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-
-
-
- (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_081.tar.Z compressed tar file for Unix systems
-
- COSY_PAK_081.sit compressed sit file for Macintosh systems
-
- COSY_PAK_IBM_081.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_081.tar.Z | tar xvf -
-
- In IBM Command line type the following command:
-
- unzip -o -d COSY_PAK_IBM_081.zip
-
- In Macintosh use program StuffIt 1.5.1 to decompress COSY_PAK_081.sit.
- (StuffIt 1.5.1 is also available in veda.esys.cwru.edu)
-
- 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_081.tar.Z" or unzipping
- "COSY_PAK_IBM_081.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.
-