Technical Applications of Computers
with Matlab, FreeMat, and other
free and open software
APPENDIX***
Jerry V McMichael
Part III
CHAP TE R 6
An Introduction to
Longitudinal Stability.
TAC Appendix
105
Missile Aerodynamic Coefficients
106
TAC Appendix
Systems Integration
give a coefficient that has not dimensions, or dimensionless. A same proceedure is used on the lift and drag equations to get Cl and Cd, for the coefficient
of lift and coefficient of drag respectively. Much of what is needed for background on flight and flight dynamics, that is for data analysis, centers around
these three coefficients: Cm, Cl, and Cd.
3-1: Cl, Cd, and Cm on seleted Aircraft.
It is necessary to look at some numbers for these three coefficients in order
to get a feel for the coefficient of lift, the coefficient of drag, and the
moments coefficient; even before we look at the equations. Dr. Robert C. Nelson1 has made an excellent contribution in Appendix B in providing many
detailed specs for specific aircraft, 14 specs for the C coefficients; but now
we will only compare the three primary Cs of Cl, Cd, and Cmalpha for the following aircraft: the Jetstar business aircraft, the General Aviation Navion, the
Convair 8802,and the Boeing 747.
TABLE 1.
Aerodynamic Coefficients for Aircraft.a
Cl
Cd
Wing Area, S in
square feet
Cmalpha
Convair 880
.68
.08
2000
-0.903
Boeing 747
1.11
.102
5500
-1.26
Jetstar Bussines Aircraft
.737
.095
542.5
-3.0
A-4D
.28b
.03
260
-0.38
Navion General Aviation
Aircraft
.41c
.05
184
-.683
F-104
.735
.263
196.1
-.64
STOL trans-
1.5
.127
945
-0.78
portd
a. Actually these coefficients, in order to simplify at this point in the book are for the longitudinal axis only,
only at a speed of Mach .25, and only for sea level.
b. Those delta wings in those days did not provide as much lift, however it should be noted that the wings had
only 260 square feet of area.
c. Much lower lift than Convair 880, 747, and Jetstar, but more lift than A4-D. But compare the wing areas.
1. FLIGHT STABILITY AND AUTOMATIC CONTROL.
54
Technical Applications of Computers
Systems Integration
d. We need one low speed tuboprop aircraft for comparison since another focus of this book will be on simulation with MATLAB of a transport aircraft and of the F-16. The closest spec FS&AC offers us of a jet like
the F-16 is the A-4D, which is a ways back in history before the F-16; but some of the first elogated experiment flights at NASA on a UAV was on an A-4D offered to them by Naval Aviation.
1. You will come to expect low numbers like .68, .08, and -.903--all less than 1;
andthe why of this will be discussed when we take a look at the equations.
2. It would make sense that the Aerodynamic Coefficients for the Boeing 747
would have higher numbers than for the Convair 880 since it is a much larger aircraft. The weight of the 747 is 636,600 pounds, and that of the Convair 880
was 126,000 pounds. And you notice that 2 of the coefficients for the 747 are
above 1, Cl = 1.11 and Cmalpha = -1.26.
3. I guess that we are not surprised that the Jetstar has more lift than the 880
and less than the 747. If we respectively compare the surface area of the wings
respectively of the Jetstar at 542.5 square feet, that of the 747 at 5,500
square feet, and that of the 880 at 2,000 square feet, that relationship is
exactly what we would expect for the coefficients.
4. Wow {and not for Weight on Wheels}, look at the lift of the STOL transport
aircraft, so we are not surprise to see a wing area of 945 square feet and a
weight of only 40,000 pounds. The wing area of the transport aircraft we will
simulate in MATLAB has a weight of 162,000 pounds and a wing area of 2170
square feet.
Please keep in mind that we an only provide in summary form a drop in the bucket
of both basic aerodynamics and stability and control dynamics; that only which is
required for TECHNICAL APPLICATIONS OF COMPUTERS, and in particular
Data Analysis, and such is the way it should be lest we feebly try to compete
with uncessarily with the experts like Anderson, and Stevens and Lewis. In
other words, if you want a good, thorough book on Flight and Flight Mechanics
read a book like the one by Anderson or on flight contol and simulation, read the
one by Stevens and Lewis. {This chapter has tried to cull some of their
essentials, by research while avoiding plagarism, combing those salient points
of stability and control aerodynamics with many other recognized authori2. When Lockheed Martin at Fort Worth was still General Dynamics {in one of the dumbest moves in history the
former astronaut Bill Anders sold GDFW to Lockheed even though it made over 50% of the profit for GD}, the Convair 880 made its last flight to Europe dropping off our F-16 teams at various bases to unground the F-16s. My team
was dropped at Brussels to go to Beuvechan AFB; and as far as I know was the first to fly after the world-wide
grounding.
Technical Applications of Computers
55
Systems Integration
ties, also with the practical applications in Flight Test Reports from the
NASA Dryden and Langley servers.}
For the purpose of this book only and in this one chapter, we will do a little
Systems Integration of our own, briefly integrating the two diverse subjects
of flight Aerodynamics with that of Automatic Control, also in the Transport
Aircraft MATLAB simulation, adding optimization. Actually the integration will
be larger than that consisting of the bringing together in one chapter what has
generally be called the disciples of and the title of books on flight mechanics,
aerodynamics, the history of flight, automatic control, and flight test and simulation.1 Ambitious yes; but that is far better than trying in one book on DATA
ANALYSIS for Systems Integration to attempt an inclusion of even one complete
chapter on
these
Fig 3-1: Flight Test
diverse
Parameters.
but
closely
related
subjects.
Then
except
for a
few
“aerodynami
c
moment
s” in each chapter, we will have sufficient background to proceed into simulation, automatic control, and flight itself. The challenge of such integration will
be assisted by a focus on those aspects of flight aerodynamics and automatic
control that most easily lend themselves to data analysis. As a matter of fact,
if a more scholarly and longer title were chosen for this chapter, it could be
“Systems Integration of Flight Aerodynamics and Automatic Control for Simulation and Data Analysis”. Never forget that when large flight simulators are
1. For example Anderson on INTRODUCTION TO FLIGHT and Stevens and Lewis on AIRCRAFT CONTROL
AND SIMULATION. Also FLIGHT DYNAMICS and THE AERODYNAMICS OF FLIGHT.
56
Technical Applications of Computers
Systems Integration
used like at NASA Dryden and Wright Patterson, the simulator comes first then
the simulator data; and during actual flight test, that previously collected and
analyzed data from the simulation both gives clues for flight test and gives
another standard for comparison. {That is actual flight test data versus flight
simulator data.} And in this day and time of fuel costs and the economic crunch,
more and more aircraft and missile companies are turning to increased simulation
for testing.
3-2: Steady State Flight with Principles of Stability and Control.
(NOTE: Sect 2.6, 3.6, and 3.7 of S&L and chp 7 of Anderson)
We pilots call this flight condition, “straight and level”: in aerodynamics the more
acceptable terminology is “Principles of Stability and Control.” Airplane control,
according to a recognized authority on Flight1 is defined as:
Deflections of the flight control surfaces like the ailerons, elevators, and rudders to shift equilibrium positions {we will shortly come to the energy concept
and equations for aircraft which is much like the basic kinetic energy versus
potential energy concepts of physics, K.E. = 1/2 mv^2 and P.E. = h g}, or produce
nonequilibrium accelerated motions called flight manuvers2.
For purposes of data analysis, this entails a measurement of the deflections of
these flight control surface, generally with transducers on motion sensors connected physically to those control surfaces; then the data collected in an
onboard computer like in ATIS or the newer CAIS, then transmitted to ground
for analysis by a special kind of radio signal called Telemetry. So ultimately
designers, and the pilot learning to fly that particular aircraft, must decide what
amount of deflection is required to do what is expected at that time, and beyond
that how much force is required for that amount of deflection. Of course, technically we must have numbers of the deflection and for the force. Remember
while the force in such small aircraft like the Piper Cherokee Arrow that most of
us fly is almost directly on the control surfaces {that is directly and physically
connected by a mechanical linkage}, the force in aircraft such as the F-16 and
newer FBW (Flight By Wire) commercial aircraft is on a transducer. That proper
1. For enjoyable research and reading you can not beat John D. Anderson Jr’s INTRODUCTION TO FLIGHT. In this
easy to read and understand book, he combines his knowledge and skill from being a Curator of Aerodynamics at the
Smithsonian and Professor Emeritus at the University of Maryland.
2. Focus on flight and especially flight test will be on four typical manuvers of flight test: the dutch roll, short period,
phugoid, roll, and spiral.
Technical Applications of Computers
57
CHAP TE R 7
History of TAC
development.
The online and off line development of the TECHNICAL APPLICATIONS OF
COMPUTERS with Matlab, FreeMat, and other Free, Open Software, can be
considered with an upfront {before you read this chapter} summary as follows:
(1) from the experience of an Engineer and Assistant Professor of Electronics,
it was found that so many in the general public thought of, and used, computers
more for games, the internet, and office work that there was that natural
market to reach out with a book on the other side of computer applications, the
side common to engineers at work on systems and data analysis, but almost in
the category of "no need to know". That is, it might seem as if engineers
were saying to the rest of the public, like they commonly do about classified
work, "I can tell you, but I would have to shoot you"; (1) the prototype copy of
the TAC textbook was written and printed based primarily on 40 years of
experience before retirement from Lockheed Martin {GD most of the time}
as a Engineering Specialists Flight Test Engineer and from Raytheon Missile
Systems as a Principal Systems Engineer Flight Test Engineer {the former was
flight test of aircraft, primarily the F-16, and the later on missiles, primarily
the standard missile with a Kinetic Warhead {called because it has no bomb,
TAC Appendix
105
Missile Aerodynamic Coefficients
working simple on the kinetic energy of direct contact {yes, back in our days
on the Atlas and Minuteman missiles it was thought that for a missile like
the KW to shoot down an incoming ICBM would be like hitting a bullet with
a bullet, but thanks to some very ingenious designers and maybe us testers
too, it does happen now}; (3) having developed electronics technology
courses and curriculum for 10 years at Lee College, Eastern NM University,
and INTELLEC in Algeria, it was natural in the writing of a book to take
both the teacher and engineer approach; (4) parts of the first draft of TAC
were put online at www.biblecombibleman.com {yes even as science and religion can be combined as in Christian evidences and apologetics, so also the
practical applications of Bible and engineering applications can be combined
on one website, and are {included in this chapter will be the technical
resume of the instructor, course developer, and writer}; (5) sort of like
open software in the nature of FreeMat and SciLab, from the website,
surfers insterested were encouraged to participate in the further development {in the pages to follow, the original contract, the many Matlab and
technical searches by surfers {hundreds of them from spiders and visitors
have come in and are still coming in}; (6) some of those demands from web
site consitituents caused immediate answers to search questions in briefs
on such subjects as "Longitudinal Stability", "Missile Aerodynamic Coefficients", and Bungee jump math in Matlab, and they have been inserted on a
web page or in the TAC Appendix; (7) the overflow in the 362 page TAC
textbook demanded an Appendix, soon to be put available free on the website, and will continuously be updated {it is a free download in PDF, requiring
only that you have Adobe reader on your computer, also free from the
website of www.adobe.com; and finally (8) the correspondence course on
TAC, developed with material from the book, the Appendix, and the expressed interest of the surfing public, a course which will be done both
online at www.biblecombibleman.com and by email at sungrist@gmail.com.
This is a long paragraph, goodness it is a long single sentence; and perhaps what has taken 6 years, plus a lifetime, to develop should become
clearer as you browse through this chapter. When you see only the outline
of TAC, called TAC TOC, that will perk up your ears and interest!
106
TAC Appendix
TAC
Correspondence Course on TAC
The 20 lessons of Technical Applications of Computers with Matlab and FreeMat,
at $35 each, are offered by correspondence through email. {You can complete
the course by regular mail, and each lesson as the previous ones are completed
will be sent to you in PDF.} The foundation for the course content, of course is
to reinforce and implement, and even advance beyond the level of the textbook
with the 23 sections which you noticed were saved for later.
1. The Process in CMMI (Sect 5-13) and in Embedded Systems Architecture
(Sect 5-14). You can not get any more systems level than this unless you go all
the way to the system of sytems of the 17 vehicles of the Future Combat System.
2. Some of the NASA reports mentioned but not discussed from Section 5-15
in the chapter on “The Process”.
(1). Stability and Control Derivative and Dynamic Characteristics. {Sounds
like the job description for Gulfstream of “Flight Dynamics/S& C”.} In our
respect for NASA Edwards and the flight test engineering work of the past, we
must give due respect to this early {1966} look at efforts to get the S&C derivatives from flight test data in AGARD-AR-549, part 1.
(2). A FORTRAN program for S&C derivatives that derives those derivatives
from flight test data, NASA TND-7831, 1975.
NOTE: There is the well-known saying in flight test engineering that “we do not
want to re-invent the wheel”. While we may not want to, quite often we do and
often although frustrating you must appreciate the trend of Naval Aviation, like
in Flight Test at Pax River, to stick with the traditional.
(3). A New Method, in 1976, for Test and Analysis of Dynamic S&C, AFFTCTD-75-4. This publication out of Edwards AFB makes a significant contribution
to the history, if not the technical advance, of flight test engineering at
Edwards.
(4). Sometimes Systems ID and parameter estimation have been confusing, so
that any paper like AGARD-CP-172, paper 16 of May 1975 that clarifies the
“Practical Aspects of Using a Maximum Likelihood Estimator” will be welcome.
Technical Applications of Computers
13
TAC Appendix
NOTE: Did you notice some of those computer and data analysis methods
required on the Systems Engineering for the B-52 radar replacement such as:
Broad knowledge of detection and estimation techniques (e.g., maximum likelihood, maximum a posteriori [MAP], non-parametric, constant false alarm rate
[CFAR], amplitude/frequency/phase). Broad knowledge of classification techniques (e.g., pattern recognition, feature extraction, correlation, demodulation,
multiple hypothesis tracking, template techniques, neural networks, support
vector machines)
Of course these parametric methods are the most common for radar, but you
see how the estimation technique of maximum likehood gets into the systems
and data analysis with computer numerical methods.
3. Cost Function (Sect 6-8) in Model Methology of Operations Research1.
4. “Fminsearch” (Sect 6-9) of MATLAB, the Nelder and Mead Simplex algor i t hm .
5. Place of the cost function, J, in parametric estimation (Sect 6-10).
6. MATLAB program for Aircraft Trim plus more.
7. (Sect 7-7) Coefficients from Flight Test versus Mach and Altitude.
8. Working with the Pendulum System in MATLAB, Sect 7-12, sometimes
the simplest of systems can be the model for much more complex systems. For
example some of the parameters in the MIL specs for flight test, were originally derived from simple models like the pendulum. We will us the pendulum in
MATLAB to explore the flight test requirments for manuvers like the Dutch
roll and Phugoid method.
9. Files/Directories, the computer handling of data, and interfacing with
external programs (Sect 8-3 on drill). It is very approriate in this Last
Chance that our drill with MATLAB also become integrated in Flight Test Engineering. After all, most of us do it for more than fun!
1.
14
Did you notice the mention of the methods of Operations Research in the Systems Engineering job for
Boeing? This was previously the more popular title for numerical methods in computers.
Technical Applications of Computers
TAC Appendix
10. The Fourier Transform (Sect 8-4).
11. Plotting Polynomials (Sect 8-5) with the “polyval” of MATLAB with some
typical polynomials of flight test engineering.
12. Matrices of Data and Plotting (Sect 8-6).
13. Programming Input and Output in MATLAB (Sect 8-11).
14. Engineers are not programmers, but must be able to program. Why not use
the language of Engineers, that of MATLAB, for programming. More programming with (a) looping in MATLAB (Sect 8-13), (b) control flow statements (Sect
8-14), (c) “IF” statements, necessay in all programming languages (Sect 8-15), (d)
loops for the programming of missiles (8-16) for we dare not neglect the flight
test of missiles, (e) a useful program routine to do the Air Data computer functions,used as a function in MATLAB programming {[Mach,Qbar] = ADC(VT,H)}.
15. A peak in our programming (8-18) with MATLAB skills as we calculate the
state derivatives for the Transport Aircraft.
NOTE: You see the wisdom of Round 2 in learning of Technical Applications of
the Computer with MATLAB. At chapter 8, this task was right there in the flow
to be introduced, but if you were still learning MATLAB the skill level was still
too high at chapter 8. Besides now, you have more motivation to get a job, or a
better job!
16. Optimization in the Excel Data Analysis ToolPak (9-4).
17. Optimization in MINITAB (9-5).
18. Modeling, Parameter Estimation, and System ID (10-7).
19. Statistics Toolbox of MATLAB versus Data Analysis ToolPak (10-8).
20. Back to a simple system again to integrate with the electronics of the LCR
circut (Sect 12-2) using the simple model of the spring mass system.
21. Then advance into other electronic circuits which provide a basis for the
understanding of the 3 types of controllers for automatic control--PID, PD, and
PI. You will remember these controllers of digital control computers as Propor-
Technical Applications of Computers
15
TAC Appendix
tional and Integrating, Proportional and Integrating and Differential, and PD
( S e c t 1 2- 3) .
22. And on to the unique circuits called filters (Sect 12-4), and from circuits
into the mathematical and computer methods of LaPlace and the TF (transfer
function).
23. Drill with the very important tool of the Transfer Function on well known
circuits of electronics technology (12-6).
NOTE: Did you see model-based design in the job description for Flight
Dynamics at Gulfstream. Of course, while they mean the more modern methologies of like modeling in Simulink, models are helpful at all levels. You might
consider that they are analogies and ways to visualize a circuit or system. You
might also recall that for every physical system there is an analogous electronic model, and vice versa.
Examples of How Chapter Subjects from which Sections Taken to
form the outline for the course
1. From chapter 5, "The Process", three sections are taken--13 and 14.
2. Since the additions NASA reports mentioned in 5-13 are really sort of
a "History of Some data analylsis technics and methods", it therefore
will be a separate lesson in the correspondence course.
NOTE: this is not necessarily the sequence of the Course Outline.
3. More studies and applications on 6-8 and 6-9 must be part of more advance
on "Aircraft Trim". This would include programming work in Matlab and/or
FreeMat, more advanced than in the text. Yes, the subject matter was introduced in Chapter 6 on "Data Parameter and Analysis" as one example of
application.
NOTE: The course like the book is heavy on applications, and you must have
access to FeeMat or Malab before you enroll. FreeMat is available free
online to all with a simple download.
16
Technical Applications of Computers
Correspondence Course
The General Subjects for this course based on Section Placeholders.
1.
2.
3.
4.
The Place of Process in Technical Work.
Data Ananysis Technics and Methods
Programming Aircraft Trim.
Applications of the coefficients of Differtial equations to the pendulum,
aircraft flight test, and other applications of physics and engineering such as
the LCR circuit and the spring-mass system.
5. Handling of data files and directories in Matlab and flight test engineering.
6. Series and the Fourier Transform, also LaPlace.
7. Programming and Plotting polynomials, matrices, and input/output.
8. Looping, flow control, and if statements in the programming of flight test of
missiles and aircraft including the Air Data Computer.
9. State Derivatives for the Transport Aircraft.
10. Optimization, the Excel Toolpack and Minitab, and the Statistics toolbox
of Matlab introduction.
11. Modeling, Parameter estimation, and System ID.
12. Using the matlab control toolbox and transfer equations with plots to
design and analyze automatic control systems like om aircraft. {This will
be compared with more classicals plots like the Bode and Niquist.
13. PID, PI. and PD controllers for aircraft, processs, and machines.
14. Math and computer methods {numerical analysis} such as LaPlace and
rhe transfer function applied to filters, other circuits with drills.
15. Model based design with Simulink.
{the last 5 lessons will be based on student problems with the first 15, on Matlab
and TAC searches on the www.biblecombibleman website, and examples out
of the previous work computers of Jerry V McMichael--retired Flight Test
Engineer and Principal Systems Engineer, also 10 years as a teacher of electronics engineering technology.}
362
Technical Applications of Computers
Data Analysis
CHAPTER 1
Data Analysis and Systems Integration
13
1-1: Simulation of Space Shuttle with MATLAB programming. 13
1-2: Numerical Analysis the Anchoring Discipline. 15
1-3: Excel and MATLAB for Data Analysis. 17
1-4: Large Modern Systems in the Evolution of the Digital Atomic Age. 18
1-5: Differential Equations and Physics Have Taken a Bad Rap. 20
1-6: Many Threads of Modern Technology Made the Technical Revolution. 23
1-7: Sharing of Learning Theory. 24
1-8 Ups and Downs of UAV Testing by John Del Frate of NASA. 26
1-9: Drilling with MATLAB Basics. 26
CHAPTER 2
The Digital Atomic Age
29
2-1: Math led the technical world into the Digital with Linear Algebra. 31
2-2: Some Things from “Optimization in Simulation Studies”. 31
2-3: New on Minimization, Optimization, and Parameter Estimation? 33
2-4: The Place of Equations in the Digital Revolution. 33
2-3: Most Physical Phenomenon is Analog, Requring Coversion to Digital. 33
2-4: The Math of Motion is a Good Starting Place for the Technical. 34
2-5: Digital and Digital Computers to Technical Applications of Computers. 36
2-6: “Digital Signal Processing”. 37
2-7: MATLAB, Path, and Workspace. (D1) 39
2-8: Plotting, Subplots, Axis and Labels. (D2) 43
2-9: Polynomial Algebra and Polynomial Roots. (D3) 44
2-10: Graphics and Descriptive Stats. (D4) 47
CHAPTER 3
Systems Integration.
53
3-1: Cl, Cd, and Cm on seleted Aircraft. 54
3-2: Steady State Flight with Principles of Stability and Control. 57
3-3: We can use the Transfer Function in MATLAB before the Theory. 59
3-4: Trim equilibrim as far as pitch when all moments at the C.G. are zero. 61
3-5: Numerical Optimization and the Trim. m Program. 62
3-6: Intro to Numerical Optimization. 64
3-7: FMIN in MATLAB. 64
3-8: FEVAL in MATLAB. 66
3-9: The Steady-State Trim Algorithms. 68
3-10: Polynomials and Plotting (D1). 69
Technical Applications of Computers
1
Data Analysis
3-11: Matrices and Plotting (D2). 71
CHAPTER 4
4-1:
4-2:
4-3:
4-4:
4-5:
4-6:
4-7:
4-8:
4-9:
UAV’s and Other Flight Test Reports
75
The Altair/Predator B. 76
Recent UAV Flight Test Experience at NASA, 1998. 77
Flight Tests of the X-48B UAV between 2007 and 2008. 79
AFTI/F-16 Flight Test Results and Lessons Learned. 82
Aircraft Parameter Estimation. 88
Graphics and Plot (D1). 91
Flow control (D2). 91
Plotting Complex Numbers and Function Plot (D3). 91
Normal Distribution (D4). 91
CHAPTER 5
The Process
93
5-1: The 10 step Process of this book. 93
5-2: The 10 step Process of Aerospace. 95
5-3: The Process of Learning: ILS. 95
5-4: Historical PROCESS of The Digital Atomic Age. 96
5-5: Math led the technical world into the Digital with Linear Algebra. 98
5-6: The Place of Mathematical Equations in the Digital Revolution. 98
5-7: Most Physical Phenomenon is Analog, Requring Coversion to Digital. 99
5-8: The Math of Motion is a Good Starting Place for the Technical. 99
5-9: Digital and Digital Computers & Applications of Computers. 99
5-10: Digital Signal Processing. 100
5-11: Evolution in Math Techniques for Engineering Applications. 102
5-12: Software, Firmware, and Digital Math. 102
5-13: The Process in CMMI. 103
5-14: The Process in “Embedded Systems Architecture”. 103
5-15: Global Hawk Unveiled the Process at work in UAVs. 104
5-16: Files/Directories, Handling Data, & External Programs (D1). 106
5-17: Fourier Transform (D2). 106
5-18: Plotting Polynomials with “polyval” (D3). 106
5-19: Matrices of Data and Plotting (D4). 106
2
Technical Applications of Computers
Data Analysis
CHAPTER 6
Parameters and Data Analysis.
107
6-1: Practical Aircraft Parameter Estimation. 109
6-2: List of Parameters. 111
6-3: Approach of NASA Report # NASA TM-88281. 111
6-4: Modern Minimization {Curve Fitting} Techniques. 113
6-5: Cost Function, J or PI, for a Transport Aircraft. 115
6-6. Basic Aircraft Parameters and Equations. 116
6-7: The Cost Function, J. 117
6-8: Cost Function in Model Methology of Operations Research. 117
6-9: “Fminsearch” of MATLAB, Nelder and Mead Simplex Algorithm. 117
6-10: Place of the Cost Function in Parametric Estimation. 117
6-11: MATLAB Program for Aircraft Trim plus. 117
6-12: Model Differencing Tool (D) 117
CHAPTER 7
Systems and Parameters.
119
7-1: Ways to Model Linear Systems: State-Space and Transfer Function. 121
7-2: Some history of State Space and the Transfer Function. 123
7-3: Large Scale Digital Computer as Catalyst to Digital Atomic Age. 124
7-4: The notions of State and Space. 125
7-5: Linear Systems. 126
7-6 Background for Cl, Cd, and Cm. 127
7-7: Coefficients from Flight Test versus Mach and Altitude. 128
7-8: From Aerodynamic Coefficients to Aerodynamic Derivatives. 128
7-9: Plot of Moment Coefficient Curve with a Negative Slope. 130
7-10: Aerodynamic Derivatives Simply Mean the Use of Partial DEs. 131
7-11: Questions About Table 1 on Lift, Drag, and Moments. 131
7-12: Working with the Pendulum System in MATLAB. 132
7-13: Data In/Out, Printing, and Exporting Figures (D1). 132
7-14: Text in Graphics, Symbols and Greek Letters (D2). 132
7-15: Low Pass Filter and Log Plots (D3). 132
7-16:Trend Analysis (D4). 132
CHAPTER 8
Programming with MATLAB.
133
8-1. Measurement of the Damping Roll (NASA Dryden). 133
8-2: Study of Longitudinal Dyanamic Stability in Flight. 134
8-3: Files/Directories, Handling Data, & External Programs (D1). 134
Technical Applications of Computers
3
Data Analysis
8-4: Fourier Transform (D2). 134
8-5: Plotting Polynomials with “polyval” (D3). 134
8-6: Matrices of Data and Plotting (D4). 134
8-7: Programming Simulation of a Transport Aircraft. 134
8-8: The Use of Functions in MATLAB programming. 136
8-9: The Transport Aircraft Simulation in C&S. {Trim.m Program} 138
8-10: Examples of “cost function” in CONTROL AND SIMULATION. 141
8-11: Programming Input/Output in MATLAB. 145
8-12: Relational and Logical Operators. 145
8-13: Looping in MATLAB. 146
8-14: Control Flow Statements in MATLAB programming. 146
8-15: If-Else-If Statement in Programming. 146
8-16: Using Loops in Programming Missiles. 146
8-17: Function for [Mach,Qbar] = ADC(VT,H). 146
8-18: Program 8-1 to Calculate State Derivative Vector for Transport plane. 146
CHAPTER 9
9-1:
9-2:
9-3:
9-1:
9-2:
9-3:
9-4:
9-5:
9-6:
9-7:
9-8:
156
147
Aircraft State and Parameter Identification. 147
A Good Place to Introduce the Wing Standards of NACA. 148
The three types of Numerical Optimization are repeated here: 148
Zero routines in Optimization. 149
MATLAB calls it “Optimization”. 150
Optimization in MATHEMATICA. 152
Optimization in the Excel Data Analysis ToolPak. 154
Optimization in MINITAB. 154
“Cost Function” in Mathematica. 154
Cost Function is Often Called Performance Index. 155
Two Experts on Optimization and Parameter Estimation. 155
CHAPTER 10
10-1.
10-2:
10-3:
10-4:
10-5:
4
Programming Optimization.
System ID
157
Basic Aircraft Parameters and Equations. 158
The Cost Function, J. 159
Cost Function in Model Methology of Operations Research. 159
“Fminsearch” of MATLAB, Nelder and Mead Simplex Algorithm. 159
Place of the Cost Function in Parametric Estimation. 159
Technical Applications of Computers
Data Analysis
10-6: MATLAB Program for Aircraft Trim plus. 159
10-7: Modeling, Parameter Estimation, and System Identification? 159
10-8: Statistics Toolbox of MATLAB versus Data Analysis ToolPak of Excel. 159
10-14: Model Differencing Tool (D). 160
CHAPTER 11
Automatic Control 161
11-1: Start with a Model of the Model. 161
11-2: How Did We Get the transfer function for the Controller? 164
11-3: “step(deltae*sys,t)” 165
11-4: “rlocus(num,den)” and “rlocfind(num,den)” 165
11-5: “[P,Z] = pzmap(num,den)”. 166
11-6: “[y,z] = lsim(num,den,u,t]”. 166
11-7: “[r,p,k] = residue(num,den)” 166
11-8: “[num,den] = residue(r,p,k)” 166
11-9: “sys1 = tf(num,den)” 166
11-10: “[A B C D] = tf2ss(num,den)” 166
11-11: “[re,im,w] = nyquist(num,den)” and “plot(re,im),grid”. 166
11-12: “[mag,phase,w] = bode(num,den)” 166
11-13: “margin(mag,phase,w)”. 166
11-14: “nichols(num,den,w)” and “ngrid”. 166
CHAPTER 12
Integrated Electronics: Circuits and Systems.
167
12-1: The Transfer Function makes this Evolution Process Evident. 168
12-2: Modeling of Spring-Mass System and an LCR electronic Circuit. 168
12-3: The PIDs, PD, and PI of today understandable with Circuits. 168
12-4: Large Part of Digital Signal Processing is Circuits called Filters. 169
12-5: From Circuits to LaPlace to Transfer Function. 169
12-6: Select Electronic Circuits into Transfer Functions and Analysis. 169
12-7: MATLAB for a “Gravity” function. 169
12-8: MATLAB uses a lot of built in functions like “mean”. 170
12-9: MATLAB Built-in Functions are in C:\MATLAB\toolbox\matlab\.. 172
12-9: The Quadratic Equation function script with MATLAB. 173
12-10: Strings and “feval” (D2). 173
12-11: Data Markers and Line Types (D3). 174
12-12: Linear Regression and Curve Fitting (D4). 174
Technical Applications of Computers
5
Data Analysis
CHAPTER 13
Integration.
175
13-1: Programming in MATLAB. 176
13-2: Programming Weather Data. 176
13-3: Some More Work with Input/Output. 177
13-4: Input/Output in Aircraft Time-History Simulation. 180
13-5: Programming the NLSIM.m for Aircraft time-histor simulation. 182
13-6: Methods of Aircraft State and Parameer Identification. 185
13-7: Measurement of the Damping Roll. 185
13-8: Study of Longitudinal Dyanamic Stability in Flight. 186
13-9: Creating Graphical User Interfaces in MATLAB (D1). 186
13-10: Guide for Drawing GUIs and “help unitools” (D2). 186
13-11: Function Discovery (D3). 186
13-12: Fourier Series (D4). 186
13-13: Arrays, Matrices, Vectors, and Data Types (D5). 186
CHAPTER 14
MATLAB Matrix Manipulations.
193
14-1: Differential Equations and Matrix Manipulations. 193
14-2: Matrix Manipulations from Raytheon Training. 194
14-3: Matrix Manipulations from MATLAB training and books. 194
14-4: Linear Algebra and Vector Calculus from Engineering Math and MATLAB. 194
14-5: The Applied Physics of Practical Differential Equations and Matrices. 194
14-6: Equations of Electrical Circuits like Equations of Motion. 198
14-7: Equations of Motion are Differential Equations of Matrix Manipulations. 200
14-8: More Programming and Vectorized Computations (D1). 201
14-9: Another Drill on Saving and Loading Data in Other Formats (D2). 202
14-10: Input, Eval, Feval, Debugging, and Profiling (D3). 202
14-11: Subplots, Double Axis, and Labels (D4). 202
14-12: Progressing on Finess of Plots (D5). 202
14-13: Filters (D6). 202
CHAPTER 15
15-1:
15-2:
15-3:
15-4:
15-5:
6
Applied Physics and Electronics.
203
MATLAB and Simulink. 203
Laplace Transform and Transfer Function. 204
More RC Functional Networks with their TF(s) Equivalency. 207
Programming the Motion of the Pendulum into MATLAB. 207
RLC Circuit of Electricty also deals with physical motion. 208
Technical Applications of Computers
Data Analysis
15-6: The TF to solve Motion Problems of an F-16 Accelerometr. 208
15-7: The Spring Mass System Measures Acceleration of the F-16. 210
15-8: Continuous Systems and Model for Bungee Jumping. 213
15-9: Electromagnetic Spectrum, Microwaves, and Radar. 213
15-10: Load Line Analysis of an Electric Circuit (D1). 213
15-11: Time Series and Autocorrelaton (D2). 213
CHAPTER 16
From DEs to the Transfer Functions.
215
16-1: Conversion of the DE to a Transfer Function Can be Done Directly. 216
16-2: Applications of the Transfer Function. 217
16-3: The Transfer Function. 219
16-4: LaPlace Transform, parameters in s. 219
16-5: State-Space Variable Equations. 220
16-6: Solution of Second Order DE by State-Space. 222
16-6: Concepts/Techniques Applied to the Electric Circuit. 223
16-7: Program 5-1, MATLAB for the RLC Circuit of Figure 6-1. 225
16-8: Put MATLAB to work for you! 226
16-9: Damping and Natural Frequency with the Transfer Function. 226
16-10: Transfer Function and State-Space. 226
16-11: Fun Applications of TF to F-14 and F-16. 226
CHAPTER 17
MATLAB and Simulink.
235
17-1: Blocks and Models of Simulink. 235
17-2: Laplace Transform and Transfer Function. 237
17-3: More RC Functional Networks with their TF(s) Equivalency. 239
17-4 The Pendulum, Programmed and Simulated with Simulink. 239
17-5 RLC Circuit of Electricty also deals with physical motion. 241
17-6: The TF to solve Motion Problems of an F-16 Accelerometr. 241
17-7 The Spring Mass System Measures Acceleration of the F-16. 241
17-8: Continuous Systems and Model for Bungee Jumping. 245
17-9: More Programming and Vectorized Computations (D1). 245
17-10: Data Analysis. 245
17-11: Another Drill on Saving and Loading Data in Other Formats (D2). 245
17-12: Load Line Analysis of an Electric Circuit (D3). 245
17-13: Time Series and Autocorrelaton (D4). 245
Technical Applications of Computers
7
Data Analysis
CHAPTER 18
18-1:
18-2:
18-3:
18-4:
18-5:
18-6:
18-7:
18-8:
18-9:
Applications of The Transfer Function.
247
The Boeing Aircraft Plant. 247
What we need is some sort of Controller, An FCC. 248
A Kp Controller. 249
A PD or Pd Controller. 250
The PID Controller. 250
Simulation with Simulink (Flight of a Mission). 250
Data Analysis of the Test Mission. 250
Computation and Plotting of a Least-Squares Polynomial (D1). 250
Numerical Evaluation of a Polynomial (D1). 250
CHAPTER 19
Equations of Flight
259
19-1: Practical Equations of Motion for the Longitudinal Axis. 259
19-2: We must Derive the Coefficients of Lift, Drag, and Moments. 262
19-3: Numbers into the Equations of Motion. 262
19-4: Some Equations Necessary for CL and CD calculations. 265
19-5: Parameter Estimation and Modeling Save Our Hide. 267
19-6: FS&AC summarize Equations of Motion in 5 separate sets. 267
19-7: Steady State Trim Program and the State Space Concept. 268
19-8: A Definition of Steady State Flight. 268
19-9: Life, Drag, and Moment Coefficients. 269
19-10: Lift, Drag, and Moment Coefficients in NASA reports. 270
19-11: Power for Steady State Flight. 270
19-12: Flight Mechanics. 270
CHAPTER 20
Numerical Analysis
279
20-1: POLYFIT and POLYVAL on CD versus altitude Curve Fit. 279
20-2: Three Dimensinal Plot of CD versus Altitude and Mach Number. 281
20-3: Three Dimensional Plot with Meshgrid. 281
20-4. Aerodynamic Derivatives are simple Partial Differential Equations. 281
20-5: Interpolation of F-16 Coefficients from Tables. 281
20-6: Interpolation of the Boeing Longitudinal and Lateral Aerodynamic Data. 281
20-7: More Integration for the Text. 281
20-8: Must Have Routines to Continue on in this book. 281
20-9: The cost function, J or PI, that we must Minimize. 282
20-10: Numbers and the Newton-Raphson method. 284
8
Technical Applications of Computers
Data Analysis
20-11: Interative Solution in Linear Algebra and the Jacobi. 285
20-13: Error Analysis. 287
20-14: Data Analysis. 287
1. Integral Under a Curve by the Simpson Method. 287
2. Numerical Analysis with the Newton-Rapson method. 287
3. The Taylor Series Polynomial. 287
4. The LaPlace Transform. 288
CHAPTER 21
Parameter Determination (Selection).
291
21-1: Parameter Determination (Selection). 291
21-2: Aircraft Motion and Control Variables. 293
21-3: Combining Aircraft Parameters with Non-dimensional Coefficients. 294
21-4: Categories of Coefficients by Aircraft Motion. 294
21-5: The DATCOM User’s Manual and Computer Software (Digital Datcom). 295
21-6: Parameter Coefficients. 296
21-7: Inputs to the Digital Datcom Computer Program. 296
21-8: Outputs. 297
21-9: Output Sheet for Digital Datcom from the User’s Manual. 298
21-10: DATCOM on the Boeing 737-100. 299
21-11: Motion and Analysis. 299
1. Stability and Control. 300
2. Center of Gravity and Neutral Point. 300
3. Vtrim and Static Longitudinal Stability. 300
4. A GENERIC TRIM Program. 300
5. The Bulirsch-Stoer Polynomial Interpolaton. 300
6. Polyfit Finds Coefficients of the Polynomial. 300
7. Newton’s Raphson Method of Numerical Analysis. 300
CHAPTER 22
22-1:
22-2:
22-3:
22-4:
22-5:
22-6:
Missiles, Trajectories, and Guidance
303
A Missile Program and Data Analysis (Flight Mission #22-1). 303
What the Table Looks Like. 308
Error Analysis of Calculated Pressure Vs Standard. 310
It is always easier to Analyze Data or A Routine with Plots. 311
Cleaning Up the Plot. 311
Motion and Analysis. 311
2. A Linearization Program. 311
Technical Applications of Computers
9
Data Analysis
22-7: Introduction to Handle Graphics (D1). 312
22-8: GUIs (D2) 312
22-9: Stem, Stairs, and Bar Plots (D3). 312
22-10: Time Series (D4). 312
CHAPTER 23
23-1:
23-2:
23-3:
23-4:
23-6:
23-7:
23-8:
23-9:
Telemetry Data Analysis
313
Range and Airborne Instrumentation. 313
IRIG. 314
Common Airborne Instrumentation System (CAIS). 314
Motion and Analysis. 314
Least Squares Approximation. 317
Fourier Methods such as FFT (Fast Fourier Transform). 317
Numerical Differentiation and Integration. 317
Missile Test Mission #4, Data Analysis, and Test Report. 317
CHAPTER 24
Modern Automatic Control
319
24-1: The Goal of Automatic Control is Stability of Flight. 319
24-2: Longitudinal Stability in Flight Test. 320
24-3: Flight Controls Enhanced by the Digital Revolution. 322
24-4: A Working Knowledge of MATLAB (Essentials Review of MATLAB). 323
24-5: Modeling with MATLAB. 324
24-6: The Famous PID Controller. 324
24-7: MATLAB for Root Locus. 325
24-8: Frequency Response with the Bode and Nyquist Plots. 325
24-9: State-Space with MATLAB and Simulink. 326
24-10: Controller of a Digital Computer. 326
24-11: Review of Simulink Essential Basics for Automatic Control. 327
24-12: Model Based Design with Simulink. 327
327
CHAPTER 25
25-1:
25-2:
25-3:
25-4:
10
The Flight Control Computer (FCC).
329
FBW. 329
The Pitch Actuator Simulink Model of the F-14. 330
Modified LTV Corsair actually first on Fly By Wire. 331
Simultaneous Testing on AFTI and the X36 at NASA Dryden. 331
Technical Applications of Computers
Data Analysis
25-5: The FCC of the AFTI F-16. 331
25-6: F-16 Simulation in Straight and Level Configuration. 331
25-7: Flight Control Computer. 331
25-8: FCC as Classic Feedback Control System. 331
25-9: Analogies Between FCCs and the G-H Block Diagram. 333
25-10: Negative Feedback Control. 334
25-11: Transfer Functions of the AFTI FCC. 334
25-12: Feedback Control with an Inner Loop. 334
CHAPTER 26
Predicted versus Measured.
335
26-1: Dr. R.A. Millikan’s, the Nobel Prize winning physcist, “ultimate truth”. 336
26-2: Proceedure of “Parameter Estimation”. 337
26-3: NASA Test Reports Show a Trend of 1 Calculated and 3 Measured. 337
26-4: Predicted versus Measured in Physics Lab Experiments. 337
26-5: Motion and Analysis. 338
26-6: Program to Calculate Cl, Cd, and Cm. 338
26-7: Analysis of Flight Data from the AFTI/F-16. 338
26-8: MATLAB Program to Calculate Aerodynamic Derivatives. 340
26-9: MATLAB Program to Calculate Cl, Cd, and Cm. 340
26-10: Methods for Ordinary Differential Equations. 340
26-11: The Saving and Loading of Data. 340
26-12: Plotting for Graphical Visualization. 340
CHAPTER 27
F-16 Simulation with FORTRAN and MATLAB
341
27-1:
27-2:
27-3:
27-4:
27-5:
27-6:
27-7:
Some Data Analysis of A Test on the F-14. 342
Stability Analysis of This Flight Control System. 342
The Actuator. 343
Dynamic Characteristics of the Aircraft. 344
From FORTRAN to MATLAB. 345
Data and Data Analysis of F-16 Flight Test Mission #3. 346
Variables, ADC, Engine, and Coefficients in Tables. 346
1. State and Control Variables. 346
2. Air Data Computer and Engine. 346
3. Look up Tables for Aerodynamic Derivatives. 346
27-8: Derivatives, State and Force Equations. 346
1. Damping Derivatives. 346
Technical Applications of Computers
11
Data Analysis
2. More on State Equations. 346
3. Force Equations. 346
27-9: Kinematics. 346
27-10: Moments. 346
27-11: Navigation and Outputs. 346
27-12: Functional Simulation Program for the F-16. 346
27-13: Simulations at NASA. 347
27-14: Simulator Study of F-16 Stall Characteristics. 347
352
CHAPTER 28
Flight Tests and the Process.
353
28-1: Prime Differential Equation and the Process. 354
28-2: Process Step #1: The Problem to Calculate and Measure Stability. 355
28-3: Step #2, A Sketch of the Problem with Parameters. 356
28-4: Step #3, Equations to Predict Plane Flight Characteristics. 356
28-5: Step #4, Program the Equations into MATLAB. 357
28-6: Step #5, View and Analyze the Plots in MATLAB. 357
28-7: Step #6, Simulate in MATLAB SIMULINK. 357
28-8: Animation of Flight Test for Step #7. 357
28-9: Flight Test (Step 8). 358
28-10: Data Analysis (Step 9). 358
28-11: Flight Test Report (Step 10). 359
28-12: Motion and Analysis. 359
28-13: Curve Fitting to Test Data. 361
28-14: Airfoil Data. 361
12
Technical Applications of Computers