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68 BIBLIOGRAPHY

T. Fossen. Handbook of Marine Craft Hydrodynamics and Motion Control.John Wiley & Sons, 2011b. ISBN 9781119991496.

A. J. Healey and D. Lienard. Multivariable Sliding-Mode Control forAutonomous Diving and Steering of Unmanned Underwater Vehicles.1993.

How Stuff Works. A Brief History of UAVs , 2012. URL http://science.howstuffworks.com/reaper1.htm.

IEEE Global History Network. Biography of Elmer A. Sperry, 2012. URLhttp://www.ieeeghn.org/wiki/index.php/Elmer_A._Sperry.

I. H. Johansen. UAV Autopilot Design for Recce D6. 2011.

L. J. N. Jones, C. P. Tan, Z. Man, and R. Akmeliawati. PreliminaryDesign of Sliding Mode Controller for Angualr Positional Tracking ofan Aircraft. 2009.

H. Khalil. Nonlinear systems. Prentice Hall, 2002. ISBN 9780130673893.URL http://books.google.no/books?id=t_d1QgAACAAJ.

A. L. Salih, M. Moghavvemi, H. A. F. Mohamed, and K. S. Gaeid. FlightPID controller design for a UAV quadrotor. 2010.

R. Skjetne, T. I. Fossen, and P. V. Kokotovic. Robust output maneuveringfor a class of nonlinear systems. 2003.

The Free Dictionary. The Free Dictionary - UAV, 2012. URL http://www.thefreedictionary.com/unmanned+aerial+vehicle.

Unmanned Aerial Vehicle System Association. Unmanned aerial vehiclesystem association - advantages, 2012a. URL http://www.uavs.org/advantages.

Unmanned Aerial Vehicle System Association. Unmanned aerial vehiclesystem association - uav or uas, 2012b. URLhttp://www.uavs.org/advantages.

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BIBLIOGRAPHY 69

V. Utkin. Sliding Modes in Control and Optimization. Com-munications and Control Engineering Series. Springer-Verlag, 1992.

ISBN 9783540535164. URL http://books.google.no/books?id=uzNmQgAACAAJ.

R. Walpole.Probability and statistics for engineers and scientists. PrenticeHall, 2002. ISBN 9780130415295. URL http://books.google.no/books?id=CgNEAQAAIAAJ.

Wikipedia - PID. Pid controller wikipedia, the free encyclope-dia, 2012. URLhttp://en.wikipedia.org/w/index.php?title=PID_controller&oldid=490210451. [Online; accessed 3-May-2012].

X-Plane 9. X-plane 9 flight simulator, 2012. URL http://www.x-plane.com/desktop/landing/.

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Appendix A

Definitions and Lemmas

North-East-Down (NED) coordinate frame, Fossen[2011b]

Definition 1. NED, North-East-Down (NED) , reference frame {n} =(xn, yn, zn) has its origin in on and is defined relative to the Earthsreference ellipsoid. Usually it is defined as the tangent plane on the surfaceof the Earth moving with the craft and with the x-axis pointing North, y-axis pointing East and the z-axis pointing down to the center of Earth,vertical position.

Controllability, Chen[1999]

Definition 2. The state equationx=Ax+Buor the pair (A,B) is saidto becontrollable if for any initial statex(0) = x0 and any final statex1,there exist an input that transfersx0 to x1 in a finite time. Otherwise thestate equation or (A,B) is said to beuncontrollable.

Barbalats lemma, Khalil [2002]

Lemma 1. Let: R R be a uniformly continuous function on [0,).Suppose that limt

t

0()dexists and is finite. Then,

(t) 0 as t

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Appendix B

Attachment Description and

Matlab Code

B.1 Attachment Description

Attached to this thesis is a folder namedMatlab, where all the Matlab codeand Simulink models are included, and a folder named X-plane plugin,where the plugin for simulation with X-Plane is included. Some of the

Matlab code can be found in AppendixB.2. To set up your computer forX-Plane simulation, follow the small guide in Appendix C.

The code is structured as in Figure B.1and organized as:

.m-files

SimGNCSystem.m - The main run file, simulates the different casestudies.

initGNC.m - Initializes the aircraft and the GNC system.

x plane interface.m - Initializes the X-Plane communication block.

systemIdentification.m - System identification for finding a model touse in sliding mode control.

ordlsq.m - Ordinary least square system identification function.

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74APPENDIX B. ATTACHMENT DESCRIPTION AND MATLAB CODE

SM delta e.m - Sliding mode for pitch and altitude.

plots.m - Plots the simulated case.

.mat-files

measuredSignals.mat - Storage of data for use in system identifica-tion, measured from X-Plane.

delta.mat - Storage of data for use in system identification, aileron,elevator, rudder and thrust measurements.

.mdl-files

GNCSystem PID.mdl - The whole GNC system and X-Plane inter-face with PID control.

GNCSystem PID SI.mdl - The whole GNC system and X-Plane in-terface with PID control and system identification measurements.

GNCSystem SM.mdl - The whole GNC system and X-Plane inter-face with sliding mode control.

Figure B.1: Code Structure

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B.2. MATLAB CODE 75

B.2 Matlab Code

B.2.1 Simulation of GNC System

1 %% Simulation of simulink model GNCSystem XXX.mdl

2 %

3 %

4 %

5 % Author: Ingrid Hagen Johansen

6 % Master Thesis Spring 2012

7 % Date: 26.05.2012

8 %

9 % Thanks to: Thor I. Fossen10 %

11 %

12

13 clc;

14 clear all;

15 close all;

16

17

18 %% Initialize

19 % Set waypoints [North East Altitude]

20

% The Waypoints are selected for take21 % at Vaernes (ENVA), Norway.

22 %

23 Way points = [0 0 0;

24 0 8000 500;

25 10000 8000 500;

26 10000 32000 500];

27

28

29 % Without payload

30 payload = 0; % [kg]

31

32 % With payload

33 % payload = 378; % [kg]

34

35 % Speed

36 takeoff speed = 80; %[kt]

37 cruise speed = 48; %[kt]

38

39 % If wind, +30 kt

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40 cruise speed = cruise speed + 30; %[kt]

41

42 % System Identification

43 systemIdentification44 poler = [0.00006 0.00003];

45

46 % Initialize

47

48 initGNC

49

50

51 %% Simulation

52

53 % Simulation with PID control

54 sim('GNCSystem PID')55 %

56 % Simulation with Sliding Mode Control

57 % for pitch and altitude

58 % sim('GNCSystem SM pitch')

59

60 %% Plot

61

62 plots

B.2.2 Initialize GNC System

1 %% Info

2 %

3 % Initialization file for the Guidance,

4 % Navigation and Control System (GNC)

5 %

6 %

7 % Aircraft used in simulation is the Cessna 172SP

8 % Length: 27 ft 2 in (8.28 m)

9 % Height: 8 ft 11 in (2.72 m)

10 % Wingspan: 36 ft 1 in (11.00 m)

11 % Wing area: 174 sq ft (16.20 m2)

12 % Weight: 1,717 lb (779 kg)

13 %

14 % Max Takeoff Weight: 2,550 lb (1 157 kg)

15 % Max Payload Weight: 833 lb (378 kg)

16 %

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B.2. MATLAB CODE 77

17 %

18 % Author: Ingrid Hagen Johansen

19 % Master Thesis Spring 2012

20 % Date: 26.05.201221 %

22 % Thanks to: Thor I. Fossen

23 %

24 %

25 %% Initialize simulation

26 %

27 %

28

29 % Initialize simulation variables

30

31 sim start = 0.0;32 sim stop = 400;

33

34 % Real time setings

35 realtime.scalingfactor = 0.05;

36

37

38 % Physics

39

40 % Payload

41 init payload = [payload 0 0 0 0 0;

42 0 payload 0 0 0 0;

43 0 0 payload 0 0 0;

44 0 0 0 0 0 0;

45 0 0 0 0 0 0;

46 0 0 0 0 0 0];

47

48 physics.g = 9.81;

49 mass = [743.44 0 0 0 0 0;

50 0 743.44 0 0 0 996.21;

51 0 0 743.44 0 996.21 0;

52 0 0 0 2008.76 0 0;

53 0 0 996.21 0 3827.04 0;

54 0

996.21 0 0 0 5408.32]+ init payload;55

56

57

58 %% Xplane Interface

59

60 x plane interface

61

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62

63

64 %% Reference Model

65

66 % Commanded Speed [kt]

67 reference.commandedSpeed.time = [0 150 150 sim stop];

68 reference.commandedSpeed.signals.values = [takeoff speed;

69 takeoff speed;

70 cruise speed;

71 cruise speed];

72 reference.commandedSpeed.signals.dimension = 1;

73

74

75 % Commanded Altitude

76 reference.commandedHeight.time = [0 10 10 sim stop];77 reference.commandedHeight.signals.values=[Way points(1,3);

78 Way points(1,3);

79 Way points(2,3);

80 Way points(2,3)];

81 reference.commandedHeight.signals.dimension = 1;

82

83 reference.lp.height.omega = 0.05;

84

85

86 %% Guidance

87

88

89 % Kp Kinematic Control Altitude

90 guidance.altitude.Kp = 1;

91

92 % LOS Guidance

93 % Calculate waypoint matrix for NorthEast

94

95 for i = 1:length(Way points)

96 for j = 1 : 1

97 guidance.waypoints(i,j) = Way points(i,j);

98 guidance.waypoints(i,j+1) = Way points(i,j+1);

99 end100 end

101

102 % Kp = 1 / Lookahead Distance

103 guidance.los.Kp = 1/600;

104

105 % Natural Frequency Altitude LP

106 guidance.alt.lp.omega = 0.05;

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