DESIGN OF CONTROL SYSTEMS FOR A QUADROTOR FLIGHT VEHICLE EQUIPPED WITH INERTIAL SENSORS A MASTER���S THESIS in Mechatronics Engineering At��l��m University by ARDA ��ZG��R KIVRAK DECEMBER 2006

ii DESIGN OF CONTROL SYSTEMS FOR A QUADROTOR FLIGHT VEHICLE EQUIPPED WITH INERTIAL SENSORS A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF ATILIM UNIVERSITY BY ARDA ��ZG��R KIVRAK IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN THE DEPARTMENT OF MECHATRONICS ENGINEERING DECEMBER 2006

iii Approval of the Graduate School of (Name of the Graduate School) _____________________ (Title and Name) Director I certify that this thesis satisfies all the requirements as a thesis for the degree of Master of Science/Arts. _____________________ (Title and Name) Head of Department This is to certify that we have read this thesis and that in our opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Science/Arts. _____________________ _____________________ (Title and Name) (Title and Name) Co-Supervisor Supervisor Examining Committee Members Asst.Prof.Dr.B��lent ��RFANO��LU _____________________ Prof.Dr.Abd��lkadir ERDEN _____________________ Asst.Prof.Dr.Hakan TORA _____________________ Asst.Prof.Dr.Serhat ERPOLAT _____________________ Instr. Kutluk Bilge ARIKAN _____________________

iv ABSTRACT DESIGN OF CONTROL SYSTEMS FOR A QUADROTOR FLIGHT VEHICLE EQUIPPED WITH INERTIAL SENSORS K��vrak, Arda ��zg��r M.S. Mechatronics Engineering Department Supervisor: Kutluk Bilge Ar��kan December 2006 104 pages This thesis reviews the Design of Control Systems for a Quadrotor Flight Vehicle Equipped with Inertial Sensors in detail. The control system is developed in Matlab/Simulink and real time implementation is achieved by using Simulink Real Time Windows Target utility. Linear Quadratic Regulator is designed for the stabilization of the attitude and shown to work in real time. The hardware consists of the data acquisition card, DC motor drivers, sensor set, the DC motors, and the DraganFlyer V Ti structure. Keywords: Control, Quadrotor platform, Inertial Sensors, Matlab/Simulink, Real Time Windows Target (RTWT), Real Time Control, Linear Quadratic regulator.

v ��Z ATALETSEL ALGILAYICILARA SAH��P D��RT MOTORLU U��U�� ARACI ������N DENET��M S��STEMLER�� TASARIMI K��vrak, Arda ��zg��r Y��ksek Lisans, Mekatronik M��hendisli��i B��l��m�� Tez Y��neticisi: Kutluk Bilge Ar��kan Aral��k 2006, 104 sayfa Bu cal����ma, d��rt motorlu u��u�� arac��n��n denetim sistemlerini incelemekte ve detay�� ile vermektedir. Denetim sistemi Matlab/Simulink ortam��nda geli��tirilmi�� ve Simulink Real Time Windows Target kullan��larak ger��ek zamanl�� uygulamas�� yap��lm����t��r. Sistemin y��nelim kararl��l������n��n denetimi i��in Lineer Quadratik Reg��lat��r tasarlanm���� ve donan��ml�� sistemle ger��ek zamanl�� ��al����t��r��lmas�� g��sterilmi��tir. Donan��m veri toplama kart��, do��ru ak��m motor s��r��c�� devresi, alg��lay��c�� seti, do��ru ak��m motorlar�� ve DraganFlyer V Ti g��vdesinden olu��maktad��r. Anahtar Kelimeler: Denetim, D��rt motorlu platform, Matlab/Simulink, Real Time Windows Target (RTWT), Ger��ek zamanl�� denetim, Lineer Quadratik Reg��lat��r.

vi To My Parents

vii ACKNOWLEDGMENTS I express sincere appreciation to my supervisor Kutluk Bilge Ar��kan and B��lent Irfano��lu for their guidance and insight throughout the research. And to my family, I offer sincere thanks for their continuous support and patience during this period.

viii TABLE OF CONTENTS ABSTRACT...............................................................................................................IV ��Z ............................................................................................................................... V TABLE OF CONTENTS........................................................................................ VIII LIST OF TABLES...................................................................................................... X LIST OF FIGURES ...................................................................................................XI CHAPTER 1.INTRODUCTION............................................................................................... 1 1.1 Aim and Scope........................................................................................ 2 1.2 Layout of the Dissertation....................................................................... 3 2. LITERATURE SURVEY ABOUT QUAD-ROTOR SYSTEMS..................... 4 2.1 Designs in Literature............................................................................... 4 2.1.1 European Aeronautic Defense and Space Company.................... 5 2.1.2 Pennsylvania State University...................................................... 5 2.1.3 Middle East Technical University................................................ 7 2.1.4 Australian National University..................................................... 7 2.1.5 University of British Columbia Vancouver, BC, Canada ............ 8 2.1.6 Cornell University ...................................................................... 10 2.1.7 Swiss Federal Institute of Technology ....................................... 10 2.1.8 University of Technology in Compiegne, France ...................... 12 2.1.9 Stanford University .................................................................... 13 2.1.10 Australian National University, Canberra, Australia ............... 14 2.2 Applied Control Systems ...................................................................... 15 2.3 Employed Sensors................................................................................. 16 3. MATHEMATICAL MODEL OF THE HOVERING PLATFORM............... 17 3.1 Assumptions of the Model .................................................................... 17 3.2 Derivation of the State Equations ......................................................... 18 3.3 Motor-Propeller Models........................................................................ 22 3.4 Linearization of the Nonlinear State Equations .................................... 27 4. LQR DESIGN FOR ATTITUDE STABILIZATION ..................................... 30 4.1 Linear Quadratic Regulator................................................................... 30

ix 5. STRUCTURE AND TEST BENCH................................................................ 34 5.1 The Frame of the Quadrotor.................................................................. 34 5.2 Sensors Used in the System .................................................................. 34 5.2.1 Accelerometer............................................................................. 36 5.2.2 Gyroscopes ................................................................................. 38 5.2.3 Magnetometer............................................................................. 39 5.3 Drivers................................................................................................... 41 5.4 Proposed Driver Circuitry..................................................................... 43 5.5 Power Supplies...................................................................................... 48 5.6 Driver Test Results................................................................................ 49 5.7 Test Bench............................................................................................. 51 6. REAL TIME CONTROL IMPLEMENTATION............................................ 54 6.1 The Control Software............................................................................ 54 7. TESTS AND RESULTS.................................................................................. 61 7.1 Eliminating Sensor Noise...................................................................... 61 8. DISCUSSIONS AND CONCLUSIONS ......................................................... 68 REFERENCES........................................................................................................... 70 APPENDICES 1.CONTROLLABILITY AND OBSERVABILTY MATRIX ........................... 74 2.MOTOR DATASHEET.................................................................................... 76 3.SENSOR DATASHEETS................................................................................. 78

x LIST OF TABLES TABLE Table 1 Inertial Parameters ........................................................................................ 26 Table 2 Available Sensors.......................................................................................... 35 Table 3 Calibration constants (at room temperature ~200)........................................ 57 Table 4 Mabuchi motor specs. ................................................................................... 76 Table 5 IRFZ44N specs. ............................................................................................ 77

xi LIST OF FIGURES FIGURES Figure 1 Mesicopter ..................................................................................................... 4 Figure 2 DraganFlyer................................................................................................... 4 Figure 3 Quattrocopter................................................................................................. 5 Figure 4 Quadrotor designed in Pennsylvania State University .................................. 6 Figure 5 Quadrotor tracking with a camera ................................................................. 6 Figure 6 Quadrotor designed in Middle East Technical University, Turkey............... 7 Figure 7 The X4-Flyer developed in FEIT, ANU........................................................ 8 Figure 8 Setup developed in Department of Electrical and Computer Engineering University of British Columbia Vancouver, BC, Canada.................................... 9 Figure 9 Quadrotor designed in Cornell University................................................... 10 Figure 10 Quadrotor designed in Swiss Federal Institude of Technology................. 11 Figure 11 Quadrotor designed in University of Technology in Compiegne, France. 12 Figure 12 Quadrotor designed in Stanford University............................................... 14 Figure 13 X-4 Flyer Mark II. ..................................................................................... 15 Figure 14 All of the States (b stands for body and e stands for earth)....................... 17 Figure 15 Motor test setup for thrust calculation....................................................... 23 Figure 16 Test results of the 1st Motor (voltage vs. thrust(T))................................... 23 Figure 17 Test results of the 2nd motor (voltage vs. thrust(T)) .................................. 24 Figure 18 Test results of the 3rd motor (voltage vs. thrust(T))................................... 24 Figure 19 Test results of the 4th motor (voltage vs. thrust(T))................................... 24 Figure 20 The LQR system for nonlinear and linear state-space models ................. 32 Figure 21 Comparison of the nonlinear and state space models for a 0.1 rad disturbance in yaw angle (continuous line represents the State space model and dashed line represents nonlinear model)............................................................ 33 Figure 22 (a) Accelerometer (Analog devices) (b) Magnetometer (Honeywell) (c) Accelerometer (Memsic) (d) Gyroscope (Murata) (e) Compass Module (Parallax) (f) Gyroscope (Silicon sensing) (g) Gyroscope (Silicon Sensing).... 35 Figure 23 Accelerometer (ruler is in centimeters) ..................................................... 37 Figure 24 ADXL203EB accelerometer evaluation board.......................................... 37 Figure 25 A picture of the gyroscope evaluation board ADXRS150EB ................... 39

xii Figure 26 Magnetometer at the lower left corner and three gyros at the back of it (magnetometer shown with an arrow) ............................................................... 40 Figure 27 Circuit diagram of the gyro hardware........................................................ 40 Figure 28 IRFZ44N n-channel Mosfet transistor schematic for motor drivers ......... 41 Figure 29 Mosfet IRLZ44N driven in switching mode [34]...................................... 41 Figure 30 ASTRO 204D speed controller.................................................................. 43 Figure 31 Driver system block diagram..................................................................... 44 Figure 32 Terminal board........................................................................................... 44 Figure 33 The Block diagram for the data acquisition card terminal board .............. 45 Figure 34 A view of the hardware system ................................................................. 45 Figure 35 Voltage to 5 V PWM converter................................................................. 46 Figure 36 Mosfet gate driving optocouplers (TLP250) ............................................. 46 Figure 37 Electronic Hardware.................................................................................. 47 Figure 38 By-pass capacitor for high reverse inductive voltages .............................. 48 Figure 39 Agilient 15 A / 35 V Power supply ........................................................... 48 Figure 40 Power supply for the sensor set ................................................................. 49 Figure 41 emergency button....................................................................................... 49 Figure 42 PWM driven Mabuchi motor���s RMS voltage............................................ 50 Figure 43 Assembled Quadrotor................................................................................ 51 Figure 44 Cable connection ....................................................................................... 52 Figure 45 Side sways ................................................................................................. 52 Figure 46 The kneecap or spherical joint................................................................... 52 Figure 47 Experimental setup .................................................................................... 53 Figure 48 The hole at the centre of PCB................................................................... 53 Figure 49 Simulink blocks for one motor .................................................................. 55 Figure 50 A Sample Gyro Block................................................................................ 56 Figure 51 A sample accelerometer block................................................................... 57 Figure 52 A sample magnetometer block .................................................................. 57 Figure 53 The Control Blocks in Simulink................................................................ 59 Figure 54 Hardware in the Loop System ................................................................... 60 Figure 55 Unfiltered sensor output for roll angle....................................................... 61 Figure 56 Filtered Roll angle measurement with a 8th order Butterworth lowpass filter with 10 Hz bandwidth ............................................................................... 62 Figure 57 Unfiltered sensor output for pitch angle.................................................... 62

xiii Figure 58 Filtered pitch angle with a 8th order Butterworth lowpass filter with 10 Hz bandwidth........................................................................................................... 63 Figure 59 yaw rate unfiltered (only factory-set filter on the sensor) sensor output... 63 Figure 60 pitch rate unfiltered (only factory-set filter on the sensor) sensor output.. 64 Figure 61 roll rate unfiltered (only factory-set filter on the sensor) sensor output.... 64 Figure 62 Three spikes in the accelerometer signal (one at the top and two at the bottom)............................................................................................................... 65 Figure 63 LQR control of pitch rate with a disturbance ............................................ 66 Figure 64 LQR control of roll rate with a disturbance............................................... 67 Figure 65 LQR control of yaw rate with a disturbance.............................................. 67

xiv LIST OF ABBREVIATIONS UAV ��� Unmanned Aerial Vehicle MEMS ��� Micro Electromechanical Systems INS ��� Inertial Navigation System LQR ��� Linear Quadratic Regulator EKF ��� Extended Kalman Filter VTOL ��� Vertical Take Off and Landing GPS ��� Global Positioning System PHB ��� Popov, Hautus and Belevitch PWM ��� Pulse Width Modulation EADS ��� European Aeronautic Defense and Space Company FEIT ��� Faculty of Engineering and Information Technology ANU ��� Australian National University STARMAC ��� Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control A.M. ��� Amplitude Modulation

xv LIST OF SYMBOLS p ��� pitch angular rate q ��� roll angular rate r ��� yaw angular rate �� ��� pitch angle �� ��� roll angle �� ��� yaw angle x ��� position along x axis y ��� position along y axis z ��� position along z axis u ��� linear speed along body x axis v ��� linear speed along body y axis w ��� linear speed along body z axis Ix ��� The inertia around the x axis Iy ��� The inertia around the y axis Iz ��� The inertia around the z axis