(Public Domain)
COSY_PAK
(A symbolic COntrol SYstems analysis PAcKage)
Version 0.81
for
Mathematica Version 2.0 and higher
by
C.K.Chen N. Sreenath
Systems Engineering
Case School of Engineering
Case Western Reserve University
Cleveland, OH, 44106-7070
e-mail: sree@veda.cwru.edu
--> Copyright
:Copyright: Copyright 1992 by C. K. Chen and N. Sreenath, Case
Western Reserve University.
Permission to use, copy, modify and distribute this software and
its documentation for any purpose and without fee is hereby granted,
provided that the above copyright notice appear in supporting
documentation, and the name of the Case Western Reserve University,
Case School of Engineering not be used in advertising or publicity
pertaining to distribution of the software without specific, without
prior permission. Case Western Reserve University makes no
representations about the suitability of this software for any
purpose. It is provided "as is" with out express or implied warranty.
--> Acknowledgements
Support from CWRU Information and Network Services - Dr. Ray
Neff, Case Alumni Association, The Lilly Foundation and the Systems
Engineering Department of Case Western Reserve University is
gratefully acknowledged. Special thanks to Brian Evans of Georgia
Tech for letting us use the LaPlace transform and signals packages
which is a part of the Signal Processing Packages :Copyright:
Copyright 1989-1991 by Brian L. Evans, Georgia Tech Research
Corporation.
--> FTP
COSY_PAK is available by anonymous `ftp' from veda.esys.cwru.edu
(Internet No. 129.22.40.9). A sample ftp session is given at the end
of this file.
--> Introduction
This is an unsupported release of COSY_PAK - a COntrol SYstems
analysis PAcKage for symbolic control systems analysis using
Mathematica 2.0 and higher. Classical control systems analysis
and design methods and some modern control systems methods
have been implemented in this package.
This package and the attendant notebooks were developed on a
NeXT (TM) computer (an UNIX based workstation). They have been
used as a supplementary teaching aid along with a standard control
engineering text (Ogata [1991]) for an undergraduate course in
`Control Engineering I' taught at the Systems Engineering Department
of CWRU. In addition to the NeXT, they have also been tested
successfully on Apple Macintosh computers (TM), and, IBM PC's
(TM) running MS Windows(TM). We would be very much interested
to hear from you if you or anybody you know use this software on
platforms not mentioned above. IBM users however will have to
evaluate the notebooks first to visualize the graphics.
Once installed (see below for instructions), this collection of
Mathematica packages can be loaded by any user. Bundled with the
packages are many notebooks ("COSY_Notes") which demonstrate
the functionality of these packages. The notebooks follow a plan of
many fine, standard, undergraduate Control Engineering text books
listed in the references. Examples used in these notebooks have
been collected from the various references given at the end of this
file.
--> Compressed Files
The files that contain a complete set of the COSY_PAK
packages and Notebooks for Mathematica are:
COSY_PAK_08.tar.Z compressed tar file for Unix systems
COSY_PAK_08.hqx compressed hqx file for Macintosh systems
COSY_PAK_IBM_08.zip zip file for the IBM PC running MS-DOS
Once expanded the Mathematica files can also be used on
Macintosh / IBM PC / Unix systems also.
--> Installation of COSY_PAK
In UNIX Command line type the following command:
zcat COSY_PAK_08.tar.Z | tar xvf -
In IBM Command line type the following command:
unzip -o -d COSY_PAK_IBM_08.zip
Note: IBM PC's may limit the directory name characters to eight. In
that event type "unzip -o -d COSY_PAK.zip.
Uncompressing and untarring "COSY_PAK_08.tar.Z" or unzipping
"COSY_PAK_IBM_08.zip" will create a directory called "COSY_PAK_Main".
Once the files are expanded you should see a single directory
"COSY_PAK_Main" containing the following three files, four sub-directories
and their contents:
FILES in "COSY_PAK_Main":
Index - index of files in directory COSY_PAK_Main
README - this file,
README2 - some tips,
SUB-DIRECTORIES in "COSY_PAK_Main":
COSYPAK - contains control tool box packages
SignalProcessing - supporting files from Georgia Tech
Signal Proc. Package (only those files that
COSY_PAK notebooks use is provided, but the
heirarchy of the Signal Proc. Packages is
preserved)
MANUAL - COSY_PAK manual "COSY_MAN" in .ps, .rtf,
.txt, and .wn formats.
COSY_Notes - contains notebooks
FILES in directory "COSY_PAK":
chap1.m chap2.m chap3.m chap4.m chap5.m chap6.m chap7.m
FILES in directory "COSY_Notes":
01_Introduction.ma
02_Math_Model.ma
03_Transient_Response.m
04_Steady_State_Response.ma
05_Root_Locus.ma
06_Freq_Response.ma
07_State_Space.ma
The notebook example files(.ma files) will be under the
"COSY_Notes" directory. In order to install them in the proper place,
move the directories `COSY_PAK' and `SignalProcessing' (with their
contents intact) to the directories that Mathematica can recognize as
indicated below.
~/Library/Mathematica/Packages on a UNIX machine
MY_HardDisk:Mathematica:Packages on an Apple Macintosh
c:\winmath\packages on an IBM PC
NOTE : The files in "SignalProcessing" directory are from the very
fine Signal Processing Packages courtesy Brian Evans of Georgia Institute of Technology. We use their Laplace and Inverse Laplace
transform in our packages instead of the buggy one in Mathematica 2.0.
The complete Signal Processing packages are available in anonymous ftp
site (gauss.eedsp.gatech.edu or IP # 130.207.226.24). In addition
we also use standard signals such as `impulse', `step' and `ramp' from
this package. If you already have the Georgia Tech Signal Processing
Packages installed on your machine, only the COSY_PAK directory need
to be moved.
At the beginning of the "Initialization" cell of each notebook in "COSY_Notes" directory, we list the example about how to make
Mathematica identify the directory:
(* Initialization of Path *)
(* Example For a UNIX machine *)
(*
$Path=Join[$Path,
{"~/Library/Mathematica/Packages"}];
*)
(* Example For an Apple Macintosh *)
(*
$Path=Join[$Path,
{"MY_HardDisk:Mathematica:Packages"}];
*)
(* Example For IBM PC
*)
(*
$Path=Join[$Path,
{"c:\winmath\packages"}];
*)
Change the pathname according to your machine by removing the
Mathematica comment sign `(*' and `)*' before and after `$Path'
setting.
This command make Mathematica recognize the directory
~/Library/Mathematica/Packages on a UNIX machine
MY_HardDisk:Mathematica:Packages on an Apple Macintosh
c:\winmath\packages on an IBM PC
NOTE : If you have `root' privileges and you have a NeXT or a Sun
workstation then the following directory heirarchy is recommended
/LocalLibrary/Mathematica/Packages on a NeXT
/usr/local/math/Packages on a Sun
Do not forget to edit the beginning of the "Initialization" cell of each notebook in "COSY_Notes" directory accordingly.
--> Getting started
After installation, start Mathematica and open the notebooks in
the "COSY_Notes" directory. All notebooks load their own packages.
Navigate in the notebooks and enjoy. IBM users however will have to
evaluate the notebooks to visualize the graphics.
--> Contents of Notebooks
The contents of the notebooks in the "COSY_Notes" directory are
given below.
----------- Begin "COSY_Notes" Contents -----------
NOTEBOOK FILE NAME: 01_Introduction.ma
CHAPTER 1: Introduction to Control Systems
Sections:
Analyticity
Poles and Zeros
Signals
Forward Laplace Transforms
Inverse Laplace Transforms
Differential Equation With Zero-Valued Initial Conditions
Differential Equation With Initial Conditions
-----------
NOTEBOOK FILE NAME: 02_Math_Models.ma
CHAPTER 2: Mathematical Modeling of Dynamic Systems
Sections:
ODE to State Space
Linearization of a Nonlinear System of Equations
State Space to Transfer Function
-----------
NOTEBOOK FILE NAME: 03_Transient_Response.ma
CHAPTER 3: Transient-Response Analysis
Sections:
Time Response Analysis
First order System
First Order System (Step Response vs. Time Const)
Second Order System
Second Order System (Step Response vs. Damping Ratio)
Third Order and Higher Order Systems
-----------
NOTEBOOK FILE NAME: 04_Steady_State_Response.ma
CHAPTER 4: Steady-State Response
Sections:
Routh's Stability
Steady-State Error Analysis
-----------
NOTEBOOK FILE NAME: 05_Root_Locus.ma
CHAPTER 5: Root-Locus Analysis
-----------
NOTEBOOK FILE NAME: 06_Freq_Response.ma
CHAPTER 6: Frequency-Response Analysis
Sections:
Bode Plot Analysis
Magnitude vs. Phase Plot (Nichols Plot)
Polar Plot
Nyquist Plot
Combined Example
-----------
NOTEBOOK FILE NAME: 07_State_Space.ma
CHAPTER 7: State Space Methods
Sections:
Introduction
State Transition Matrix
Time Response Using State Space Methods
Controllability
Observability
Output Controllability
Pole Placement Design
Observer Design
----------- End Notebook Contents -----------
***************************************************************
--> USER RESPONSIBILITIES
We request you to take a few minutes and fill out the
information below and mail it to us by e-mail / FAX / U.S. Mail. This
will help us to keep your abreast of the improvements and release new
versions of COSY_PAK. Suggetsions for improvements are welcome.
-------------------------------cut here-------------------------------
YOUR NAME: ________________________________________
ORGANIZATION: ________________________________________
TITLE: ________________________________________
e-mail: ________________________________________
POSTAL ADDRESS:________________________________________
________________________________________
Comments & ________________________________________
Suggestions: ________________________________________
________________________________________
-------------------------------cut here-------------------------------
Mail this information to :
INTERNET: sree@veda.cwru.edu
U.S. Mail:
Prof. N. Sreenath Tel.: (216) 368-6219
Systems Engg., Crawford Hall FAX: (216) 368-3123
Case Western Reserve Univ.
Cleveland OH 44106-7070
***************************************************************
--> REPORT BUGS
Please report bugs and leave comments to the address above.
Any suggestion for improvements and criticism are welcome.
We will do our best to fix any reported bugs. However, we cannot
fix those bugs that have not been reported to us and those we do not
know of. We would very much apprecite you taking a few minutes to
communicate to us via e-mail / US Mail / Telephone / FAX. This will
help us to release bug-free versions in the future.
***************************************************************
--> Disclaimer and Future Releases
This software is the property of the Case Western Reserve
University. Use this software at your own risk. We make no express
or implied warranty.
The packages and the notebooks can also be made to run under
Mathematica versions 1.2 or lower with modification. We do not
guarantee the outcome.
--> Documentation
COSY_PAK functions are indexed in the files in the
`COSY_MAN'directory according the chapters. Usage is illustrated in
notebooks residing in `COSY_Notes' directory. If your computer does
not support notebooks find a Macintosh computer and acquire MathReader
which is a public domain notebook reader. MathReader will atleast
allow you to peruse notebooks but you will not be able to evaluate
any code fragments.
--> References
Dorf, R. C., "Modern Control Systems", Sixth Edition, Addison
Wesley, New York, 1992.
Fortmann, T. E., and Hitz, K. L., "An Introduction to Linear Control
Systems", Marcel Dekker, 1977.
Franklin, G. F., Powell, D. J., and Emami-Naeini, A., "Feedback
Control of Dynamic Systems", Second Edition, Addison Wesley, New
York, 1991.
Kuo, B. C., "Automatic Control Systems", Sixth Edition, Prentice Hall,
New Jersey, 1990.
Ogata, K., "Modern Control Engineering", Second Edition, Prentice
Hall, New Jersey, 1991.
Phillips, C. L., and Harbor, R. D., "Feedback Control Systems",
Second Edition, Prentice Hall, New Jersey, 1991.
=====================================================================
TYPICAL `ftp' session :
-----------------------
%ftp veda.esys.cwru.edu
Connected to veda.
220 veda FTP server (Version 5.20 (NeXT 1.0) Sun Nov 11, 1990) ready.
Name (veda.esys.cwru.edu:sree): anonymous
Password:
ftp> cd /pub
ftp> binary
ftp> ls
200 PORT command successful.
150 Opening ASCII mode data connection for file list.
COSY_PAK_08.tar.Z
COSY_PAK_IBM_08.zip
Index
README
.places.wmd
COSY_PAK_untar
226 Transfer complete.
78 bytes received in 0 seconds (15.35 Kbytes/s)
ftp> get COSY_PAK_08.tar.Z
200 PORT command successful.
150 Opening BINARY mode data connection for COSY_PAK_08.tar.Z (460822 bytes).
226 Transfer complete.
local: COSY_PAK_08.tar.Z remote: COSY_PAK_08.tar.Z
460822 bytes received in 1.33 seconds (3.38e+02 Kbytes/s)
ftp> quit
221 Goodbye.
***************************************************************
General Words of Wisdom
from
Brian Evans'Signal Processing Packages
:Copyright: Copyright 1989-1991 by Brian L. Evans,
Georgia Tech Research Corporation.
***************************************************************
--> Macintosh Users
Please let Mathematica allocate as much memory as possible.
Conventional wisdom says 8Mb is adequate. You can check the value
by clicking once on the Mathematica icon and select the Get Info
option from the Finder's File menu. It is the number that appears
in the lower left-hand corner of the info window.
--> Warning
A warning about opening some Notebooks under Mathematica 2.0.
The new version of Mathematica changes the storage of PostScript
graphics. PostScript graphics are now stored WITH the 20 kb header that
was "assumed" to be there under Mathematica 1.2. When you open a 1.2
Notebook under 2.0, Mathematica will prepend this 20 kb to each
PostScript graphic and render the graphic. Therefore, those
Notebooks containing many graphics cells will take a long time to
open under Mathematica 2.0. It also means that Notebooks will grow in
size. Some of the signal processing Notebooks will quadruple in size,
thus overwhelming the machine.
--> Suggestion
Please, please, use lower case one-letter symbols as
variables and do not assign values to them. This includes variables
like n, t, x, and y, as well as t1, t2, etc. Use one-letter upper
case variables to represent constants (A, G,...), although Mathematica
reserves I and N and we reserve L and Z.
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.