**CHAPTER 1 ***Data Analysis and System Integration **11*

**CHAPTER 2 ***The Digital Atomic Age ***15**

2-1: Math led the technical world into the Digital with Linear Algebra. 17

2-2: The Place of Equations in the Digital Revolution. 17

2-3: Most Physical Phenomenon is Analog, Requiring Conversion to Digital. 18

2-4: The Math of Motion is a Good Starting Place for the Technical. 18

2-5: Digital and Digital Computers to Technical Applications of Computers. 18

2-6: “Digital Signal Processing”. 19

2-7: (D1) MATLAB, Path, and Workspace. 21

2-8: (D2) Plotting, Subplots, Axis and Labels. 24

2-9: (D3) Polynomial Algebra and Polynomial Roots. 24

2-10: (D4) Graphics and Descriptive Stats. 24

**CHAPTER 3 ***Systems Integration of Aerodynamics and Control. ***29**

3-1: Steady State Flight with Principles of Stability and Control. 30

3-2: Background for Cl, Cd, and Cm. 33

3-3: Trim equilibrium as far as pitch when all moments at the C.G. are zero. 34

3-4: Coefficients from Flight Test versus Mach and Altitude. 35

3-5: From Aerodynamic Coefficients to Aerodynamic Derivatives. 35

3-6: Plot of Moment Coefficient Curve with a Negative Slope. 37

3-7: Aerodynamic Derivatives Simply Mean the Use of Partial DEs. 38

3-8: Data Analysis Example #1: Elevator Deflection versus Pilot Force. 39

3-9: Energy, Momentum, and Moments of an Aircraft. 39

3-10: Classical Modes of Aircraft Flight Test. 39

**CHAPTER 4 ***F-16 Simulation with FORTRAN and MATLAB ***41**

4-1: Stability Analysis of This Flight Control System. 42

4-2: The Actuator. 43

4-3: Dynamic Characteristics of the Aircraft. 44

4-4: All Programs/Simulations Work and Economically. 46

4-5: Simulations at NASA. 46

4-6: Simulator Study of F-16 Stall Characteristics. 46

4-7: (D1) Arrays, Matrices, Vectors, and Data Types. 53

4-8: (D2) Some Basic Built In Data Analysis Functions in MATLAB. 53

4-9: (D3) Files, Functions, and Data Structure. 53

4-10: (D4) Histograms and Cumulative Curves. 53

**CHAPTER 5 ***UAV’s and Other Flight Test Reports ***57**

5-1: The Altair/Predator B. 58

5-2: Recent UAV Flight Test Experience at NASA, 1998. 59

5-3: Flight Tests of the X-48B UAV between 2007 and 2008. 60

5-4: AFTI/F-16 Flight Test Results and Lessons Learned. 62

5-5: Ups and Downs of UAV Testing by John Del Frate of NASA. 65

5-6: Aircraft Parameter Estimation. 66

5-7: Predicted and Flight Derived Stability and Control Derivatives. 70

5-8: Stability and Control Derivatives from Space. 70

5-9: Measurement of the Damping Roll. 71

5-10: Study of Longitudinal Dynamic Stability in Flight. 71

5-11: Estimation Accuracy of Flight Determined Coefficients. 71

5-12: Aircraft State and Parameter Identification. 71

5-13: Dynamic Stability and Control Flight Research. 71

5-14: Stability and Control Derivatives and Dynamic Characteristics. 71

5-15: FORTRAN Program for Aircraft Stability and Control Derivatives. 71

5-16: New Method for Dynamic Stability and Control. 71

5-17: Methods of Aircraft State and Parameter Identification. 71

5-18: (D1) 2-D and 3-D Plots, Mesh, Color, and Shading. 71

5-19: (D2) Flow control. 71

5-20: (D3) Plotting Complex Numbers and Function Plot. 71 3-21: (D4) Normal Distribution. 72

**CHAPTER 6 ***The Process ***73**

4-1: The 10 step Process of this book. 73

4-2: The 10 step Process of Aerospace. 75

4-3: The Process of Learning: ILS. 75

4-4: Historical PROCESS of The Digital Atomic Age. 76

4-5: Math led the technical world into the Digital with Linear Algebra. 78

4-6: The Place of Mathematical Equations in the Digital Revolution. 78

4-7: Most Physical Phenomenon is Analog, Requiring Conversion to Digital. 79

4-8: The Math of Motion is a Good Starting Place for the Technical. 79

4-9: Digital and Digital Computers & Applications of Computers. 79

4-10: Digital Signal Processing. 80

4-11: Evolution in Math Techniques for Engineering Applications. 82

4-12: Software, Firmware, and Digital Math. 82

4-13: Linear Continuous Systems with Simulink Modeling. 83

4-14: (D1) Files/Directories, Handling Data, & External Programs. 84

4-15: (D2) Fourier Transform. 84

4-16: (D3) Plotting Polynomials with “polyval”. 84

4-17: (D4) Matrices of Data and Plotting. 84

**CHAPTER 7 ***Basic and Technical Applications of MATLAB ***85**

5-1: MATLAB for a “Gravity” function. 85

5-2: MATLAB uses a lot of built in functions like “mean”. 86

5-3: MATLAB Built-in Functions are in C:\MATLAB\toolbox\matlab\.. 87

5-4: The Quadratic Equation function script with MATLAB. 89

5-5: (D1) Programming in MATLAB. 90

5-6: (D2) Strings and “feval”. 90

5-7: (D3) Data Markers and Line Types. 90

5-8: (D4) Linear Regression and Curve Fitting. 90

**CHAPTER 8 ***Differential Equations and Matrices ***91**

6-1: A Simple RC Circuit. 93

6-2: Equations of Motion are Differential Equations. 94

6-3: MATLAB and Simulink. 95

6-4: Laplace Transform and Transfer Function. 96

6-5: More RC Functional Networks with their TF(s) Equivalency. 99

6-6: Programming the Motion of the Pendulum into MATLAB. 100

6-7: RLC Circuit of Electricity also deals with physical motion. 101

6-8: The TF to solve Motion Problems of an F-16 Accelerometer. 101

6-9: The Spring Mass System Measures Acceleration of the F-16. 101

6-10: Continuous Systems and Model for Bungee Jumping. 104

6-11: (D1) More Programming and Vectorized Computations. 105

6-12: (D2) Another Drill on Saving and Loading Data in Other Formats. 105

6-13: (D3) Load Line Analysis of an Electric Circuit. 105

6-14: (D4) Time Series and Autocorrelation. 105

**CHAPTER 9 ***Using MATLAB for Calculus. ***107**

7-1: Differential Command, diff(x), in MATLAB. 107

7-2: The Integration Command, int(x) in MATLAB. 107

7-3: Linear and Cubic Interpolation, interp1, in MATLAB. 107

7-4: Computation and Plotting of a Least-Squares Polynomial. 107

7-5: Numerical Evaluation of a Polynomial. 107

7-6: Integral Under a Curve with the Numerical Analysis of Simpson. 107

7-7: Numerical Analysis with the Newton-Rapson method. 107

7-8: The Taylor Series Polynomial. 107

7-9: The LaPlace Transform. 107

7-10: (D1) Input, Eval, Feval, Debugging, and Profiling. 107

7-11: (D2) Subplots, Double Axis, and Labels. 107

7-12: (D3) Progressing on Finer Points of Plots. 108

7-13: (D4) Filters. 108

**CHAPTER 10 ***Applications of The Transfer Function. ***109**

8-1: The Transfer Function. 109

8-2: LaPlace Transform, parameters in s. 110

8-3: State-Space Variable Equations. 111

8-4: Concepts/Techniques Applied to the Electric Circuit. 112

8-5: Let MATLAB do it all for you. 116

8-6: Damping and Natural Frequency with the Transfer Function. 116

8-7: Transfer Function and State-Space. 116

8-8: Fun Applications of TF to F-14 and F-16. 116

8-9: (D1) Data In/Out, Printing, and Exporting Figures. 116

8-10: (D2) Text in Graphics, Symbols and Greek Letters. 116

8-11: (D3) Low Pass Filter and Log Plots. 116

8-12: (D4) Trend Analysis. 116

**CHAPTER 11 ***Missiles, Trajectories, and Guidance ***117**

9-1: A Missile Program and Data to Play With. 117

9-2: What the Table Looks Like. 121

9-3: Error Analysis of Calculated Pressure Vs Standard. 124

9-4: It is always easier to Analyze Data or A Routine with Plots. 124

9-5: Cleaning Up the Plot. 125

9-10: (D1) Introduction to Handle Graphics. 125

9-11: (D2) GUIs. 125

9-12: (D3) Stem, Stairs, and Bar Plots. 125 9-13: (D4) Time Series. 125

**CHAPTER 12 ***Numerical Analysis ***127**

10-2: Error Analysis. 128

10-3: The Bulirsch-Stoer Polynomial Interpolation. 128

10-4: Polyfit Finds Coefficients of the Polynomial. 128

10-5: Newton’s Raphson Method of Numerical Analysis. 128

10-6: Gaussian Elimination. 128

10-7: Jacobi Method. 128

10-7: Eigenvalues and Eigenvectors. 128

10-8: Least Squares Approximation. 128

10-9: Fourier Methods such as FFT (Fast Fourier Transform). 128

10-10: Numerical Differentiation and Integration. 128

10-11: Methods for Ordinary Differential Equations. 128

10-12: The Saving and Loading of Data. 128

10-13: Plotting for Graphical Visualization. 128

10-14: Curve Fitting to Test Data. 128

10-15: Airfoil Data. 128

10-16: Nozzle Aerodynamics. 128

10-17: Graphing an Electrical Diagram. 128

10-18: (D1) Creating Graphical User Interfaces in MATLAB. 128

10-19: (D2) Guide for Drawing GUIs and “help unitools”. 128

10-20: (D3) Function Discovery. 128 10-21: (D4) Fourier Series. 129

**CHAPTER 13 ***Automatic Control ***131**

11-1: A Working Knowledge of MATLAB (Essentials Review of MATLAB). 131

11-2: Modeling with MATLAB. 132

11-3: The Famous PID Controller. 132

11-4: MATLAB for Root Locus. 133

11-5: Frequency Response with the Bode and Nyquist Plots. 133

11-6: State-Space with MATLAB and Simulink. 134

11-7: Controller of a Digital Computer. 134

11-8: Review of Simulink Essential Basics for Automatic Control. 135

11-9: Model Based Design with Simulink. 135

11-10: (D1) Linear Systems. 135

11-11: (D2) Printing Graphics. 135

11-12: (D3) Interpolation, Extrapolation, and 3-D Plots. 136 11-12: (D4) Filtering in the Frequency Domain. 136

**CHAPTER 14 ***Model Based Design ***137**

12-1: A Definition from Wikipedia. 138

12-2: Value of Model Based Design. 139

12-3: To Model the AFTI F16 Flight Control Computer in Simulink. 140

12-4: Present and Future of Embedded Systems. 143

12-5: Hybrid Electric Vehicle Design Example with Model Based Design. 144

12-6: Model Based Design in Aerospace. 145

12-6: Simulink. 148

12-7: Michigan Technology University Design Experience for EcoCar. 148

12-8: (D1) Power and Versatility of Simulink. 149

12-9: (D2) 3 Dimensional Modeling. 149

12-10: (D3) Linear Algebraic Equations. 149

12-11: (D4) Eigenvalue Graph. 150

**CHAPTER 15 *** Examples of Model Based Design ***151**

13-1: Forward on MATLAB and Simulink Basics to the work lab. 151

13-2: More Progress on Creating Models in Simulink. 152

13-3: Model of a Car, the ultimate plant plus controller. 152

13-4: Cruise Control for an Automobile. 152

13-5: Communications System for Modulation and Demodulation. 152

13-6: Amplitude Modulation (AM) with 2 Sources and a Multiplexer. 152

13-7: Controlling Motor Speed of a Direct Current (DC) Motor. 152

13-8: Measuring Position of a DC Motor. 152

13-9: Vertical Motion of a Bus Suspension System. 152

13-10: Control of the Angle of a Vertical Pole. 152

13-11: Pitch Controller of an Aircraft. 152

13-12: A Rolling Ball on a Beam. 153

13-13: A Switch and Relational Operator Model. 153

13-14: Simple Transducer of Slider and Gain to Control Speed. 153

13-15: (D1) Numerical Methods. 153

13-16: (D2) Vectorizing Code for Programming. 153

13-17: (D3) Matrix Commands for Solving Linear Equations. 153 13-18: (D4) The Lorentz System. 153

**CHAPTER 16 ***Modeling Discrete Systems in Simulink. ***155**

14-1: A Look at the Discrete Block Library of Simulink. 155

14-2: Difference Equation Models and Unit Delay Blocks. 155

14-3: Interface between Modeled System and Discrete Solvers. 155

14-4: The Z Doman Transfer Function Block: Discrete Cruise Controller. 156

14-5: Discrete Filter as an AM Demodulator. 156

14-6: Modeling Other Filters of Digital Signal Processing. 156

14-7: Model of Zero Crossing Detector. 156

14-8: Model of Disabling Zero Crossings. 156

14-9: (D1) External Interfacing. 156

14-10: (D2) Sub functions, Debugging, and Profiler. 156

14-11: (D3) Some Drills with MATLAB Programming. 156 14-12: (D4) Writing S-Functions in C. 156

**CHAPTER 17 *** Advanced Techniques of Simulink. ***157**

15-1: Cruise Control for an Automobile. 157

15-2: The Classic Bouncing Ball System Modeled in Simulink. 157

15-3: Controlling Motor Speed of a Direct Current (DC) Motor. 157

15-4: Building A GUI. 157

15-5: Measuring Position of a DC Motor. 157

15-6: Vertical Motion of a Bus Suspension System. 157

15-7: Control of the Angle of a Vertical Pole. 157

15-8: Pitch Controller of an Aircraft. 158

15-9: A Rolling Ball on a Beam. 158

15-10: (D1) Mex Functions in MATLAB. 158

15-11: (D2) More Skill in Programming. 158

15-12: (D3) Building User Friendly Diagrams in Simulink 158

15-13: (D3) Diagrams b. 158

15-14: (D4) Diagrams c. 158

**CHAPTER 18 ***Some Aerodynamics of Flight ***161**

16-1: Steady State Trim Program and the State Space Concept. 161

16-2: A Definition of Steady State Flight. 162

16-3: Life, Drag, and Moment Coefficients. 162

16-4: Lift, Drag, and Moment Coefficients in NASA reports. 163

16-5: Power for Steady State Flight. 163

16-6: Stability and Control. 164

16-7: Center of Gravity and Neutral Point. 164

16-8. Vtrim and Static Longitudinal Stability. 164

16-9: A GENERIC TRIM Program. 164

16-10: The State Vector and the Control Vector Outputs. 164

16-11: A Linearization Program. 164

16-12: A Time-History Simulation. 164

16-13: Current NASA flight literature and the Flight Textbooks. 164

16-14: Program to Calculate Cl, Cd, and Cm. (p 246, John) 167

16-15: Paraphrased Statements and Equations, Also Techniques from B&K. 167

16-17: (D) The Simulink Accelerator. 169

**CHAPTER 19 ***Practical Parameter Estimation ***171**

17-1. Basic Aircraft Parameters and Equations. 172

17-2: The Cost Function, J. 172

17-3: Cost Function in Model Methology of Operations Research. 173

17-4: “Fminsearch” of MATLAB, Nelder and Mead Simplex Algorithm. 173

17-5: Place of the Cost Function in Parametric Estimation. 173

17-6: MATLAB Program for Aircraft Trim plus. 173 17-7: (D) Model Differencing Tool 173

**CHAPTER 20 ***Fly-By-Wire (FBW) ***175**

18-1: The Pitch Actuator Simulink Model of the F-14. 176

18-2: Modified LTV Corsair actually first on Fly By Wire. 177

18-3: Simultaneous Testing on AFTI and the X36 at NASA Dryden. 178

18-3: The FCC of the AFTI F-16. 178

18-4: F-16 Simulation in Straight and Level Configuration. 179 18-5: (D) Simulink Profiler. 179

**CHAPTER 21 ***Flight Control Computer ***185**

19-1: FCC as Classic Feedback Control System. 185

19-2: Analogies Between FCCs and the G-H Block Diagram. 187

19-3: Negative Feedback Control. 188

19-4: The Standard PI, PD, and PID controllers of Automatic Control. 189

19-5: Transfer Functions of the AFTI FCC. 191 19-6: Feedback Control with an Inner Loop. 191

19-7: Compensator of the AFTI FCC. 192

**CHAPTER 22 ***Application #1 on Flight Test ***195**

20-1: Longitudinal Stability in Flight Test. 197

20-2: Flight Controls Enhanced by the Digital Revolution. 200

20-3: Prime Differential Equation and the Process. 200

20-4: Process Step #1: The Problem to Calculate and Measure Stability. 202

20-5: Step #2, A Sketch of the Problem with Parameters. 203

20-6: Step #3, Equations to Predict Plane Flight Characteristics. 203

20-7: Step #4, Program the Equations into MATLAB. 204

20-8: Step #5, View and Analyze the Plots in MATLAB. 204

20-9: Step #6, Simulate in MATLAB SIMULINK. 204

20-10: Animation of Flight Test for Step #7. 204

20-11: Flight Test (Step 8). 204

20-12: Data Analysis (Step 9). 204

20-13: Flight Test Report (Step 10). 206

**CHAPTER 23 ***Additional Technical Applications. ***207**

22-2: Data Analysis. 207

22-3: Common Airborne Instrumentation System (CAIS). 207

22-4: Fight Test of EVN (Enhanced Visual Navigation). 207

22-5: S Functions in C. 207

22-6: Working with Simulink Blocks from the Command Window. 207

22-7: Some Advanced Simulink Modeling Techniques. 207

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