transistors in the motor driver IC and the motor itself cause noise

and spikes that affect the rest of the circuit. Also, high current drain on the motor lines

causes ground supply voltage fluctuations. The MCUs must be isolated from these ef-

fects. Thus, the power and the signal lines are isolated from each other in order to isolate

the noise caused by the motor from the MCUs. In the design, the power lines are iso-

lated by using different power supplies. The signal lines are isolated by transferring the

PWM signal via an optocoupler. As an optocoupler, a one channel optocoupler PC817

manufactured by Sharp company5 is used.

5Sharp Corporation, Osaka, Japan. http://www.sharp-world.com/26

Figu

re2.

18.M

otor

cont

rolle

rcir

cuit.

27

CHAPTER 3

COMPUTER SOFTWARE DESIGN

The computer software is written on LabVIEW Development Environment1. The

interface program developed on LabVIEW enables us to monitor the TRMS and to com-

municate with it online.

In the following subsections, a brief information about LabVIEW development

environment will be given and the developed user interface program will be explained.

3.1. LabVIEW

LabVIEW programming language is a dataflow programming language which

means that activation of operations or processes depends on the availability of the in-

put data. The programmer wires connections between variables and operators that carry

data from outputs to inputs.

A LabVIEW program consists of subroutines which are called virtual instruments

(VI). Each VI has a front panel and a block diagram. The front panel is a graphical user

interface with a combination of controls and indicators. Controls allow user to supply

inputs to the VI and indicators display the results. The block diagram contains the source

code. The objects in the front panel appear as terminals in the block diagram and the user

wires these terminals to predefined functions or other VIs. The user also adds structures

and functions to perform operations on controls and supply data to indicators.

3.2. User Interface Program

The interface program runs on the computer and communicates with the electronic

modules via the serial bus. The user interface of the program is shown in Figure 3.1.

1www.ni.com/labview28

Figu

re3.

1.V

iew

ofth

eus

erin

terf

ace.

29

The computer software can be explained in four parts. The first part seen in Figure

3.2 is designed to adjust the serial port parameters, termination character and the timeout.

Figure 3.2. User interface of adjusting serial port parameters, termination characterand the timeout.

The user interface in Figure 3.3 is designed to set the control parameters which

are the proportional gain constant, integral gain constant, and derivative gain constant for

pitch and yaw axes. Two reference inputs are added to set the desired angular position

values for pitch and yaw axes. Additionally, the quantized input voltage values and the

tracking error values are added for online observation.

In Figure 3.4, the size of the data packet coming from the TRMS is adjusted

and the bytes waiting in the buffer are observed online to see if there is an unexpected

congestion in the data traffic.

The graphic outputs are added, as shown in Figure 3.5, to observe the tracking

errors for pitch and yaw axes online. The errors are drawn continuously while the TRMS

is operating.

Controller algorithm is applied by combining Matlab scripts with available Lab-

VIEW modules like derivative block, integral block etc. The error and torque logs are

stored in user–defined plain text files. These files are used to draw graphs with Matlab for30

Figure 3.3. User interface of setting controller gains and desired angular position val-ues, and observing tracking errors and quantized input voltage values.

further analysis and reporting.

When the program is started, an initialization sequence is sent to the system hard-

ware. This lets the electronic modules send angular position and angular velocity data to

the computer. The software then calculates the controller inputs according to the control

algorithm and the desired angular position settings. The controller inputs are converted to

duty cycle values with 10 bits resolution and then sent to the motor driver circuits. The

control procedure is repeated until it is terminated by the user.

31

Figure 3.4. User interface of configuration of data bytes received from the TRMS.

Figure 3.5. Graphic view of pitch and yaw tracking errors.

32

CHAPTER 4

MATHEMATICAL MODELLING OF TRMS

In this chapter, development of a mathematical model of the TRMS is described.

The TRMS is designed as shown in Figure 1.6. The two rotors in the TRMS correspond

to the main and tail rotor of a real helicopter. The control of the TRMS is applied by

adjusting the angular velocities of these two rotors, whereas in a real helicopter, the angu-

lar velocities of the rotors vary slowly and the control is mainly applied by adjusting the

rotor blade angles. The angular velocity of the rotors are adjusted by changing the supply

voltage of the DC motors. Thus, the control inputs of the TRMS are the supply voltages

of the motors. The outputs of the TRMS are the vertical and horizontal angular positions

that are measured by the optical sensors located on it.

In the literature, a significant amount of research was devoted to derive a mathe-

matical dynamic model for the twin rotor systems. However, mostly due to the difficulties

in modelling aerodynamic effects, there is no commonly agreed dynamic model for these

systems.

The dynamic model developed by Rahideh and Shaheed (2007) is one of the

highly acknowledged models in the literature and is presented as

f θh + f1θv + f2 + f3 = τh (4.1)

Jθv + f1θh + f4 + f5 = τv (4.2)

where θv (t), θv (t), θv (t) ∈ R are the angular position, angular velocity and acceleration

of the beam in the vertical plane, respectively, θh (t), θh (t), θh (t) ∈ R are the angular po-

sition, angular velocity and acceleration of the beam in the horizontal plane, respectively.

J ∈ R is equal to the sum of the moment of inertia of the counter balance beam and

the free-free beam, f (θv), f1 (θv), f2(θv, θv

), f3

(θv, θv, θh

), f4

(θv, θh

), f5 (θv) ∈ R

are nonlinear functions, and τh (t), τv (t) ∈ R are the controller inputs for horizontal and

vertical planes, respectively.

In order to express the dynamic model in Equations 4.1 and 4.2 in a compact form,

the dynamic model can be combined as

Mθ +N = τ (4.3)

where θ (t) ∈ R2 represents the angular position vector, M (θ) ∈ R2×2 represents the33

inertia matrix, N(θ, θ)∈ R2 represents other dynamic effects such as coriolis and cen-

trifugal forces, and τ (t) ∈ R2 represents the control input vector. These terms are defined

as

θ ,

[θh

θv

]M ,

[f f1

f1 J

](4.4)

N ,

[f2 + f3

f4 + f5

]τ ,

[τh

τv

]. (4.5)

The nonlinear functions of the system model in Equations 4.1 and 4.2 are given below

Rahideh and Shaheed (2007), Rahideh et al. (2008)

J , J1 + J2 (4.6)

f , J1 cos2(θv) + J2 sin2(θv) + h2(m1 +m2) + J3 (4.7)

f1 , h[m1l1 sin(θv)−m2l2 cos(θv)] (4.8)

f2 , h[m1l1 cos(θv) +m2l2 cos(θv)]θ2v (4.9)

f3 , 2(J2 − J1) sin(θv) cos(θv)θvθh (4.10)

f4 , (J1 − J2) sin(θv) cos(θv)θ2h (4.11)

f5 , g[m1l1 cos(θv) +m2l2 sin(θv)] (4.12)

where J1 is the moment of inertia of the free-free beam, J2 is the moment of inertia

of the counter balance beam, J3 is the moment of inertia of the pivoted beam, g is the

gravitational acceleration, h is the length of the pivoted beam, m1 is the total mass of

the free-free beam, m2 is the total mass of the counter balance beam, l1 is the center of

gravity of the free-free beam, and l2 is the center of gravity of the counter balance beam.

The moment of inertia terms are expressed as

J1 ,(mt

3+mtr +mts

)l2t +

(mm

3+mmr +mms

)l2m

+mms

2r2ms +mtsr

2ts (4.13)

J2 ,mb

3l2b +mcbl

2cb (4.14)

J3 ,mh

3h2 (4.15)

where mt is the mass of the tail beam, mtr is the mass of the tail rotor, mts is the mass

of the tail shield, lt is the length of tail part of the free-free beam, mm is the mass of the

main beam, mmr is the mass of the main rotor, mms is the mass of the main shield, lm is

the length of main part of the free-free beam, rms is the radius of the main shield, rts is

the radius of the tail shield, mb is the mass of the counter balance beam, lb is the length of34

the counter-weight beam, mcb is the mass of the counter-weight, lcb is the length between

the counter-weight and the joint, and mh is the mass of the pivoted beam. In our system,

no weight was added as the counter-weight, and main and tail shields are not plugged to

the rotors, and weights due to these are chosen as zero in the calculation. The terms m1,

m2, l1 and l2 are expressed as

m1 , mt +mtr +mts +mm +mmr +mms (4.16)

m2 , mb +mcb (4.17)

l1 ,(mm/2 +mmr +mms)lm − (mt/2 +mtr +mts)lt

m1

(4.18)

l2 ,mblb/2 +mcblcb

m2

. (4.19)

The parameters of the developed TRMS are listed in Table 4.1.

Table 4.1. System parameters

Parameter Definition Valuemm Mass of main beam 0.200 kgmmr Mass of the main rotor 0.450 kgmms Mass of main shield 0 kgmt Mass of the tail beam 0.200 kgmtr Mass of the tail rotor 0.435 kgmts Mass of tail shield 0 kgmb Mass of counter balance beam 0.065 kgmcb Mass of counter balance beam 0 kglm Length of main beam 0.3275 mlt Length of tail beam 0.3275 mlb Length of counter-weight beam 0.306 mlcb Length between the counter-weight and the joint 0.306 mrms Radius of the main shield 0 mrts Radius of the tail shield 0 m

The calculated parameters for the presented model, in Equations 4.13, 4.14, 4.16,

4.17, 4.18 and 4.19 are given in Table 4.2.

35

Table 4.2. Calculated parameters

Parameter Definition Valuem1 Total mass of the free-free beam 1.2850 kgm2 Total mass of the counter-weight beam 0.0650 kgl1 Center of gravity of the free-free beam 0.0038 ml2 Center of gravity of the counter-weight beam 0.1530 mJ1 Moment of inertia of the free-free beam 0.1092 kg m2

J2 Moment of inertia of the counter balance beam 0.0020 kg m2

36

CHAPTER 5

CONTROL OF TRMS

In this chapter, the control algorithms applied to the TRMS will be explained. The

experiments were conducted based on the restriction that the TRMS dynamic model is

unknown, thus, the dynamic model of the TRMS presented in Chapter 4 was not used in

the controller design.

The performance of proportional (P), proportional–integral (PI), proportional–

derivative (PD) and proportional–integral-derivative (PID) control algorithms were an-

alyzed. The experimental results will be presented.

In all the experiments, the initial value of the angular positions was chosen as

θ(t0) = [0, 0]T where t0 is the initial time. The desired angular position was taken as

θd(t) = [30, 20]T in degrees. The controller gains were selected via a trial-error method.

Several experiments for each controller were conducted, however the ones that we ob-

tained the best performance in average maximum steady-state error (SSE) are presented.

5.1. Proportional (P) Control

In proportional control, the control input is produced as proportional to the error

value. In analog systems, the error signal is amplified to obtain the control input. In digital

systems, the error value is multiplied by a constant which is the proportional control gain.

The P controller is defined as

u(t) = KP e(t) (5.1)

where KP is the constant diagonal proportional gain matrix with appropriate dimension.

Proportional control increases the speed of response, but as a disadvantage it

causes larger transient overshoot. Thus, the gain constant KP should be adjusted to an

optimum value. Lower proportional gain results in a smaller control input and makes the

system less sensitive to disturbances. When the error is small, the control input can be

a very small value which results the system not to respond. Additionally, proportional

control may have steady-state error and may not be able to completely reject a constant

disturbance Astrom and Murray (2008).

37

To experimentally verify the performance of the proportional control, we applied

the control input in Equation 5.1 to the TRMS. Several experiments were conducted for

different control gains and the best results are presented. The best performance was ob-

tained when KP is chosen as

KP =

[20 0

0 2000

]. (5.2)

In Figure 5.1, angular position on pitch and yaw axes are given, respectively. Both axes

show the characteristics of proportional control. High overshoot is observed on both axes.

In Figure 5.2, the tracking error on pitch and yaw axes are given, respectively. The track-

ing error on pitch axis shows that the controller is less sensitive to the disturbances in the

TRMS. As an example of this, a peak is observed at the 47th second due to an external

disturbance most probably as a result of aerodynamic effects, and the proportional con-

troller can not handle it. The tracking error on yaw axis shows that the controller has

steady-state error and the controller can not handle it. In Figure 5.3, control input on

pitch and yaw axes are given, respectively. The torques are amplified form of the tracking

errors simply due to nature of the proportional control.

0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

70

Time(s)

Deg

ree

Angular Position on Pitch Axis

Position

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

Time(s)

Deg

ree

Angular Position on Yaw Axis

Position

Figure 5.1. [P control] angular position on pitch and yaw axes, respectively.

38

0 5 10 15 20 25 30 35 40 45 50−40

−30

−20

−10

0

10

20

30

Time(s)

Deg

ree

Pitch Error

Error

0 5 10 15 20 25 30 35 40 45 50−15

−10

−5

0

5

10

15

20

Time(s)

Deg

ree

Yaw Error

Error

Figure 5.2. [P control] tracking error on pitch and yaw axes, respectively.

5.2. Proportional - Integral (PI) Control

In proportional-integral control, the control input is produced by adding an integral

term to the proportional control. Integral term is evaluated by integration of the error and

multiplying the result with a constant integral gain. PI controller is defined as

u(t) = KP e(t) +

t∫0

KIe(σ)dσ (5.3)

where KP is the constant diagonal proportional gain matrix and KI is the constant diag-

onal integral gain matrix. The PI controller can alternatively be presented as

u(t) = KP

e(t) +1

Ti

t∫0

e(σ)dσ

(5.4)

where KP is the constant proportional gain and Ti is the integral time constant.

Integral term in PI control is the sum of instantaneous error from the initial time

to the current time. After adding the integral term, PI control is expected to eliminate

the steady-state error that P control could not eliminate. As the integral term consists of

the accumulated error values from the past, it accelerates the movement of the system

to the desired set point. On the other hand, it may cause larger overshoot. Although39

0 5 10 15 20 25 30 35 40 45 5015.3

15.4

15.5

15.6

15.7

15.8

15.9

Time(s)

Vol

tage

(V)

Pitch Control Input

Input

0 5 10 15 20 25 30 35 40 45 505

10

15

20

25

Time(s)

Vol

tage

(V)

Yaw Control Input

Input

Figure 5.3. [P control] control input on pitch and yaw axes, respectively.

the integrator accelerates the movement, it has a tendency to make the system slower

by reducing the response of the system. Additionally, integral feedback can give nonzero

control even if the error is zero because of memory, and it can be very oscillatory. Another

problem is integrator wind up. There are limitations in the actuators. It may happen that

the control variable reaches the actuator limits. If the actuator remains saturated, the

error will continue to be integrated and the integral term may become very large. After

that, the integral term will cause overshoot and continue to increase the error until this

accumulated error is unwound. It may take a long time before the integrator and the

controller input comes inside the saturation range. Considering these effects, the integral

gain constantKI should be adjusted according to the design requirements in order to have

an acceptable trade-off. With high KI , the system can have a zero steady-state error, but

with an unacceptable overshoot and slower response in the system.

To experimentally verify the performance of the PI control, we applied the control

input in Equation 5.3 to the TRMS where KP and KI are chosen as

KP =

[20 0

0 2000

], KI =

[0.5 0

0 20

]. (5.5)

In Figure 5.4, angular position on pitch and yaw axes are given, respectively. Both axes

show the characteristics of PI control. Higher overshoot is observed on both axes com-

pared to the P control. In Figure 5.5, tracking error on pitch and yaw axes are given,40

respectively. The tracking error on yaw axis clearly shows that the controller has ability

to remove the steady-state error (that the P control could not eliminate) and pitch axis

shows the tendency to reduce the steady-state error. Higher oscillation is observed on the

tracking error on pitch axis as a trade-off. In Figure 5.6, control input on pitch and yaw

axes are given, respectively. Although the tracking error on yaw axis goes to zero, the

control input on yaw axis goes to a constant value due to the memory of the integrator.

0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

70

80

Time(s)

Deg

ree

Angular Position on Pitch Axis

Position

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

Time(s)

Deg

ree

Angular Position on Yaw Axis

Position

Figure 5.4. [PI control] angular position on pitch and yaw axes, respectively.

5.3. Proportional - Derivative (PD) Control

In proportional-derivative control, the control input is produced by adding a deriva-

tive term to the proportional control. The derivative term is obtained by the slope of the

error over the time multiplied with a constant derivative gain. PD controller is defined as

u(t) = KP e(t) +KDde(t)

dt(5.6)

where KP is the constant diagonal proportional gain matrix and KD is the constant diag-

onal derivative gain matrix. The PD controller can alternatively be presented as

u(t) = KP

(e(t) + Td

de(t)

dt

)(5.7)

where KP is the constant proportional gain, and Td is the derivative time constant.

41

0 5 10 15 20 25 30 35 40 45 50−50

−40

−30

−20

−10

0

10

20

30

Time(s)

Deg

ree

Pitch Error

Error

0 5 10 15 20 25 30 35 40 45 50−20

−15

−10

−5

0

5

10

15

20

Time(s)

Deg

ree

Yaw Error

Error

Figure 5.5. [PI control] tracking error on pitch and yaw axes, respectively.

Derivative term is proportional to the rate of change on error and has a role to

speed up the system response. Derivative predicts the system behaviour from the slope

and improves the stability of the system. It usually reduces the settling time and improves

the response of the system to sudden changes. However, it may amplify the system noise

at high frequencies. If the error signal is noisy or if the closed-loop system has a slow loop

rate, the derivative response can make the system unstable. Additionally, it does nothing

to reduce constant error, since the derivative of the error will be zero if there is no change

on error.

To experimentally verify the performance of the PD control, we applied the control

input in Equation 5.6 to the TRMS where KP and KD are chosen as

KP =

[250 0

0 2000

], KD =

[4500 0

0 4500

]. (5.8)

In Figure 5.7, angular position on pitch and yaw axes are given, respectively. It is seen

that derivative term reduces the overshoot in both axes. It is also observed that derivative

term can handle the oscillation occured in P controller. In Figure 5.8, tracking error

on pitch and yaw axes are given, respectively. The steady-state error on yaw axis stays

the same as in P control, since the derivative of the error goes to zero for constant or

slowly varying error values. There is a considerable improvement on tracking error on

pitch axis as the response of the system to sudden changes was improved by the addition42

0 5 10 15 20 25 30 35 40 45 5015

15.2

15.4

15.6

15.8

16

Time(s)

Vol

tage

(V)

Pitch Control Input

Input

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

Time(s)

Vol

tage

(V)

Yaw Control Input

Input

Figure 5.6. [PI control] control input on pitch and yaw axes, respectively.

of the derivative term. In Figure 5.9, control input on pitch and yaw axes are given,

respectively. The sudden changes on the control inputs are observed due to the derivative

term. Additionally, since the yaw error becomes constant or slowly varying after some

time, the derivative term has a small effect in the control input and thus it practically

becomes a P controller and thus could not eliminate the steady-state error as seen in

Figure 5.8.

5.4. Proportional - Integral - Derivative (PID) Control

In proportional-integral-derivative control, the proportional term, the integral term,

and the derivative term are added together. PID controller is defined as

u(t) = KP e(t) +

t∫0

KIe(σ)dσ +KDde(t)

dt(5.9)

where KP is the constant diagonal proportional gain matrix, KI is the constant diagonal

integral gain matrix and KD is the constant diagonal derivative gain matrix. The PID

controller can alternatively be presented as

u(t) = KP

e(t) +1

Ti

t∫0

e(σ)dσ + Tdde(t)

dt

(5.10)

43

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

Time(s)

Deg

ree

Angular Position on Pitch Axis

Position

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

Time(s)

Deg

ree

Angular Position on Yaw Axis

Position

Figure 5.7. [PD control] angular position on pitch and yaw axes, respectively.

where KP is the constant proportional gain, Ti is the integral time constant and Td is the

derivative time constant.

PID control has control actions based on the past, the present and the future, which

are due to integral, proportional and derivative terms, respectively. Pure proportional

control will have a steady-state error. The steady-state error can be reduced with a higher

gain but this will result in increasing the oscillation. Adding an integral term helps to

eliminate the steady-state error but it will also increase the tendency for oscillation and

will slow down the response of the system. Thus, a damping effect is required and an

increase in system response is needed. This is provided by adding a derivative term.

All three terms are dependent each other. Their seperate effects on the system can be

summarized as in Table 5.1.

Table 5.1. Independent effects of the gains of PID control

Control effect Rise Time Overshoot Steady-State Error Settling TimeIncreasing KP Decrease Increase Decrease Minor effectIncreasing KI Decrease Increase Eliminate IncreaseIncreasing KD Minor effect Decrease No change Decrease

To experimentally verify the performance of the PID control, we applied the con-

44

0 5 10 15 20 25 30 35 40 45 50−5

0

5

10

15

20

25

30

Time(s)

Deg

ree

Pitch Error

Error

0 5 10 15 20 25 30 35 40 45 50−5

0

5

10

15

20

Time(s)

Deg

ree

Yaw Error

Error

Figure 5.8. [PD control] tracking error on pitch and yaw axes, respectively.

trol input in Equation 5.9 to the TRMS where KP , KI and KD are chosen as

KP =

[450 0

0 2000

], KI =

[20 0

0 60

], KD =

[6000 0

0 4500

]. (5.11)

In Figure 5.10, angular position on pitch and yaw axes are given, respectively. As ex-

pected, PID control gives the best tracking performance. In Figure 5.11, tracking error

on pitch and yaw axes are given, respectively. In this experiment, integral gain is chosen

high enough in order to improve the settling time and to reduce the steady-state error. As

a trade-off, higher overshoot is observed when compared with the PD controller. Since

the PID controller is flexible, the characteristics of the system may be adjusted to achieve

different design requirements as well. In Figure 5.12, control input on pitch and yaw axes

are given, respectively.

5.5. Analysis of the Experimental Results

In the analysis of the experiments, average maximum steady-state errors are cal-

culated Dupree et al. (2011). It is defined as the last 15 seconds of the errors in the

experiments where the total duration was 50 seconds. Average root-mean-square (RMS)

errors and standard deviation (SD) of the errors are calculated. Average RMS control in-45

0 5 10 15 20 25 30 35 40 45 5010

15

20

25

Time(s)

Vol

tage

(V)

Pitch Control Input

Input

0 5 10 15 20 25 30 35 40 45 5010

15

20

25

Time(s)

Vol

tage

(V)

Yaw Control Input

Input

Figure 5.9. [PD control] control input on pitch and yaw axes, respectively.

puts and standard deviation of control inputs are also calculated. The results are shown in

Tables 5.2 and 5.3. The best average maximum SSE are obtained with the PID controller,

as expected. Considering average RMS errors, the worst controller is PI controller due to

higher overshoot. The controllers that contain derivative, which are PD and PID, reduce

overshoot significantly on pitch axis. This results in a lower SD of errors with PD and

PID controller on pitch axis. SD of errors is higher in PI controller due to the oscillatory

characteristic of integral controller.

Table 5.2. Analysis of the errors for different controllers

P control PI control PD control PID controlAvg. Max SSE Pitch 10.2540 7.4826 1.5455 1.0196Avg. Max SSE Yaw 1.9143 0.338 1.4895 0.1856Avg. RMS Error Pitch 14.6281 15.3851 5.1686 5.9592Avg. RMS Error Yaw 3.4801 3.6254 3.0696 3.5022Error SD Pitch 11.5225 15.2474 5.137 6.0039Error SD Yaw 2.9079 3.6482 2.8176 3.4294

46

0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

Time(s)

Deg

ree

Angular Position on Pitch Axis

Position

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

Time(s)

Deg

ree

Angular Position on Yaw Axis

Position

Figure 5.10. [PID control] angular position on pitch and yaw axes, respectively.

0 5 10 15 20 25 30 35 40 45 50−30

−20

−10

0

10

20

30

40

Time(s)

Deg

ree

Pitch Error

Error

0 5 10 15 20 25 30 35 40 45 50−15

−10

−5

0

5

10

15

20

Time(s)

Deg

ree

Yaw Error

Error

Figure 5.11. [PID control] tracking error on pitch and yaw axes, respectively.

47

0 5 10 15 20 25 30 35 40 45 505

10

15

20

25

Time(s)

Vol

tage

(V)

Pitch Control Input

Input

0 5 10 15 20 25 30 35 40 45 505

10

15

20

25

Time(s)

Vol

tage

(V)

Yaw Control Input

Input

Figure 5.12. [PID control] control input on pitch and yaw axes, respectively.

Table 5.3. Analysis of the control inputs for different controllers

P control PI control PD control PID controlAvg. RMS Control Input Pitch 15.5442 15.3420 15.5367 15.3090Avg. RMS Control Input Yaw 14.0465 13.1041 14.4498 14.7675Control Input SD Pitch 0.0975 0.1654 0.7223 1.5703Control Input SD Yaw 1.7641 2.3914 1.3296 1.8638

48

CHAPTER 6

CONCLUSION

In this thesis, design, development and control of a TRMS were studied. The

design and development can be categorized as

• mechanical system design

• electronic system design

• user interface.

In the mechanical system design, the mechanical components were explained and

the CAD model was shared. In the electronic system design, hardware parts of the TRMS,

mainboard, encoder reader circuits, and motor controller circuits, and the embedded al-

gorithms were presented.

A computer software was developed on LabVIEW Development Environment in

order to monitor the TRMS and to communicate with it online. The computer software

provided the ability to try different control algorithms easily by modifying Matlab script

blocks on LabVIEW.

Nextly, a mathematical model for the TRMS was derived. The Lagrangian-based

general dynamic model in Rahideh and Shaheed (2007) was explained to present the

methodology of developing the dynamic model of a TRMS. The mechanical differences

between the TRMS in Rahideh and Shaheed (2007) and the one we developed were high-

lighted. The parameters of our TRMS were given. It is noted that the dynamic model

of the TRMS was derived for the sake of completeness and was not utilized for control

design purposes.

Finally, P, PI, PD and PID control algorithms were applied and their performances

were observed on the developed TRMS. Several experiments for each controller were

conducted, and the ones that we obtained the best performance in average maximum SSE

were presented. The analysis of the experiments were shared. The experiment results

were compared in :

• Average Maximum SSE

• Average RMS Error

49

• Error SD

• Average RMS Control Input

• Control Input SD.

Review of relevant literature highlighted the fact there is not much past studies

on development of a TRMS in an academic setting. The only past work, according to

our best knowledge, is Verzilli (2007). There were no relevant past work conducted in

Turkish universities. Thus this thesis is one of the few works that focused on design and

development of a TRMS.

There is much to be considered as future work. During the design and develop-

ment phases, the electronic subsystems (i.e. feedback, driver and sensor circuits) of a

control laboratory setup were investigated closely. This knowledge can later be utilized in

design and development of different laboratory setups such as 3 or 4 DOF rotor systems

or inverted pendulum. Removing the computer from the loop and performing control al-

gorithms on the mainboard processor may also be considered as a future work. In this

case, we will not deal with operating system related issues. In this thesis, standard linear

controllers were applied without conducting any stability analysis. Thus possible future

research may focus on investigating the stability of both open-loop and closed-loop sys-

tem. Furthermore, effects of known disturbances on the system may be analyzed. Other

future research may focus on designing nonlinear controllers for TRMSs. Comparing the

performances of the controllers applied on the TRMS and on a laboratory helicopter could

be an interesting future research as well.

50

51

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