MINIFp'R FORTRAN PROGRAMMING THROUGH SIMULATION...

MINIFOR: minicomputer real-timeFORTRAN programming through simulation

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Authors Upchurch, James Kimble, 1943-

Publisher The University of Arizona.

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MINIFp'R

MINICOMPUTER REAL-TIME

FORTRAN PROGRAMMING THROUGH SIMULATION

byJames Kimble Upchurch

A Thesis Submitted to the Faculty of the

COMMITTEE ON. COMPUTER SCIENCE

In Partial Fulfillment of the Requirements For the Degree of

MASTER OF SCIENCE

In the Graduate College

THE UNIVERSITY OF ARIZONA

1 9 7 2

STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowersunder rules of the Library,

Brief quotations from this thesis are allowable without special, permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED:

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

Assbqiate Professor of Chemical Engineering

ACKNOWLEDGMENT

The author is sincerely grateful to Professor James Wm. White

for suggestion of the topic and guidance during its development. Many

thanks are extended to Professor John V. Wait for his discussion and

helpful suggestions. The author is also very grateful to the United

States Air Force for allowing him to pursue the degree culminating in

this thesis .while on active duty.

TABLE OF CONTENTS- ■ .* •

Page

LIST OF T A B L E S ................ ..... ........... . . . . ... . vi

LIST OF ILLUSTRATIONS . . . . . . . viil

ABSTRACT . .......... . . . . . . . . . . . x

CHAPTER

1 INTRODUCTION «, . . . . . . . . . 1

Motivation e . e . ............... . » • « » 1An Alternative a . 3Processing Performed . . • .. . , e » . . . » e , 5Restrictions and Limitations , « ..... ....... 7

2 HOW TO USE MINIF^R . . ........ . .... ....... 11

■ Specifying the Program Input a . . . . . . 0. * . 11FORTRAN Subroutines . . » . e.... ....... 12Input Data . . . . 20

Specifying the Processing Desired » , » » . = <, 29Executive Interfaces „ . » e « e . . „ . . . 30Process Input/Output Interfaces 30

Submitting a Processing Request . . . . . . . . 43Processing at The University of Arizona . . 43Processing at Other Installations . . . . . 45

Error Correction and Resubmission . . . . . . . 46Errors in the Input Data ... . . . . . . . . 46Abnormal Termination . . . . . . . . . * . . 46

Requesting Punched Paper Tape SourcePrograms . . . . . . . . . . . . . . . . . . . 52Organizing the Data and Submitting

a Request . . . . . . . . . . . „ . . . . 53CARDTP Diagnostics . . . ......... 56

3 SPECIFIC APPLICATIONS . . . . . . . . . . . . . . . 58

Data Acquisition . . . « . . . . . . . . . . . .. 58Process Control . . . . . . . . . . . . . . . . 63

iv

TABLE OF CONTENTS— Continued

Page

4 SUMMARY AND SUGGESTED FUTURE DEVELOPMENT . . . . . . 99

APPENDIX A: GLOSSARY OF TERMS . . . . . . . . . . . . . . . . . 102

APPENDIX B: MINIF0R. CODING FORMS . . . . . .......... 104

APPENDIX C: INTEGRATION ROUTINES . . . . . . . .......... ". . 118

REFERENCES . . . . . . . . '. _. . . . . . . . ............. 121

LIST OF TABLES

Table Page

1, Program Dimension Limitations . . . . . . . . . . . 10:

20 Program Components of MINIF^R 13

3. Rules for Constructing SUBROUTINE MODEL . . . . . . 15

4. MINIF0R Dead Time Functions . . . . . . . . . . -..o' . 16

5. Data for Stirred-Tank Reactor . ......... . . . 19

6. Instructions for Coding Card 2 . . . . . . . . . . . 23

7. Instructions for Coding Card 3 . . .............. 24

8. Delaying Continuation of a Program,SUBROUTINE WAIT(l,K,M) . . . . . . . . . . . . . . . 31

9. Analog Inputs in a Sequential Order,SUBROUTINE A I S Q W ( I , . . .......... 33

10. Analog Inputs in a Random Order,SUBROUTINE AIRDW(l,J,K,M) . . 34

11. Digital Inputs, SUBROUTINE DIW(l,J,K,M) . . . . . . 35

12. Analog Outputs, SUBROUTINE A0W(I,J,K,M) . . . . . . 36

13. Latching Digital Outputs, SUBROUTINEDOLW(l,j,Kl,K2,M).......... . . . . 37

14. Momentary Digital Outputs, SUBROUTINED0MM(I,J,K,N,M)......... . . . ........... . 38

15. Encoding an Integer Array . . . . . . . . . . . . . 42

16. Decoding an Integer Number .............. 42

17. MINIF0R Input/Output Unit Assignments.......... . 45

18. • -MINIF0R Diagnostics and Fatal Errors . . . . . . . . 47

. . vi . „ '

vii

LIST OF TABLES— Continued

Table Page

19. Typical Structural Changes for APPGM . . . . . . . . 53

20. Input Data for C A R D T P . 54

21. CARDTP Input/Output Unit Assignments . . , . . « . . 54

22. CARDTP Diagnostics . . . . . . . . . . . . . . . . . 57

LIST OF ILLUSTRATIONS

Figure Page

1. MINIF0R Run-Time Structure . . . . . . . . . . . . 8

2. Schematic of Stirred-Tank Reactor . . . . . . . . . .. 17

3. MODEL for Stirred-Tank Reactor . . . . . . . . . . . 21

4. Programming Transducer Characteristics . . . . . . . 27

5. Programming Final Control Element Characteristics . . 28

6. Sample Run Deck for MINIF0R . . . . . . . . . . . . . 44

7. Sample Run Deck for CARDTP . . . . . . . . . . . . . 55

8. Application Program for Chromatograph Analysis . . . 59

9. MODEL for Chromatograph Example . . . . . . . . . . . 65

10. MINIF0R Data for Chromatograph Example . . .. . . . . 66

11. MINIF0R Output’ for Chromatograph Example . . . . . . 71

12. User Output for Chromatograph Example . . . . . . . . 75

13j Application Program for Stirred-Tank Reactor . . . . 79

14. A Position Algorithm for DDC .. . . . . . . . . . . . 80

15. MINIF0R Data for Stirred-Tank Reactor . . . . . . . . 81

16. MINIF0R Output for Stirred-Tank Reactor. . . . . .. . . 89

17. Card 1 - Title and Identification . . . . . . . . . . 105

18. Card 2 - Simulation Specifications . . . . . . . . . 106

19. Card 3 - Hardware Specifications . . . . . . . . . . 107

20. Card(s) 4 - Input Variables . . . . . . . . . . . . 108

21. Card(s) 5 - State/Algebraic Variables . . . . . . . . 109

' - viii .

LIST OF ILLUSTRATIONS-— Continued

Figure > Page

22. • Card (s) 6 - Contact Sensors/On-Off Devices 110

23 * Card (s) 7 - Disturbances . * ............. . . . . . Ill

. 24* Card(s) 8 - Input Variables Delayed . . . . . . . . . 112

25. / . Card(s) 9 - State/Algebraic Variables Delayed „ . . . 113

26* Card(s) 10 - Transducer Characteristics forOutput Variables Measured .. . . . . . . . . . . . . 114

27. Card(s) 11 - Transducer Characteristics forInput Variables Measured . . . . . . . . . . . . . . . 115

28* Card(s) 12 - Final Control Element Characteristics . . . . . . . . . . . . . . . . . . . . . . 116

29* Card(s) 13 - Pulse Outputs c . * . 117

ABSTRACT

This thesis.described MINIF0R, a batch process system for de

bugging 9 developing, and updating real-time FORTRAN IV programs. The

system is processed off-line on a large computer system where exten

sive compiler diagnostics and debugging aids can be utilized. Avail

able with the system is a card-to-tape conversion program which

produces FORTRAN IV source programs in ASCII code on paper tape with

user specified parity. The system aids minicomputer program develop

ment in real-time data acquisition and process control applications

which have a minimum input/output configuration of paper tape and tele

type. However, users with additional peripherals and storage may still

find MINIFffe real-time simulation features attractive for use in both

industrial and academic environments.

The real-time structure of MINIF0R is realized by FORTRAN simu

lation of the functions of both a real-time clock and a process input/

output interface. MINIF0R uses the process input/output interface

standards established by the Fifth Workshop on Standardization of In

dustrial Computer Languages.

Since both MINIF/R and the card-to-tape conversion program are

coded in ANSI FORTRAN IV, the MINIF/R system is essentially large

machine independent. Jobs can be processed on most large general

purpose computer systems.

x

CHAPTER 1

INTRODUCTION

The phenomenal growth of the minicomputer’ industry in the last

decade has resulted from the continuing decrease in the cost of com

ponents. . Progress in the semiconductor and memory technology fields

has been the primary contributor, reducing minicomputer main frame cost

significantly. A leading minicomputer manufacturer recently advertised

(5) that in 1965 one of his models cost $18,000, and to-day a more reli

able line of the same model costs only $4,000. Each of 77 minicomputer

models surveyed by' Murphy (14) was available in the $2,000 to $23,000

price range. This price included a standard processing unit, basic

memory, and occasionally included as standard equipment a teletype, low

speed paper tape read-punch, and real-time clock. This low cost has

now made installation of a small computer very attractive, whereas

previously computer-based alternatives to conventional data acquisition

and control systems were uneconomical. Minicomputer annual shipments

are forecast by Kaenel (8) to grow from 6,000 units in 1969 to 40,000

units by 1975* Approximately half of these units will require real-

time capabilities for data acquisition and process control applica

tions.

. . Motivation

Each minicomputer is programmable in its own assembly language.

Thus, programs developed on one machine are in general not transferable

2

to another machine without extensive modification. While the•existence

of emulator and translator programs does ease assembly language program

ming, Williams (19) has shown that their use is restricted to the as

sembler mode of programming where the minicomputer to be programmed is

emulated on another computer of the same manufacturer, While assembly

language is more efficient from the standpoint of memory requirements

and execution time, the advantages are decreasing as minicomputer main

frame costs continue to drop. This is especially true in areas where

memory requirements or timing considerations are not critical„ In the

early stages of system development companies such as General Electric,

Honeywell, and Westinghouse, as reported by Jarvis (7), Mensh and Diehl

(10), and Roberts (15), respectively, found standard FORTRAN IV inade

quate for real-time applications, However, because FORTRAN had such

influence in the engineering community and had become, in effect, a de

facto standard, these companies as well as others included extensions

to basic FORTRAN IV to facilitate real-time programming in a compiler

level language.

Standardization for some of these extensions has been proposed

by the FORTRAN Committee of the Workshop on Standardization of Indus

trial Computer Languages (ll). The Instrument Society of America (ISA)

accepted these extensions recently (12), Pressure for vendor follow-

through must be gene-rated by user demand as well as ISA publication of

these new real-time standards.

■ Efficiency of real-time FORTRAN program development suffers on

a small computer for several reasons. Efficient compiler operation

cannot be realized in less than 8,000 words of core memory. Even at

this level small computer FORTRAN compilers are extremely simple and do

not produce extensive diagnostics as do compilers on large computer

systems. The.classic debugging aid is the run-time memory dump which

prints the core contents at a stage of computation where execution is

unexpectedly halted. However, the memory dump is not practical for

small machines with very limited input/output devices. Spencer, Shep

ard son, and McGowan (16) report that most minicomputers marketed have

available basic program development software consisting of an assembler,

text editor, loader, and an on-line debugging aid. Of the minicomputer

models surveyed by Murphy (14), 54 had FORTRAN compilers. Program de

velopment on a minimum machine configuration of paper tape and teletype

is awkward and time consuming even with the software aids previously

mentioned<> If control of a process requires the dedication of a small

computer, then on-line program development, debugging, and updating may

not be practical. . Thus, a need exists for an application system which

allows the user to accomplish most program development and debugging

off-line on a large general purpose machine where extensive compiler

diagnostics and debugging aids can be utilized.

An Alternative

This thesis describes an application system that can be used

off-line for program development, debugging, and updating of real-time

FORTRAN IV programs. The system, hereafter called MINIF0R, is envis

aged as an aid in minicomputer real-time data acquisition and process

control applications which have a minimum input/output configuration of

paper tape and teletype. Available with the system is a card-to-tape

conversion program which produces FORTRAN IV source programs in ASCII

(American Standard Code for Information Interchange) code on paper

tape. Options are available for requesting non, even, or odd parity.

tapes. The source program can be transported to the minimum configur

ation small computer for utilization in an actual real-time applica

tion.

Since MINIF^R and card-to-tape conversion program coding is in

ANSI (American National Standards Institute) FORTRAN IV, the MINIF0R

system is essentially large machine independent. Jobs can be processed

on most large general purpose computer systems,

MINIF0R can be utilized by industry to develop and update real

time programs for data acquisition and process control applications.

The system is well suited for applications in laboratory automation,

data acquisition, and process control of chemical and petroleum proc

esses. Also, the real-time simulation features of MINIFjZfR. are appeal

ing for use as an educational tool. The student can use MINIF0R to

investigate or specify a process control strategy for a designated

mathematical model of a process. In laboratories where desired unit

operations equipment is not available, MINIF0R can be used in a data

acquisition application to emulate the process operation needed. In

well equipped laboratories where a.minicomputer and interfacing hard

ware are available, the student can utilize MINIF^R to develop real

time programs to be used in laboratory exercises without the need to

test the program under development against the actual process.

Processing Performed

MINIFgfe processes an application subroutine and any other sub

routines required by the application subroutine. The processing per

formed must be described by a subroutine rather than a main program

because MINIF0R is structured to read and analyze all input data prior

to relinquishing control to the userTs application subroutine, In

order to debug and develop a real-time application subroutine off-line

the application subroutine, .must have a process or environment upon

which to operate. Further, the operation must be on a real-time basis

and include communication to and/or from the process through interfac

ing hardware. This is accomplished within MINIF/R by simulation. The

user provides a model of the process, an application subroutine to op

erate on the process, and input data to describe the simulation and

hardware specifications, The process description may be wholly alge

braic using FORTRAN coding, or it may include dynamic process simula

tion capability using first-order ordinary differential equations in

state variable form. To solve such a dynamic model, MINIF/R calls on

one of three system integration routines selected by the user to update

the process simulation as required by the pseudo real-time input/output

subroutines. MINIF/R allows the user to program disturbances in the

form of step changes entering the process at specified times. Also,■

dead time can be inserted for selected variables. To increase the rel

evance of the simulation, transducer and final control element charac

teristics must be specified as part of the input data.

6

The real-time structure of MINIF0R is realized by simulating

with FORTRAN subroutines the functions of both the real-time clock and

process input and output assembly language handlers. The system emu

lates input of process analog signals to an analog-to-digital converter

(ADC) and output of analog signals to the process from a digital-to-

analog converter (DAC). The emulation of a digital input channel al

lows the position of contact sensors or on-off devices to be monitored.

Emulation of a digital output channel allows digital outputs requiring

a momentary signal and digital outputs which are latched in either the

set or reset state. User.control of real-time execution is accom

plished by simulating delay of execution in a program for a specified

time. To control program execution and communicate with the process

the user must issue calls to system subroutines which perform the de

sired function. These calls conform to the standards established by

the Fifth Workshop on Standardization of Industrial Computer Languages

(11) and accepted by ISA (12).

Real-time processing is accomplished by using the forementioned

calls to input and/or output information from/to the process. The user

may, as in data acquisition systems, interrogate the process for alarm

conditions or operate.on process data as in a chromatograph data analy

sis. If the application is closed-loop process control, then manipu

lated variables are computed and output to the process in the form of

analog signals or digital outputs. MINIF0R is structured to implement

user supplied control algorithms for various types of control, such as

Direct Digital Control (DDC) or Supervisory Set Point control (SSP).

7

Figure 1 illustrates the information paths connecting user sup

plied subroutines and system routines in a simulation run.

Restrictions and Limitations

The restrictions and limitations presented here depend largely

upon the type of processing performed by the user’s application sub

routine and the complexity of the simulation and, hence, may not con

cern all users. Within these limitations MINIF0R can be utilized as a

tool for debugging and developing real-time FORTRAN IV source programs.

MINIF0R is not a translator/compiler program which produces as

sembly language or object code for the user’s minicomputer. Rather,

MINIF0R produces ANSI FORTRAN IV source code. Individual computer

manufacturers provide compilers, with exceptions or extensions to the

ANSI standard due to software or hardware constraints„ Alternatively,

the manufacturers.may provide features not included in ANSI FORTRAN TV.

Therefore, the FORTRAN code used to describe the process and the appli

cation subroutine must be compatible with the batch process machine on

which the MINIF0R application is processed. Further, the application

subroutine must also be compatible with the minicomputer used in the

actual real-time application.

To process a MINIF0R application the user’s application sub

routine must issue calls to ISA standard input/output subroutines im

plemented by MINIFgfR. To process MINIF0R paper tape source programs

on the user’s minicomputer these standard subroutines must also be

available as assembly language handlers on the user’s installation.

^ START ^

. INITA L INCK < ----r ' "

INPUT DATA

< M IN IF 0R ><:-----

APPGM

WAIT

3 T E :l____

ANALYSISOFDATA

AISQW

CLOCK

AIRDW DIM

ANA IN

STOP ^

DOLW

ENCODE

DOMW

DECODE

OUTPT HISTRY UPDATE DEADT

MASSSTORAGE

DUMMY SECRK FOURK

AOW

ANAOUT

CALAH

TIMEHISTORY

YDLYMODEL

ADLYDECOMP SOLVE

Figure 1. MINIF0R Run-Time Structure.

9

The state variable concept is used here for dynamic representa

tion of the process. State equations describing dynamic systems are

restricted to first-order ordinary differential equations.

Not currently implemented is the simulation of priority inter

rupts originating from either the minicomputer operating system or from

the process.

Dimension limitations in MINIF0R are illustrated in Table 1.

MINIF0R can be redimensioned for larger simulations by making minor

changes in the system source code.

Digital input/output registers must not exceed 18 bits in

length. Again, this can be changed with only minor modification of the

source code.

10

Table 1* Program Dimension Limitations„

Limitation Dimension

Input variable 65

Input variables delayed 25

State/algebraic variables 25

State/algebraic variables delayed 25

Output variables . 25

Disturbances 5

. Digital inputs 64

ADC channels 50

Latching digital outputs 64

Momentary digital outputs 40

DAC channels 25

CHAPTER 2

HOW TO USE MINIF0R

Real-time FORTRAN IV program development through simulation is

accomplished in two phasese. First, MINIF0R and its support subroutines .

are used to debug and develop application subroutine(s)„ Generally,

minor changes must be made to the application subroutine(s) prior to

requesting paper tape source programs0 Typical changes include modify

ing the program header card* inserting a desired common block, and im

plementing other changes required for the actual application. The

system could be expanded through development of a simple translator to

extract the program header card and to insert a desired common block

but only at the cost of portability and increased storage requirements.

Therefore, this feature was excluded from this version of MINIF0R. The

second phase of processing requests paper.tape source programs using '

the card-to-tape conversion program.

Specifying the Program Input

There are two categories of program input: FORTRAN subroutines

and input data. User supplied FORTRAN subroutines must include a sub

routine for modeling the user1s real-time process and an application

subroutine for interrogating and/or controlling the process. Input

data consist of specifications for describing and controlling the simu

lation, hardware descriptions, and transducer and final control element

characteristicso

12

FORTRAN Subroutines

All user supplied FORTRAN subroutines must contain a subroutine

name that does not coincide with system subroutine names. Table 2 sum

marizes all system FORTRAN subroutines and their function.

The real-time process is simulated using a subroutine which

must be named MODEL; the process may be described by a single subrou

tine or by several subroutines nested within MODEL„ A user selected

system integration routine calls MODEL many times during a simulation

run. MINIF0R allows for the description of two types of.multivariable

nonlinear models. Algebraic models are described by

Y = FCA, ■ Y, T) (1)

and dynamic models are described by

YDOT = £(A, Y, T) (2)

where

= a vector containing algebraic variables for algebraic simulations and state variables for dynamic simulations.

A_ = an input vector containing constants5 manipulated variables, and variables to be disturbed.

YDOT = A derivative vector containing first-order derivatives of state variables.

, T = independent variable time, seconds.

F_ and G_ = functions for algebraic and dynamic simulations,respectively.

Any state of algebraic variable, which is sampled by the ADC, must be

placed in an output vector defined by

Table 2. Program Components of MINIFjZfR.13

Programname Description

MINIF0R MINIF0R ExecutiveADLYa Recall values of designated A variablesAIRDWb , Input random analog points from ADCAISQWb Input sequential analog points from DACANAOUT Apply,DAC output signal to a final control elementANA IN Generate a transducer output signal for input to ADCAOWb Output random analog points from ADCCALAH Third-order Calahan integration ruleCLOCK Maintain simulation time; terminate programDEALT Store values of designated variables for dead timeDECODEb Decode an integer number into an array of ones and zerosDECOMP Decompose a matrix by triangularizationDIWb • Determine state or position of contact sensors and on-off devicesDOLWb Output latched digital signals in the set or reset stateDOMWb Output momentary digital signals in the form of pulsesDUMMY Dummy integration routine for use with algebraic modelsENCODEb Code an array of ones and zeros into an integer numberFOURK Fourth-order Runge-Kutta integration ruleHISTRY Store time historyINCK Read input data and perform analysisINITAL Initialize program variables in COMMONSOLVE Solve a triangularized matrixUPDATE Supervise integration, enter disturbances, and store varia™

• bles for dead time and time historyOUTPT . Output time historyWAITb Delay any further execution for a specified timeYDLYa Recall values of designated Y variablesAPPGMC Application subroutineMODEL0 Simulates real-time process

unction subprograms which the user may call in MODEL, ^Subroutines which the user may call in APPGM, ^Subroutines which the user must provide.

where _C_ is the output vector and _H is a function. The position of two-

state devices, such as contact sensors or.on-off devices, is described

by a vector IRELAY. A vector element with a value of one represents a

closed contact or a device that is on, while a vector element with a

value of zero represents an open contact or a device that is off. Po

sitions of these devices are monitored on a digital input channel.

FORTRAN statements are used in MODEL to form the vectors.in

equations (l) through (3). Vectors are represented by arrays of the

same variable name. To provide the system with.current values of these

variables, the user must insert the following labeled COMMON block and

DIMENSION statement after the MODEL subroutine header card

COMMON/USER/A, Y, YDOT, IRELAY, C, T-DIMENSION A (65), Y (25), YDOT(25), IRELAY(128), 0(25)

Known functions of time are programmed utilizing the program

variable T. However, the user is cautioned to avoid assigning values

to T, for this is a system function.

Rules governing the construction of SUBROUTINE MODEL are sum

marized in Table 3.

Simulation of dead time by- MINIFffe is accomplished by storing

values for designated Y and A variables. _ Storage of these variables

is supervised by a system subroutine UPDATE. The user accesses "de

layed" values of these variables in MODEL by using two system function

subprograms, YDLY and ADLY. Their use is described in Table 4.

15

Table 3. Rules for Constructing SUBROUTINE MODEL.

Rule Description

1 The subroutine name must be MODEL. If other subroutines are used, then these subroutines must be nested within MODEL.

2 Subroutines simulating the process must contain the following COMMON and DIMENSION statement:

COMMON/USER/A, Y, YDOT, IRELAY,.C, T,DIMENSION A(65), Y(25), YD0T(25), IRELAY(128), C(25)

3 Any FORTRAN statement may be used which is legal on both the batch machine on which MINIF0R is processed and.the process minicomputer.

4 Vectors described in equations (l) through (3) arerepresented by one-dimensional arrays of the same variable name. *

5 T may be used to program known functions of time. The user must not assign values to T.

6 Assignment of variables prior to their usage is a user responsibility.

7 ‘ IRELAY must be used to represent positions of contactsensors and on-off devices. An array element with avalue of one represents a contact closed or a device on; a value of zero represents a contact sensor open or a device off.

8 State or algebraic variables to be sampled by the ADCmust be assigned to an output variable.

9 A RETURN and END statement must be provided.

16

Table 4, MINTF0R Dead Time Functions.

Function Valuereturned Rules

YDLY(l,X) g g = Y(l) at T = 0 if Xg = Y(I) at T - X if T>X

ADLY(I,X) g g = A C l ) at T = 0 if T— X

.Note: X must be specified in seconds

g = a (i ) at T - X if T > X

An example is presented to illustrate how MODEL is constructed

for a real-time process/ In Chapter 3 construction of the application

subroutine and coding of input data is illustrated. This example dem

onstrates a control algorithm to simulate a Direct Digital Control

(DDC) application. The real-time process considered is a stirred-tank

reactor control system described by Coughanowr and Koppel (4). A sche

matic of the process is illustrated in Figure 2. A feed stream, F,

containing reactant A at a concentration of C^ enters tank 1. Reactant

A decomposes in the tanks according to an irreversible first-order re

action. The purpose of the control system is to maintain the concen

tration of reactant A leaving tank 2, C , at a desired value despite

variations of feed composition. This is accomplished by adding a

stream of pure A to tank 1. From the product stream of tank 2 a sample

is continuously withdrawn to a remotely located concentration measuring

element. Dead time for the sample line is 30 seconds. The change in

concentration for the system is represented by two coupled, first-order

17

FeedStream

TankTankPure ProductStream

MeasuringElement

Transmitter

DAC ADCProcessMinicomputer

Figure 2. Schematic of Stirred-Tank Reactor.

18

differential equations where the variables and data for equations (4)

^ 1 "dt" = “C1 + 1 +k1V/F Co + F(l +k1V/F) M (4)

dCo 12 "dt" = "C2 + 1 +kgV/F C1

and (5) are defined in Table 5. Inputs to the process consist of feed

composition and flow rate of pure A into tank 1. The concentration of

A leaving each tank represents a state variable, while the output of

the process is the concentration of A leaving tank 2. The MODEL for

the process is constructed by making the following assignments to pro

gram variables:dCiYD0T(1)

YDOT(2)dc2dt

Y(l) = C1

Y(2) = C2

A(l) = Co

A ( 2 ) = M

Since the effluent of tank 2 is sampled by a measuring element and the

concentration transmitted to the ADC, the concentration of tank 2 ef

fluent is assigned to an output variable. To simulate dead time in the

sampling line, a dead time function for state variables is used. The

output variable is

C(3) = YDLY(2, 30.0)

Table 5. Data for Stirred-Tank Reactor.

Variable Description Value Units

co Concentration of A in feed stream 0.1 lb. moles A/ft3

ci Concentration of A in tank 1 effluent 0.0733 lb. moles A/ft3

C2 Concentration of A in tank 2 effluent 0.0244 lb. moles A/ft3

.M Flow rate of pure A into tank 1 0.0166 lb. moles/sec

V Volume of each reactor 300.0 ft3 .

F Feed rate to tank 1 1.66 ft^/sec

Time constant for tank 1 120.0 sec

^2 Time constant for tank 2 60.0 sec

kl Reaction rate constant for tank 1 0.00278 —1sec

k9 Reaction rate constant for tank 2 0.01112 . "1sec

20

SUBROUTINE MODEL for the stirred-tank reactor is illustrated in Fig

ure 3.

The user's application subroutine determines the type of real

time processing performed by the simulation run. Details for con

structing this subroutine are presented in the section on Specifying

the Processing Desired.

Input Data

The amount of data input is dependent upon the type of process

ing performed and the complexity of the simulation. Data are input us

ing the MINIF0R Coding Forms illustrated by Figures 17 to 29 in Appendix

Be Do not remove these forms from this thesis. Instead, make copies

as needed. Each form represents a single card to be coded. Cards 1

through 3 must be supplied for all simulations. Each card is discussed

in detail in this section.

Cards 1, 2, and 3 consist of simulation and hardware specifica

tions. Default conditions exist for many items, and processing is at

tempted if at all possible. An analysis of the data input on these

cards is made by the system. Results are printed with error conditions

and comments noted. If fatal errors are present, the program is ter

minated for error correction and resubmission. If fatal errors are not

present, a card inventory is printed to identify the order and number

of each type of card which the program expects to read.

Card 1 consists of a title and identification which is read in

alphanumeric format and printed at the top of each page of system out

put.

S U B R O U T I N E M O D E LC O M M O N / U S E R / A , Y , Y O O T , I R E L A Y , C , TD I M E N S I O N A ( 6 5 ) , Y ( 2 5 ) , Y D O T ( 2 5 ) , I R E L A Y ( 1 2 8 ) , 0 ( 2 5 )C C H A N G E I N C O N C E N T R A T I O N O F T A N K 1 E F F L U E N TY D O T ( l ) = - ( Y ( i ) / 1 2 Q • ) + ( A d ) / < l # + O e G 0 2 7 3 * 3 0 C # / 1 . 6 6 ) ) / 1 2 3 1 ( ( A ( 2 ) * . 8 / ( 7 . 4 8 * 6 3 . ) ) / ( 1 . 6 6 * ( 1 . * 3 . C G 2 7 8 * 3 0 C . / 1 . 6 6 ) ) ) / 1 2 0 .C C H A N G E I N C O N C E N T R A T I O N O F T A N K 2 E F F L U E N TY D O T ( 2 ) = - ( Y ( 2 ) / 6 0 . 0 ) + ( Y d ) / d . + C . 0 1 1 1 2 * 3 0 , J . / 1 . 6 6 ) ) / 6 3 C A S S I G N O U T P U T V A R I A B L EC N O T E U S E O F D E A D T I M E F U N C T I O N F O R D E L A Y I N S A M P L I N G L I N EC C D = Y d )C (2) = Y (2)C ( 3 ) = Y D L Y ( 2 , 3 0 . 3 )R E T U R NE N D

Figure 3. MODEL for Stirred-Tank Reactor.

22

Instructions for coding Card 2 are presented in Table 6.

Guidelines for selection and integration routine are presented in Ap

pendix C, as well as a caution in using Calahan1s method with time

varying systems. If SUBROUTINE MODEL does not contain state varia

bles, code item 12A as DUM. For dynamic simulations code RK2, RK4, or

CAL for the desired integration routine.

Instructions for coding Card 3 are summarized in Table. 7.

Specification of .items 6A, 6B, and 6C allows the system to simulate

pulse outputs. MINIF0R simulates pulse outputs from a digital regis

ter to a stepping motor/integrating amplifier which outputs a DC sig

nal to a final control element.

Instructions for coding Cards 4 through 13 are summarized on

each coding form. Details are presented here.

Card 4 specifies initial conditions for input variables. In

clude manipulated variables and set points manipulated by final control

elements receiving a DC signal from a DAC; also, include constants if

desired. Initial conditions for input variables manipulated by pulse

outputs are specified on Card 13.

Card 5 specifies initial conditions for state or algebraic var

iables at time T = 0. Initial conditions for these variables are re

quired by the system for storage in the time history and the dead time

‘tables.

Card 6 specifies the initial state or position of contact sen

sors and on-off devices. Code one card to specify the initial state

Table 6„ Instructions for Coding Card 2.

Item Default value Description

1A,B,C 0.0 Simulation time for a run

2A 5.0 Simulation time in seconds between storage of input and output variables by the system for a time history. Time history

- is suppressed if item 2A is 0.0.

2B BLANK Amount of time history to output. Code YES for all input and output variables; code blank for up to first 6 output variables

3 0 Number of output variables assigned in MODEL. 4 0 Number of state or algebraic variables. 5 0 Number of state variables delayed for dead time6 0 Number of input variables7 0 Number of input variables delayed for dead time8 0 Number of disturbances to enter simulation9 0 Number of output variables measured by ADC10 0 Number of input variables measured by ADC

11 0 Number of contact sensors and on-off devices

12A RK4 Integration rule (DUM, RK2, RK4, CAL)12B 0.05 Integration step size in seconds

Table 7e Instructions for Coding Card 30

Item Default value Description

1A 18 Number of bits per word for object machine

IB 16.667 ' Resolution of real-time clock in milliseconds

2 1000.0 ADC scale factor; MINIF0R multiplies signals input to the ADC by this scale factor

3A 0 Number of digital inputs

3B 16 Number of bits per register on digital input channel

4A 0 Number of DAC channels utilized, DAC outputs may be applied to first 25 input variables

4B 1000.0 DAC scale factor; MINIF0R divides the DAC input variable by this scale factor to produce a DAC output signal

5A 0 Number of latching digital outputs

5B 16 Number of bits per register used to output signals latched in either the set or reset state

6A 16 Number of bits per register used to output momentary digital signals (pulses)

6B 0 Number of stepping motors/integrating amplifiers driven by momentary digital output signals

6C 1 Number of pulses generated for one clock count

.25

for digital inputs represented by elements 1 through 64 of IRELAY. If

latching digital outputs are made, code an additional card to specify

the initial state for elements 65 through 128 of IRELAY. The user is

responsible for keeping track of which bit position in the input and

output register is connected to each element of IRELAY.

Card 7 specifies information for programming disturbances in a

simulation. Three items are required to specify one disturbance. The

first item designates the input variable receiving the step change.

The second item gives the time in seconds when the input variable is

changed. Item three specifies the new value of the input variable.

Any input variable may be programmed for a step change, and a single

variable may be changed as many times as desired, providing the number

of such disturbances does not exceed 5.

Cards 8 and 9 specify information for programming dead time in

a simulation. Use Card 8 for input variables and Card 9 for state/

algebraic variables. Two items are required to specify dead time for

one variable. The first item designates the variable. Any of the

first 25 A variables may be designated on Card 8 and any Y variable may

be designated on Card 9. The second item specifies the dead time in

seconds for the designated variable.

Cards 10 and 11 specify the characteristics of transducer out

puts to the ADC and channel connections for these signals. MINIF/R

utilizes these specifications to generate analog signals for designated

measured input and output variables. Inputs on the coding sheets are

discussed from left to right. First, the variable measured is

26

designated; Card 10 is used for output variables and Card 11 for input

variables. Next, the user specifies engineering units. Minimum and

maximum values of the measured variable are next specified; these val

ues correspond to the range of the measured variable for the input span

of the transducer. MINIFj2fR allows for the representation of nonlinear

transducer outputs as described by Marks and Skillern (9). Figure 4

illustrates the technique; the measured variable is M and the signal in

hardware units read by the computer is S. Hardware units could be

milHamperes, volts, or percent of full scale. Nonlinearities are rep

resented by specifying the seven ordinate points, through S- qqj in

Figure 4. The system interpolates linearly between points. If a

transducer output is linear, then specify only and the system

generates and stores S^q through S^q . Finally, the user designates the

channel number on which the variable is measured. Use channels 1

through 25 for measuring output variables and channels 26 through 50

for input variables.

Card 12 specifies channel connections for DAC outputs to final

control elements. MINIF0R utilizes these specifications to change

designated manipulated input variables whenever DAC outputs are used.

Inputs on the coding sheet are discussed from left to right. First,

the input variable manipulated is designated. Next, the user specifies

engineering units for the manipulated variable. MINIF0R allows for the

representation of nonlinear final control element characteristics as

described by Buckley (l). Figure 5 illustrates the nonlinearity of a

valve; .the manipulated variables is represented by A and the signal in

Signal Read by

ADC, Hardware Units

27

100

NonlinearCurve

IdealLinearCurve30

10

100Measure Variable, Engineering Units

Figure 4. Programming Transducer Characteristics.

Manipulated

Variable,

Engineering

Units

28

100

LinearIdealCorve

NonlinearCurve

30

SSSSSSS 1009010Signal Output by DAC, Hardware Units

Figure 5. Programming Final Control Element Characteristics.

29

hardware units from the DAG is S. Nonlinear characteristics are repre

sented by specifying the seven ordinate points, through s^qqj in

Figure 5» The program interpolates linearly between points. If the

characteristics are linear, specify only and S- qq> the system cal

culates and stores through Next, the minimum and maximum DAG

output signals, A^ and A ^ q, are specified. Finally, the user desig

nates the channel number.on which the DAG signal is output.

Proper organization of input variables is important to success

ful execution of the program. Initial program values.for input varia

bles manipulated by DAG outputs are assigned to elements of the A array,

first. This is done using Card 4. If input variables are manipulated

by stepping motors or integrating amplifiers receiving pulse signals,

then the initial level of each input variable is specified on Card 13.

Three items are input for each pulse output. First, specify the ini

tial level of the input variable. Next, specify engineering units for

the input variable. The.third item designates the change, in engineer

ing units, of the input variable per positive pulse.

Specifying the Processing Desired

After the input data have been read and analyzed by the system

routine INCK, MINIF0R calls the user's application subroutine. This

section presents guidelines for successful program implementation and

describes the system subroutines which the user may utilize. The sys

tem subroutines which the user can call are flagged in Table 2.

The user's application may be described by one or more sub

routines, but the control point for the real-time application should be

30

SUBROUTINE APPGM. Typical examples of additional subroutines are con

trol algorithms and output routines for printing alarm conditions or

process reports.

Executive Interfaces

In an actual application the real-time clock is updated by

software or hardware interrupt servicing. In either case the user

would check the time of the real-time clock to determine if it is time

to sample data from the process or perform a desired operation, In

MINIF0R a pseudo real-time clock is advanced when SUBROUTINE CLOCK is

called. The user must never call CLOCK. Instead, the user calls

SUBROUTINE WAIT which delays execution in the calling program for a

specified length of time by issuing a call to CLOCK, incrementing the

program clock, and returning control to the requesting program. The

form of this call is

CALL WAIT (j,K,M) '

where the arguments are described in Table 8. Information for this

table was extracted from Minutes of Fifth Workshop on Standardization

of Industrial Computer Languages (11). WAIT is one of three executive

interface routines accepted by ISA. The other two interface routines,

START and TRNON, are not currently implemented in MINIF^R.

Process Input/Output Interfaces

If real-time processing in a MINIF0R application involves the

input or output of information to or from the process, the user must

issue calls to one of six real-time input/output subroutines. These

31

Table 8„ . Delaying Continuation of a Program, SUBROUTINE WAIT(l,K,M).

Argument Description

ia Specifies the length of time, in units as specified by K, to delay before continuing execution in the requesting program. If the value is zero , or negative, no delay will occur.

Ka Specifies units of time as follows:.

0 - Basic counts of the system's clock1 - Milliseconds2 - Seconds3 - Minutes

Mb Is set on return to the calling program to indicate the disposition of the request as follows:

0 or less - Undefined1 - Request accepted2 or greater - Request not accepted

aSet by requesting program.

Set on return.

subroutine names and argument lists conform to process input and output

standards established by the Fifth Workshop on Standardization of In

dustrial Computer Languages. By issuing a call to one of these sub

routines the user simulates transferring either analog or digital sig

nals to or from the process. In the actual minicomputer real-time

application these same subroutines must be implemented as assembly

language handlers which issue input/output transfer statements to in

terfacing hardware such as an analog-to-digital converter. In MINIF0R

the functions of these assembly language handlers are simulated byi

FORTRAN subroutines having identical subprogram names and argument

lists. Tables .9 through 14 summarize the subprogram names and argument

lists for these standard input and output interfaces. The information

in these tables was extracted from the Minutes of the Fifth Workshop on

Standardization of Industrial Computer Languages (11).

Standard input and output interfaces established by the Fifth

Workshop allow for two forms. The first form accommodates executive

systems which permit overlapped input/output and processing; the second

form accommodates executive systems which suspend execution in the re

questing program until the process input or output is completed. The

second form is flagged by the addition of a W as the last letter in

the subroutine name. MINIF0R accommodates only the second form. If

the minicomputer executive system requires use of the first form, then

prior to requesting punched paper tape source programs the ’W 11 in the

subroutine name should be dropped.

33

Table 9. Analog Inputs in a Sequential Order, SUBROUTINE AISQW(l,


ia Specifies the number of analog points to be input.

ja Specifies terminal connection data of the first analog point to be input. Specific information relevant to construction of this.argument must be provided by the vendor since various types of analog~.to~digital converters are available.

Kb Designates a one-dimensional [integer] array into which the converted values are stored.

Mb Indicates the disposition of the request as follows:

0 or less - Undefined .. 1 - All data collected2 - Operation incomplete3 or greater - Error condition

aSet by the requesting program.

^Set on return.

34

Table 10. Analog Inputs in a Random Order, SUBROUTINE AIRDW(l,


ia Specifies the number of analog points to be input.

ja Specifies terminal connection data for each analog point to be input. Specific information relevant to construction of this argument must be provided by the vendor.

Kb Designates a one-dimensional [integer] array into which the converted values are stored.


0 or less ~ Undefined1 - All data collected2 - Operation incomplete3 or greater - Error condition

aSet by the requesting program*bSet on return,

35

Table 11. Digital Inputs, SUBROUTINE DIW(l,J,K,M).


Ia Specifies the number of digital words to be input.

Ja Specifies terminal connection data for each digital input word. Specific information relevant to construction of this argument must be provided by the vendor since various types of digital inputs are available. The digital input words will be input in the order that they are listed in J.

Kb Designates a one-dimensional integer array into which the requested digital input values are stored. For every closed contact input or logi^ cal input, "one" will correspond to a corresponding bit set in the image input.


0 or less - Undefined1 - All data collected2 - Operation incomplete3 or greater - Error condition

aSet by requesting program.bSet on return.

36

Table 12. Analog Outputs, SUBROUTINE AOWCl,


ia . ‘ Specifies the number of analog points to .output.

ja Specifies terminal connection data of the analog output points. Specific information relevant to construction of this argument must be provided by the vendor since various type of digital-to-analog converters are available.

K8 Designates a one-dimensional integer array from which the analog output values are taken.


0 or less - Undefined1 - All data output2 - Operation incomplete3 or greater - Error condition


^Set on return.

37

Table 13. Latching Digital Outputs, SUBROUTINE DOLW(l,J,K1,K2,M).


; la Specifies the number of words of digital output.

Ja Designates terminal connection data for each word of digital output. Specific information relevant to the construction of this argument must be provided by the vendor.

Kla Specifies a one-dimensional integer array whose contents are the image words to be output.

K2a Designates a one-dimensional integer array whose contents define digital output which can be changed by the subroutine. A bit set in the K2 array indicates that the digital output will be changed to a state defined by the corresponding bit position in a corresponding word in Kl.

- Mb ,. Indicates the disposition of the request as follows:

0.or less - Undefined1 - All output accomplished2 - Operation incomplete3 or greater - Error


Set on return.

38

Table 14. Momentary Digital Outputs, SUBROUTINE DOMW(l,J,K,N,M).


■ ia Specifies the number of digital output words.

ja Specifies terminal connection data for each word of output; information relevant to the construction of this argument must be provided by the vendor.

Ka Specifies a one-dimensional integer array whose contents are the image words to be output.

Na Specifies the duration measured in basic system clock counts that the outputs are to remain set. If the computer system on which the subroutine is run does not allow selection of duration5 this . argument is ignored.


0 or less - Undefined1 - All output accomplished.2 - Operation incomplete3 or greater - Error


^Set on return.

39

Analog inputs are directed to an analog-to-digital converter

(ADC); MINIF^R allows addressing up to fifty channels. Analog points

are input sequentially using the following call:

CALL AISQW(I,J,K,M)

where the arguments are described in Table 9. Alternatively5 analog

points are input randomly using

CALL AIRDW(I,J,K,M)

where these arguments are described in Table 10. Argument J is an in

teger array of channels to be converted.

A digital input is connected to one bit position of an m bit

digital input register. The entire register is then input as a single

word. MINIF0R allows addressing of up to n digital input registers

such than mxn 64.

The user is responsible for setting bit positions of a register

by assigning one or zero to the corresponding element of IRELAY. Ele

ments 1 through 64 of IRELAY are reserved for digital inputs which are

then accessed by the following call:

CALL DIW(I,

where these arguments are described in Table 11.

Analog outputs are directed to a digital-to-analog converter

(DAC); MINIF0R. allows for addressing up to twenty-five channels. Ana

log points are output randomly by issuing the following call:

40

CALL A0W(I,J,K,M)

These arguments are described in Table 12,

Latching digital outputs in either the set or reset state are

made by digital output registers where a full register of bits is out

put* A register output produces a discrete signal to a two-state de

vice for each bit. MINIFffe allows addressing of up ton latching output

registers where mxn fz 64, and again m is the .number of bits per register

specified in the input data. Latching digital outputs are directed by

the system to elements 65 through 128 of IRELAY by using the following

call:

CALL D0LW(I,J,K1,K2,M)

where the arguments for this call are described in Table 13. The user

is responsible for keeping track of the connections between bit posi

tions of an output register and their corresponding elements of IRELAY.

Momentary digital outputs are made by digital output registers

where a full register of bits is output. A register output produces for

each bit set a pulse signal which can drive a stepping motor or inte

grating amplifier. MINIF0R allows addressing up ton output registers

which have m bits per register such that mxn/2 40. MINIF0R uses two

bits per function; one to increment and one to decrement each stepping

motor or integrating amplifier. An UP bit produces a positive pulse to

increment, while a DOWN bit produces a negative pulse to decrement.

The UP bits are maintained in even numbered registers. For example, if

there are 16 bits per output register, then register 1 contains the UP

41

bits for stepping motors/integrating amplifiers 1 to 16, while regis

ter 2.contains the DOWN bits for stepping motors/integrating amplifiers

1 to 16. Each stepping motor or integrating amplifier outputs a DC

signal to a final control element which increments or decrements input

variables specified on Card 13. The user is responsible for keeping

track of which input variable is manipulated by each bit position of an.

output register. Pulse outputs are made using the following call:

CALL D0MW(I,J,K,N,M)

where the arguments for this call are described in Table 14.

M1NIF0R provides two subroutines to assist the user for process

ing digital input/output words. These FORTRAN callable subroutines,

ENCODE and DECODE, are used for encoding/decoding an integer number

representing a word into/from an array of ones and zeros. Such an array

is used to simulate bit positions "SET" or "RESET" within a word. An

alternative to using ENCODE and DECODE is to provide assembly language

routines for bit manipulation. When using ENCODE the form of the call

is ■ ■

CALL ENCODE(NUM,IDATA,NBIT)

where these arguments are described in Table 15. When using DECODE the

form of the call is

CALL DECODE(NUM,IDATA,NBIT)

where these arguments are described in Table 16.

The user should understand two restrictions regarding use of

•ENCODE and DECODE. First, when integer arrays of ones and zeros are

42

Table 15, Encoding an Integer Array„


NUMa An integer number representing an image word produced from the integer array of ones andzeros.

IDATAb An integer array of ones and zeros to be coded into an integer number.

NBITb Specifies the number of bits per image word.

aSet on return.

^Set by the requesting program.

Table 16, Decoding an Integer Number.


NUMa . An integer number to be decoded into an integer array of ones and zeros.

IDATAb An integer array of ones and zeros produced from decoding NUM.

NBITa Specifies the number of bits per image word.

Set by the requesting program.

Set on return.

43

processed by the system, the lowest numbered element of the integer ar

ray corresponds to the most significant bit of the word. Secondly,

since the corresponding argument for IDATA in ENCODE and DECODE is di

mensioned to 18, the user must dimension IDATA to 18 in his application

subroutine. This restriction is imposed because some compilers require

that an array passed as an argument must be equally dimensioned in the

requesting program as in the program being called.

Submitting a Processing Request

Program components comprising MINIF0R are stored'in both source

and object form on magnetic tape at The University of Arizona Computer

Center. Prospective users external to The University of Arizona should

contact the Chemical Engineering Department concerning access to the

system.

Processing at The University of Arizona

Processing .on campus is performed on the University Computer Cen

ter's Control Data Corporation 6400 under the SCOPE 3.3 operating sys

tem. A sample run deck with control card sequence is illustrated in

Figure 6. The TP parameter is required on the Job Card for the system

tape. Most jobs can be processed .in less than 70,000^ words of central

memory. Under the present job priority structure, a central'memory re

quest of greater than 70,000^ increases turnaround time to one day.

The job name, billing number, and MINIF0R system tape number must be

specified by the user.

JOBNAME,TP1,CM70000,BNYYYYYYYY.

REQUEST(TAPE1,HI,RO) MTAPE

REWIND(TAPE1)

C0PYBF(TAPE1,MINI)

UNLOAD(TAPE1)

FTN(B=USER)

LOAD(MINI)

LOAD(USER)

EXECUTE(MINIF0R)

SUBROUTINE MODEL

SUBROUTINE APPGM

Other user supplied FORTRAN subroutines

MINIF0R input data cards

Optional input date read by user subroutines

6-7-8--9 Card

7-8-9 Card

y//

/

7-8-9 Card

Figure 6. Sample Run Deck for MINIF0R

45

Processing at Other Installations

Since all MINIF0R coding is ANSI FORTRAN IV, the program is es

sentially machine independent and can be processed on most computers

with sufficient memorye Compilation of MINIF0R, without APPGM and

MODEL, on a GDC 6400 produces object code requiring 50,000g words,

where one real variable is stored in one 60-bit word. Processing on

smaller systems can be realized by overlaying sections of MINIF0R.

This will require modification of the source code. The system requires

a mass storage device for temporary storage of the time history while a.

job is being processed. Data are transmitted to/from this device using

an unformatted WRITE and READ statement. Prior to program termination

a REWIND is executed, and the time history is printed. Disk or drum

may be used for temporary storage rather than magnetic tape if the in

stallation operating system permits application of REWIND to random ac

cess files.

MINIF0R input/output statements have variable equipment unit

numbers which are passed through COMMON to all system subroutines.

These unit numbers are initialized by subroutine INITAL prior to read

ing input data. The assigned unit numbers are listed in Table 17.

Table 17. MINIF0R Input/Output Unit Assignments.

Unit variable Assigned value Input/output equipment

ICDRD 2 Card reader

IPR 4 Printer

ITAPE 7 Mass storage device

46

Users at other installations wishing to use different input/

output unit assignments should change the assignment of the unit vari

able in SUBROUTINE INITAL and change the MINIF0R main program header

card.

Error Correction and Resubmission

MINIF0R provides diagnostics to facilitate error correction and

resubmission. Diagnostics are printed when data are input and default

values are assigned. Fatal errors detected by the pseudo real-time •

input/output subroutines and the implicit Calahan integration routine

abort the job. All MINIF0R diagnostics and fatal errors are summarized

in Table 18.

Errors in the Input Data,

If the program is terminated after Cards 1 through 3 have been

processed, then fatal errors have been detected. System printout of

the data analysis identifies the fatal error for correction and job

resubmission. If there are no fatal errors, then a card inventory is

printed and the remaining input data cards are read and processed. If

an error has occurred while reading Cards 4 through 13, then utilize

the card inventory to identify cards out of order and extra or missing

cards.

Abnormal Termination

The argument list of the pseudo real-time input/output sub

routines identifies the number of words and channel number for each

word to be transferred. If an attempt is made to transfer too many

Table 18. MINIF0R Diagnostics and Fatal Errors.

Message Error condition/comment Correction

SIMULATION TIME NOT SPECIFIED

FREQUENCY OF MINIF0R OUTPUT— SUPPRESSED

FREQUENCY OF MINIF0R OUTPUT— .GT. SIMULATION TIME RESET BY PROGRAM

Simulation time not given. Fatal.

System time history. suppressed.

System will never have an opportunity to store variables.

Resubmit with simulation time specified.,

None; user has supplied his own output routine.

Reset by the system to provide 10 output points.

NUMBER OF OUTPUT VARIABLES— EXCEEDS PROGRAM LIMITS

NUMBER OF INPUT VARIABLES— EXCEEDS PROGRAM LIMITS

NUMBER OF INPUT VARIABLES DELAYED— EXCEEDS PROGRAM LIMITS

INTEGRATION STEP SIZE— NOT , SPECIFIED DEFAULT ASSUMED

INTEGRATION STEP SIZE— RESET BY PROGRAM

NUMBER OF BITS PER WORD— NOT SPECIFIED DEFAULT ASSUMED

Dimension limitation for output variable exceeded. Fatal,

Dimension limitation for input variable exceeded. Fatal.

Dimension limitation for input variables delayed. Fatal.

Integration step size not given.

Integration step size greater than output frequency.

Number of bits per word for object machine not specified.

Reduce number output variables. Resubmit.

Reduce number input variables. Resubmit.

Reduce number input variables delayed. Resubmit.

Default of 0.05 assumed.

Step size reset to one hundredth of output frequency.

Default of 18 assumed.

Table 18. MINIFgfR Diagnostics and Fatal Errors.— Continued

Message Error condition/comment . Correction

NUMBER OF BITS PER WORD— EXCEEDS PROGRAM LIMITS

CLOCK COUNT, MILLISECONDS— NOT SPECIFIED DEFAULT ASSUMED

FATAL ERRORS FOUND IN PROGRAM INPUT, PROGRAM TERMINATED

INTEGRATION STEP SIZE RESET BY PROGRAM TO—

NUMBER OF STATE/ALGEBRAICVARIABLES— EXCEEDS PROGRAM LIMITS

NUMBER OF STATE/ALGEBRAIC VARIABLES DELAYED— EXCEEDS PROGRAM LIMITS

NUMBER OF DISTURBANCES— EXCEEDS PROGRAM LIMITS

NUMBER OF DISTURBANCES— INSUFFICIENT INPUT VARIABLES

Number of bits per word for object machine greater than 18. Fatal.

Resolution of real-time clock not specified.

Fatal errors are present in input data Cards 1-3.

Accuracy of dead-time simulation affected by step size which is too large.

Dimension limitation for state/algebraic variables exceeded. Fatal.

Dimension limitation for state/algebraic variables delayed exceeded. Fatal.

Dimension limitation for disturbances exceeded. Fatal.

An input variable is not available for step change. Fatal.

Reduce number of bits per word if possible. If not, change program restriction.

Default of 16.667 milliseconds assumed.

Correct errors and resubmit.

Program resets step size to one-tenth of smallest dead time.

Reduce number of state/algebraic variables. Resubmit.

Reduce number of state/algebraic variables delayed. Resubmit.

Reduce number of disturbances, Resubmit.

Provide input variable for disturbance. Resubmit.

oo

Table 18, MIN1F0R Diagnostic and Fatal Errors.-— Continued

Message Error condition/comment Correction

NUMBER OF CONTACT SENSORS/ ON-OFF DEVICES— EXCEEDS,PROGRAM LIMITS

INTEGRATION RULE NOT SPECIFIED FOURTH ORDER RUNGE-KUTTA, DEFAULT ASSUMED

NUMBER OF CHANNELS UTILIZED— EXCEEDS PROGRAM LIMITS

SCALE FACTOR, HARDWARE UNITS— NOT SPECIFIED DEFAULT ASSUMED

NUMBER OF DIGITAL INPUTS — EXCEEDS PROGRAM LIMITS

NUMBER OF DIGITAL OUTPUTS EXCEEDS PROGRAM LIMITS

NUMBER OF BITS PER REGISTER— NOT SPECIFIED DEFAULT ASSUMED

Dimension limitation for sensors/on-off devices exceeded. Fatal.

Integration rule for dynamic simulation not specified.

Dimension limitation for number of ADC or DAC channels exceeded. Fatal.

Scale factor for ADC and DAC not specified.

Dimension limitation for number of digital inputs exceeded. Fatal.

Dimension limitation for latching outputs exceeded. Fatal.

Number of bits per register for digital input or output channels not specified.

Reduce number of contact sensors/on-off devices. Resubmit

Default of RK4 assumed.

Reduce number of ADC inputs or DAC outputs. Resubmit.

Default of 1,000 assumed.

Reduce number of digital inputs and resubmit.

Reduce number of latching digital outputs and resubmit.

Default of 16 assumed.

\o

Table 18. MINIF0R Diagnostic and Fatal Errors. -Continued

Message Error condition/comment , Correction

NUMBER OF BITS PER REGISTER— EXCEEDS OBJECT MACHINE BITS

NUMBER OF PULSE OUTPUTS— EXCEEDS PROGRAM LIMITS

NUMBER OF CHANNELS TO BE CONVERTED BY ADC OUT OF RANGE, PROGRAM TERMINATED BY SUB- ROUTINE AISQW (AIRDW)

SPECIFIED CHANNEL NUMBER OUT OF RANGE, PROGRAM TERMINATED BY SUBROUTINE AISQW (AIRDW)

NUMBER OF DIGITAL WORDS TO BE READ OUT OF RANGE, PROGRAM TERMINATED BY SUBROUTINE DIW

CHANNEL NUMBER OF DIGITAL WORD TO BE INPUT, IS OUT OF RANGE, PROGRAM TERMINATED BY SUBROUTINE DIW

NUMBER OF WORDS OF DIGITAL OUTPUT OUT OF RANGE, PROGRAM TERMINATED BY SUBROUTINE DOLW (DOMW)

Number of bits per register for digital input or output channels greater than object machine word. Fatal. •

Dimension limitation for pulse outputs exceeded. Fatal

Number of analog points to be input exceeds program limit. Fatal.

A channel, which is out of program range, has been addressed. Fatal.

Number of digital words to be input exceeds number of digital registers. Fatal.

A channel number, which is out of program range, has been - addressed. Fatal.

Number of digital words to be output exceeds program limits. Fatal.

Correct number bits per register or number bits per word in object machine. Resubmit.

Reduce number or pulse outputs. Resubmit.

Reduce number of points to be input. Resubmit.

Correct channel number and resubmit.

Correct number of words to be input. Resubmit.


Correct number of digital words to be output and resubmit.

Table 18. HINIF^R Diagnostic and Fatal Errors. — Continued

Message • Error condition/comment. . Correction

CHANNEL NUMBER FOR SPECIFIED WORD OF DIGITAL OUTPUT OUT OF RANGE, PROGRAM TERMINATED

A channel number, which is out of program range, has been addressed. Fatal.


NUMBER OF CHANNELS TO BE CONVERTED BY DAC OUT OF RANGE, PROGRAM TERMINATED BY SUBROUTINE AOW

Number of analog points to be output exceeds program limits. Fatal.

Reduce number of points to be output and resubmit.

CHANNEL NUMBER TO BE CONVERTED BY DAC IS OUT OF .RANGE, PROGRAM TERMINATED BY SUBROUTINE AOW

A channel, which is out of program range, has been addressed. Fatal.


COEFFICIENT MATRIX IS SINGULAR, PROGRAM TERMINATED BY SUBROUTINE DECOMP

Calahan integration method fails because coefficient matrix is singular. Division by zero will occur. Fatal.

Pick another integration method and resubmit.

. 52

words or address a channel number out of range, then a fatal error mes

sage is printed and the program is terminated. If the system output

routine is used, then prior to termination the time history is printed.

The implicit Calahan integration method uses a coefficient ma

trix formed from an identity and Jacobian matrix. Division by zero

will occur if the coefficient matrix is. singular. Subroutine DECOMP

aborts the job if this condition exists.

The time history is output prior to abnormal termination ini-"

tiated by MINIF^R subroutines„ The time history is not output when the

operating system, of the host machine detects a mode error. Examples of

mode errors are storing or. reading data outside of job field length and

performing floating point arithmetic on a variable which is either in

finite or indefinite.

Requesting Punched Paper Tape Source Programs

The card-to-tape conversion program (CARDTP) converts FORTRAN

IV main programs and subroutines into punched paper tape source pro

grams. The program reads a single data card, defining.the parity re

quired and number of programs to be converted, and converts each

character of the program to its equivalent ASCII code for the specified

parity. As each card to be converted is processed, it is printed for.

reverification by the user. ,

If CARDTP is used to convert real-time programs developed uti

lizing MINIF0R, then structural change must be made to these programs

53

prior to processing CARDTP, Some typical changes are illustrated in

Table 19.

Table 19. Typical Structural Changes for APPGM.:

Number Change

1 Remove APPGM header card. Insert new main program/subroutine header card as needed.

2 Insert additional COMMON? declarative, and type statements if required for the actual application.

3 If the executive system of the user!s minicomputer accommodates cycle stealing for process input and output, then drop the nWf! appearing as the last letter of subroutine names used for process input/output.

4 Change the input/output unit equipment number as required for minicomputer assignments.

5 If APPGM is changed to a main program, remove the RETURN statement.

Organizing the Data and .Submitting a Request

Input consists of a single data card and any number of main

programs and subroutines. Format for the data card is illustrated in

Table 20. Right justify both data items within its respective input

field. If.more than one program is submitted for conversion, arrange

these programs in the order they are to be processed. CARDTP provides

an eight-inch leader between programs output.

To use CARDTP at The University of Arizona Computer Center,

organize the program input and use the control cards illustrated in

Figure 7. A TP parameter of two is needed for the system tape and the

54

Table 20. Input Data for CARDTP •

Variablemode

Defaultvalue Input Card

column

Alphanumeric Even Parity (EVEN, ODD, NON) 1

Integer One Number of programs 11-12

Table 21. CARDTP Input/Output Unit Assignments„

Unitvariable

Assignedvalue Input/output equipment

ICDRD 2 Card reader

IPR 4 Printer

I PUN 8 Paper tape punch

JOBNAME,CM50000,TP2,BNYYYYYYYY.

REQUEST(TAPE1,HI,RO) MTAPE

REQUEST(TAPES,TP,UI)

COPYBF(TAPE1,X)

COPYBF(TAPE1,CONVRT)

UNLOAD(TAPE1)

LOAD(CONVRT)

EXECUTE(CARDTP)

7-8-9 Card

Single data card

y-r

FORTRAN main program and/or subroutines

6-7-8-9 Card

Figure 7. Sample Run Deck for CARDTP.

56

paper tape punch. The system tape number is obtained from the Depart

ment .of Chemical Engineering.

To process CARDTP at other installations organize the program

input as illustrated in Figure 7. Compilation of CARDTP on a CDC 6400

produces object code requiring 16,400g.words. The program does not re

quire temporary storage. Input/output equipment unit numbers are rep

resented by variables. Users at other installations desiring to use

different input/output unit assignments should change the assignments

of the unit variables in the CARDTP executive and change the CARDTP

program header card. The present assignments are summarized in Table

21 (see p. 54).

CARDTP Diagnostics

CARDTP diagnostics are printed when default conditions must be

assumed to process a job or when the program does not recognize a spe

cial character and converts the character to a blank. All CARDTP diag

nostics are summarized in Table 22.

57

Table 22. CARDTP Diagnostics,

Message Comment

PARITY NOT SPECIFIED, DEFAULT ASSUMED.

NUMBER OF PROGRAMS NOT SPECIFIED,DEFAULT ASSUMED.

SPECIAL CHARACTER IN COLUMN— NOT RECOGNIZED CHARACTER CONVERTED TO A BLANK.

Conversion parity not specified. Even parity is assumed.

Number of programs to be converted is not specified. CARDTP will convert one program.

A special character not recognizable by CARDTP has been encountered. Conversion is made to a blank. If this character is essential, change CARDTP conversion codes for special characters and resubmit.

CHAPTER 3

SPECIFIC APPLICATIONS

This section demonstrates MINIF0R use in both data acquisition

and process control applications„ The data acquisition example shows a

dedicated minicomputer application in automation of chromatograph anal

ysis. The second example is a simple process control application il

lustrating a single DDC loop for the stirred-tank reactor problem,

previously presented.

Data Acquisition

Gas chromatography is a widely used method for determining gas

and liquid composition in both process and laboratory environments.

The application presented here illustrates an application program pre

pared for use on the Digital Equipment Corporation PDP-9 minicomputer

in the College of Mines at The University of Arizona. This example

furnished by White (18) required only minor modification for MINIF0R

processing. SUBROUTINE APPGM for this example is illustrated in Figure

8. The application program determines the composition of a chromato

graph sample for up to ten components by integrating the area under

each detected peak. Additional features include digital filtering of

analog data to reduce the effect of transmission noise and a correction

for baseline drift. When processed on the PDR-9, the application pro

gram requests teletype input data such as run duration, dump interval,

58

59

SUBROUTINE APPGM POP 2DIMENSION B(3),A(1C),H(13),INVECT(25> , R (13),NVALU(25) ,TL (1C> , POP 4

1 NCHAN(25),LOATA(18) POP 6COHMONF(IOIC) POP 8LOGICAL POSIT , START POP 10DATA POSIT,START/,TRUE.,.FALS E. / POP 12DATA AO/53./,LJ/1/ POP 14

c USER DIALOGUE INCLUDES DETECTION OF ERRORS IN INPUT POP 16WRITE (4,118) POP 18DO 2 1=1,10 POP 2 0

2 R (I) = 1. 0 POP 224 WRITE (4,76) POP 24C READ IN INPUT DATA FROM TELETYPE POP 26

READ (2,76) IS POP 28IT=IS*60 0/1003 POP 3 0FT=FLOAT(IS)*.6 POP 32IF (FLOAT(IT).NE.FT) IT=IT+1 POP 34IF (IS.LT.l) GO TO 74 POP 36WRITE (4,80 POP 38READ (2,62) JJ POP 40IF (JJ.EQ.G) GO TO 6 POP 4 2IF (JJ.LT.IT) GO TO 74 POP 44WRITE (4,100 POP 46READ (2,136) LT,BLANK POP 48JJ=JJ/IT POP 53

6 IS=(IS*60C)/IT+10 POP 52WRITE (4,102) POP 54READ (2,10m ) LX POP 56WRITE (4,84) POP 58READ (2,86) INVECT(I) POP 63

C PROGRAM SETS SLOPE CRITERION FOR FIRST PEAK DETECTION POP 62SL=FLOAT(IT)*2. POP 64

C DETERMINE IF START HAS BEEN SIGNALED POP 6 6NCHAN(l)=1 POP 68

8 CALL D1W (1,NCHAN,NVALU,MODE) POP 70NUM=NVALU(1) POP 72CALL DECODE (MUM,LDATA,16) POP 74IF (LOATA(l).EQ.O) GO TO 8 POP 76ITIME = C POP 78W d O =0. POP 80F(1C)=100 . POP 82IP = IT *10 0 POP 84

C A WINDOW OF TEN POINTS IS INCREME NTED TO DETECT PEAK 1 POP 8613 DO 12 J=1,1C POP 88

ITIME=ITIHE+IT POP 90CALL WAIT (IP,1,MODE) POP 92CALL AIROW (1,INVECT,NVALU,MODE) POP 94F(J)=NVALU(1) POP 96M = J-1 POP 98IF (M.FQ.O M = 10 POP 100W(J)=F(J)-F(M) POP 10 2IF (W(M).GT.SL.AND.W (J).GT.SL) GOi TO 14 POP 134

12 CONTINUE POP 136GO TO 10 POP 136

C DATA ADU IS IT ION BEGINS AFTER FIRST PEAK DETECTION POP 110

Figure 8. Application Program for Chromatograph Analysis.

60

14 AM = FL0AT(11IME)/10.-FLOAT(IT) POP 11200 16 1=21,IS POP 114ITIME=ITIME+IT POP 116CALL WAIT (IP,1,MODE) POP 118CALL AIROW <1 ,INVECT ,NVALU,M00E) POP 120F(I)=NVALU(1) POP 122

16 CONTINUE POP 124C THE 10 POINTS IN THE DETECTION WINDOW ARE ADDED TO MAIN ARRAY POP 126

DO 18 1=1,10 POP 126N=11-I POP 133F(N+10)=F(J) POP 132J=J-1 POP 134IF (J.LT.l) J=1J POP 136

18 CONTINUE POP 138C DIGITAL FILTERING ROUTINE POP 14 C

DO 20 1=1,10 POP 142F (I) =0 . POP 144AI=(1,-FLOAT(I))/2. POP 146W(I)=EXP(AI> POP 148

20 CONTINUE POP 15 0DO 24 1=11,IS POP 152X= 0 ♦ POP 154FX = 0. POP 156KERO=0 POP 158KM=I-9 POP 16 0DO 22 J=KM,I POP 162LL=I-J POP 164

22 X=F(J)*(1.-H(2))*H(LL+1)+X POP 16624 F (I-10)=X POP 168

IS=IS-10 POP 170C BASELINE CORRECTION POP 172

DO 26 1=1,IS POP 174F(I)=F(D- (F(IS)-F(l) ) * (FLOAT (I) /FLOAT (IS) ) POP 176IF (F(I).LT.AD) F (I)= 0 » POP 178

26 CONTINUE POP 180WRITE (4,88) LJ POP 182LJ=LJ+1 POP 184IF (JJ.EQ.O) GO TO 38 POP 186IF (LT.EO.l) GO TO 28 POP 188WRITE (4,90) POP 190GO TO 30 POP 192

28 WRITE (4,90) BLANK POP 19430 DO 32 1=1,IS,JJ POP 196

IF (F(I).GT.FX) F X = F (I ) POP 19832 CONTINUE POP 200C PRINTOUT OF DATA AT USER SUPPLIED INTERVALS POP 202

DO 36 1 = 1, IS,JJ POP 20 4FK=FLOAT(I)* (FLOAT(IT)/I:.)-FLOAT(IT)/10.^AM POP 206IF (I.EQ.l) GO TO 36 POP 208IF (LT.NE.l) GO TO 34 POP 210IST = (F (1-1) / FX) POP 212WRITE (4,92) FK,F(I-1),(KERO,K=l, 1ST) POP 214GO TO 36 POP 216

34 WRITE (4,92) FK,F(I-1) POP 21836 CONTINUE POP 220

Figure 8. Application Program for Chromatograph Analysis.— Continued

61

38 N= 0 POP 222K=0 POP 224M=1 POP 226IS=IS-3 POP 22 8

C PEAK DETECTION LOGIC POP 230DO 66 1=1,IS POP 232B(M)=F(I+1)-F(D POP 234B(M+l)=F(I+2)-F(I+l) POP 236IF (B(Hf1)) 40,h o ,52 POP 238

40 IF (POSIT) GO TO 42 POP 240GO TO 44 POP 242

42 IF (N.GT.9) GO TO 68 POP 244POSIT=.FALSE. POP 246START=.FALSE. POP 248TL(N+l)=FLOAT(!+!)♦(FLOAT(IT)/1C.)+AM POP 25 0N=N+1 POP 252

44 IF (I.EQ.IS) WRITE (4,108) N POP 254GO TO 66 POP 256

46 IF (B (H)) 48,66,66 POP 25 848 B(M+2)=F(I+3)-F(I+2) POP 26 0

IF (B(M+2)) 66,50,50 POP 26250 J=I + 1 POP 264

GO TO 62 POP 26652 IF (B(M)) 54,56,58 POP 26854 IF (K.EQ.0) GO TO 56 POP 27 C

J=I + 1 POP 272GO TO 62 PUP 274

56 IF (START) GO TO 66 POP 276K=I + 1 POP 278START = ,T RUE• POP 280

58 POSIT = .T RUE. POP 282IF (START) GO TO 60 POP 284K=I+1 POP 286START=.TRUE. POP 288

60 IF (I.EQ.IS) WRITE (4,108) N POP 290GO TO 66 POP 292

62 C=F(K)+F(J) POP 294D=0. POP 296E = 0. POP 296K=K+1 POP 300J=J-1 POP 302

C INTEGRATION ROUTINE UTILIZING SIMPSONZS METHOD POP 304DO 64 MM=K,J,2 POP 306D=F(MM)+D POP 30 8

64 E=F(MM+1)+E POP 310K = J+1 POP 312A(N)=(l./3.)+(C+4.+D+2.*E) POP 314

66 CONTINUE POP 316IF (LX.NE.l) GO TO 68 POP 316LX = C POP 32 CWRITE (4,110 POP 322

C PRINTOUT OF PEAK AREAS FOR RESPONSE FACTOR CALCULATION POP 324WRITE (4,112) (I,A(I),1=1, N) POP 326WRITE (4,114) POP 32 8READ (2,116) (R(I),1=1,N) POP 330


62

68

C

70

72

74CC76788J>8284668890

9294

9698100102104106108

1101L2114116118

WRITE (4,94)AT = C.DETERMINATION DO 70 1=1,N A(I)=A(I)*R(I)AT = A (I),ATDO 7 2 1=1, NA d ) = (A(I) /AT) ♦100.WRITE (4,96) I,TL(I),A(I) IS=IS+12 GO TO 6 WRITE (4,98)GO TO 4

OF PERCENT COMPOSITION

DUMPDATA

INTERVALOUTPUT)

INPUT CHANNEL(12)

FORMAT (//IX,26HENTER RUN DURATION(MIN),12) FORMAT (12)FORMAT (//IX,41HENTER

INTER 0 TO SUPRESS RAW FORMAT (13)FORMAT (//IX,44HENTER FORMAT (12)FORMAT (/////5X,7HRUN FORMAT (5X,4HTIME,7X,8HRAW

119X,9HBAR GRAPH/)FORMAT (4X,F5.1,5X,F8.1,3X,40I1)FORMAT (/5X,8HCOMPOUND,3X,18HELUTION

1 OS IT I ON)FORMAT (/8X,I2,2(1CX,F7.2) )

(//IX, 1C.HOATA ERROR)(//IX,31HENTER 1 IF PAR GRAPH

FORMATFORMATFORMATFORMATFORMATFORMAT

POP POP POP POP POP POP POP POP POP POP POP POP POP POP POP POP POP

(13),/lX,34HEPDP POP POP

) POPPOP

NO.,12//) POPDATA/,5X,5H (SEC) ,4X,12 H (VOLTSX1CC0) ,Ai,PDP

POP POP

TIME (SEC),3X ,19HPERCENT COMPPOPPOP POP POP

IS DESIRED) POP

IN TENTHS OF SEC

(1X,44HENTER 1 IF RESPONSE FACTORS KILL BE PROVIDED) (ID (II,Al)(IX,12HEND OF PEAK ,I2,23H NOT DETECTED,

1URATION)FORMAT (/5X,8HC0MPOUND,3X,11HACTUAL AREA)FORMAT (///8 X ,I2,1CX,E12.3)FORMAT (IX,49HENTER RESPONSE FACTOR FOR EACH FORMAT (13(F4.C,IX))FORMAT (////////15X,79HUNIVERSITY OF ARIZONA

POP POP POP

INCREASE,13H RUN DPDP POP POP POP

COMPONENT(F4.0,IX)) POPPOP

COLLEGE OF MINES /, 19FDPIX,3CHCHPOMATOGRAM ANALYSIS PROGRAM ///,IX,53HTHIS PROGRAM WILL ACCPDP 2EPT UP TO 1C COMPONENTS AND /,1X,22HUP TO ICC D DATA POINTS//////)POP END POP

332 334 336 338 340 342 344 346 348 350 352 354 356 35 8 360 362 364 366 368 370 372 374 376 378 380 332 384 386 388 390 392 394 396 398 40 0 402 404 436 408 410 412 414 416 418-


63

processing options, and ADC channel number on which the chromatograph

signal is input. To process this application program using MINIF^R,

the user dialogue is accomplished by inputting data with the card

reader to simulate teletype input; these data cards are organized and

located immediately after the last MINIF^R input data card as illus

trated in Figure 6„ After the user dialogue is completed, SUBROUTINE

DIW is called to detect a start signal generated by the user when a

chromatograph sample is injected. Once a start signal is detected,

analog inputs are made using.SUBROUTINE AIRDW.

SUBROUTINE MODEL is illustrated in Figure 9. The intensity of,

the chromatograph output is stored as a function of time using a DATA

statement. The first element of IRELAY is used to signal the injection

of a sample (see end of chapter for Figures 9 through 16)..

Coded MINIF^R data forms for this example are illustrated in

Figure 10. All system output is illustrated in Figure 11. Output gen

erated by SUBROUTINE APPGM is illustrated in Figure 12.

Process Control

The process control application consists of a DDC loop for the

stirred-tank reactor problem previously presented in Chapter 2. SUB

ROUTINE APPGM for this application is illustrated in Figure 13. Every

5 seconds the concentration of tank 2 effluent is obtained by issuing a

call to SUBROUTINE APPGM. A position algorithm, SUBROUTINE POSIN (il

lustrated in Figure 14) calculates a new valve position for the manipu

lated variable. The new valve position is then output to a final

control element using SUBROUTINE AOW.

64

Coded MINIF0R data forms and system output are illustrated in

Figures 15 and 16,' respectively. The system time history is printed

for 10-second intervals during the simulation run. Examination of the

time history will reveal two system features which are utilized. First

a step change in feed concentration, A(l), is programmed to enter at 40

seconds in the simulation. Secondly, a dead time of 30 seconds is used

to delay tank 2 effluent concentration which is assigned to output

variable C(3). Tank 2 effluent concentration without dead time is as

signed to output variable C (2). Values of C(3) lag values of C(2) by

30 seconds.

S U B R O U T I N E M O D E LC O M M O N / U S E R / A , Y , Y D O T , I R E L A Y , C , TD I M E N S I O N A ( 6 5 ) , Y ( 2 5 ) , Y D O T ( 2 5 ) , I R E L A Y ( 1 2 8 ) , 0 ( 2 5 )D I M E N S I O N X ( 1 0 1 )L O G I C A L F I R S T D A T A F I R S T / . T R U E . /D A T A ( X ( I ) , 1 = 1 , 1 0 1 ) / O . G , 0 . 0 , 0 . 0 1 , 0 . 0 2 , 0 . j 3 , 0 . u 4 , J . C 5 , D . 0 6 , 0 . 0 7 ,1 . 0 8 . 0 . 0 8 . 0 . 0 9 , 0 . 1 0 , 0 . 1 1 , 0 . 1 2 , 0 . 2 3 , 0 . 3 0 , 0 . 4 3 , 0 . 6 0 , 3 . 8 8 , 1 . 0 5 , 1 . 3 8 ,

2 1 . 5 5 , 1 . 9 , 2 . 2 0 , 2 . 4 0 , 2 . 5 0 , 2 . 5 5 , 2 . 5 3 , 2 . 5 0 , 2 . 4 u , 2 . 2 0 , 2 . 8 5 , 1 . 8 0 , 1 . 7 8 ,3 1 . 3 8 . 1 . 1 8 . 1 . 0 . 0 . 3 5 . 0 . 7 2 , u . 5 5 , j . 5 3 , 0 . 5 1 , 0 . 4 9 , D . 4 8 , 3 . 4 7 , 3 . 4 7 7 , 0 . 4 8 ,4 0 . 4 9 . 0 . 5 0 . 0 . 5 2 . 3 . 6 1 . 0 . 8 0 . 0 . 9 7 . 1 . 1 5 . 1 . 4 0 . 1 . 7 0 . 2 . 1 u , 2 . 7 0 , 3 . 6 0 , 4 . 5 0 , 5 5 . 4 , 5 . 8 1 , 5 . 8 C , 5 . 5 5 , 5 . 1 0 , 4 . 8 0 , 4 , 6 0 , 4 . 6 1 , 4 . 7 3 , 5 . 1 0 , 6 . C U , 7 . 4 0 , 8 . 3 0 ,6 9 . 0 . 9 . 5 0 . 9 . 7 0 . 9 . 6 0 . 9 . 9 0 . 7 . 71. , 6 . 6 0 , 5 . 4 U , 4 . 2 u , 3 . 3 0 , 2 . G O , 1 . 5 0 , 1 . 3 0 ,7 1 . 1 5 . 1 . 0 . 0 . 9 9 , G . 9 8 , G . 9 7 , 0 . 9 6 , 0 . 9 5 , 0 . 9 5 , 0 . 9 5 , 0 . 9 5 , 3 . 9 5 , 0 . 9 5 , 0 . 9 5 ,3 0 . 9 5 /I F ( F I R S T ) G O T O 2 0

5 1 = T / 3 . 0 1 = 1 + 1 J = I + 1I F ( J , G T , 1 0 1 ) G O T O 1 0C ( l ) = X ( I > + ( ( X ( J ) - X ( I ) ) / 3 . 0 ) * ( T - F L O A T ( I - 1 ) * 3 . C )G O T O 1 5

1 0 0 ( 1 ) = X ( 1 G 1 )1 5 C O N T I N U E R E T U R N 2 0 F I R S T = . F A L S E .I R E L A Y ( l ) = 1G O T O 5

E N D

Figure 9. MODEL for Chromatograph Example.O'V I

TITLE1 2 3 4 5 6 7 8 9 10 I t 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 33 39 40

c R O A T O A- M i l R A tv\

IDENTIFICATION41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

H h Ir Ie c O T 5 E r B R 8 ? 7

Figure 10. MINIF0R Data for Chromatograph Example

ChO'-

ITEM VARIABLE NO. MODE INPUT

67

COLUMN

1A INTEGER TOTAL HOURSi

IB INTEGER SIMULATION MINUTES4 5

71C REAL TIME SECONDS b 9 10 11

2A REALFREQUENCY OF PROGRAM 14 15 16 17

OUTPUT, SECONDS

2B ALPHA PRINTOUT ALL INPUT AND 50 21 23

NUMERIC OUTPUT VARIABLES?(YES)

3~ INTEGER NUMBER OF OUTPUT VARIABLES55 56

1

INTEGER NUMBER OF STATE/ ALGEBRAIC VARIABLES

59 504

5 INTEGER NUMBER OF STATE/ALGEBRAIC 33 34

STORED FOR DEAD TIME

6 INTEGER NUMBER OF INPUT VARIABLES37 38

7 INTEGER NUMBER OF INPUT VARIABLES 41 42


8 INTEGER NUMBER OF STEP DISTURBANCES 45 46

9 INTEGER NUMBER OF OUTPUT VARIABLES 49 50

MEASURED BY ADC 1


MEASURED BY ADC

11 INTEGER NUMBER OF CONTACT SENSORS/ 57 60

ON-OFF DEVICES 1

12A ALPHA INTEGRATION RULE 61 62 63

NUMERIC (RK2, RK4, CAL, BUM) D u m |12B REAL INTEGRATION STEP SIZE, SECONDS

66 67 68 69

I]Figure 10. MINIF0R Data for Chromatograph Example.— Continued

I

ITEM VARIABLENO. MODE INPUT COLUMN

OBJECT MACHINE

NUMBER BITS PER WORD1A INTEGER

BASIC SYSTEM CLOCK COUNT MILLISECONDSIB REAL

ANA LOG-TO-DIGITAL CONVERTER

ADC SCALE FACTOR, HARDWARE UNITSREAL

DIGITAL INPUT29 30

NUMBER OF DIGITAL INPUTSINTEGER33 34

NUMBER BITS PER REGISTER3B INTEGER

DIGITAL-TO-ANALOG CONVERTER37 33

4A NUMBER OF CHANNELS UTILIZEDINTEGER

4B REAI DAC SCALE FACTOR, HARDWARE UNITS

LATCHING DIGITAL OUTPUT49 50

NUMBER DIGITAL OUTPUTSINTEGER53 54

NUMBER BITS PER REGISTERINTEGER

MOMENTARY DIGITAL OUTPUT57 58

6A NUMBER BITS PER REGISTERINTEGER

6B NUMBER PULSE OUTPUTSINTEGER

6C INTEGER NUMBER PULSES PER CLOCK COUNT

Figure 10. MINIF0R Data for Chromatograph Example.— Continued

69

CONTACT SENSOR/ ON-OFF DEVICE COLUMN

RELAYS 1-16

RELAYS 17-32

RELAYS 33-48

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

RELAYS 49-6449 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

Figure 10. MINIF0R Data for Chromatograph Example.— Continued

PROCESS SPECIFICATIONS HARDWARE SPECIFICATIONS

I"-OUTPUT VARIABLE MEASURED SAMPLED ON CHAWEL — 1r ENG. MINIMUM MAXIMUM SIGNAL READ BY ADC FOR DESIGNATED LEVEL OF MEASURAND, HARDWARE UNITS ]c UNITS MEASURAND MEASURAND0 1 10 1 30 1 50 1 70 I 90 1 100 NO.

; i°if P.72 n U K ?t 77 28 ?9 30 31 3? 33 34 35 36 37 38 39 40 41 *2 <3 *4 45 46 *7 48 49 50 31 S? S3 54 55 56 37 31 39 60 6 1 6? 63 64 65 66 67 66 70 71 72

1 U

' I

I I

i I i !

1 2 3 4 S 6 7 8 9 >0 II 12 13 >4 15 16 t7 18 19 20 21 22 23 24 2S 26 27 28 29 » 31 32 33 34 33 36 37 38 39 40 41 42 43 44 45 46 47 48 49 SO 51 52 S3 54 S5 56 57 S8 5? 60 61 6? 63 64 6S 66 67 68 69 TQ 71 7? 73 74 75 76 77 7| 79 80

73 74 75 76 77 79 79 ac

1 5. 0!

F i g u r e 1 0 . M I N I F 0 R D a t a f o r C h r o m a t o g r a p h E x a m p l e . — C o n t i n u e d

o

V E R S I O NM I N I F O R

1 S E P T E M B E R 2 5 , 1 9 7 2 * * * * * * * * * * * * *

A N A L Y S I S O F S I M U L A T I O N A N D H A R D W A R E S P E C I F I C A T I O N S F R O M I N P U T C A R D S 1 - 3T I T L E - C H R O M A T O G R A M A N A L Y S I S P R O G R A MI D E N T I F I C A T I O N - T H R E E C O M P O N E N T S , S E P T E M B E R 28, 1 9 7 2S P E C I F I C A T I O N S F O R S I M U L A T E D E N V I R O N M E N T E R R O R C O N D l i l O N ' / C O M M E N T

T Y P E S I M U L A T I O N A L G E B R A I C M O D E LS I M U L A T I O N T I M E -0 H O U R S , 7 M I N U T E S , - 0 . 0 0 S E C O N D SF R E Q U E N C Y O F M I N I F O R O U T P U T , S E C O N D S 1 . C 3N U M B E R O F O U T P U T V A R I A B L E S 1N U M B E R O F I N P U T V A R I A B L E S -0N U M B E R O F I N P U T V A R I A B L E S D E L A Y E D - 0N U M B E R O F S T A T E / A L G E B R A I C V A R I A B L E S -0N U M B E R O F S T A T E / A L G E B R A I C V A R I A B L E S D E L A Y E D ' -0N U M B E R O F D I S T U R B A N C E S -0N U M B E R O F C O N T A C T S E N S O R S / O N - O F F D E V I C E S 1

S P E C I F I C A T I O N S F O P O B J E C T M A C H I N E A N D I / O H A R D W A R EO B J E C T M A C H I N E

N U M B E R O F B I T S P E R W O R D C L O C K C O U N T , M I L L I S E C O N D S

181 6 . 6 7 0

A N A L O G T O D I G I T A L C O N V E R T E R N U M B E R O F C H A N N E L S U T I L I Z E D S C A L E F A C T O R , H A R D W A R E U N I T S

11000.0 N O T S P E C I F I E D

D I G I T A L i n p u tN U M B E R O F D I G I T A L I N P U T S N U M B E R O F B I T S P E R R E G I S T E R N U M B E R O F R E G I S T E R S

D I G I T A L T O A N A L O G C O N V E R T E R N U M B E R O F C H A N N E L S U T I L I Z E D

1161

-0

N O T S P E C I F I E D

D I G I T A L O U T P U T N O T U T I L I Z E D

P U L S E O U T P U T SN U M B E R O F P U L S E O U T P U T S -0

N O F A T A L E R R O R S F O U N D

F i g u r e 1 1 . M I N I F O R O u t p u t f o r C h r o m a t o g r a p h E x a m p l e .

S E V E R I T Y

D E F A U L T A S S U M E D

D E F A U L T A S S U M E D

C H R O M A T O G R A M A N A L Y S I S P R O G R A MT H R E E C O M P O N E N T S , S E P T E M B E R 2 8 , 1 9 7 2

P R O G R A M E X P E C T S F O L L O W I N G C A R O I N V E N T O R YC A R D ( S ) F O R S P E C I F I E D I N P U T N U M B E R O F C A R O S

0 0 1 0 0 G 0 1 G C 0

Figure 11. MINIF0R Output for Chromatograph Example.— Continued

I N P U T V A R I A B L E S N O T P U L S E DS T A T E / A L G E B R A I C V A R I A B L E SN U M B E R O F D I G I T A L I N P U T SN U M B E R O F D I G I T A L O U T P U T SD I S T U R B A N C E SI N P U T V A R I A B L E S D E L A Y E DS T A T E / A L G E B R A I C V A R I A B L E S D E L A Y E DO U T P U T V A R I A B L E S T O B E M E A S U R E D B Y A D CI N P U T V A R I A B L E S T O B E M E A S U R E D B Y A D CI N P U T V A R I A B L E S T O B E . M A N I P U L A T E D B Y O A C ,I N P U T V A R I A B L E S T O B E M A N I P U L A T E D B Y P U L S E S

C H R O M A T O G R A M A N A L Y S I S P R O G R A MT H R E E C O M P O N E N T S , S E P T E M B E R 2 8 , 1 9 7 2

D I G I T A L I N P U T P O S I T I O NI R E L A Y C 1 ) C L O S E D


C H R O M A T O G R A M A N A L Y S I S P R O G R A M T H R E E C O M P O N E N T S , S E P T E M B E R 2 8 , 1 9 7 2

S P E C I F I E D P R O C E S S / M O D E L O U T P U T V A R I A B L E S T O BE M E A S U R E D BY A N A L O G T O D I G I T A L C O N V E R T E RP R O C E S S S P E C I F I C A T I O N S A N A L O G S I G N A L T O A D C F O R D E S I G N A T E D L E V E L O F M E A S U R A N O , H O W E U N I T Sa**********#*****.******************* $**+*******»***$+****************#»******$***$***#$*$*********#*****

V A R I A B L E M I N I M U M M A X I M U M C 10 33 50 70 90 ICCM E A S U R E D U N I T S M E A S U R A N O M E A S U R A N O P E R C E N T P E R C E N T P E R C E N T P E R C E N T P E R C E N T P E R C E N T P E R C E N TC( 1) I N T N 0 . 0 0 1 0 . 0 0 0 . 0 0 1 . C 0 3 . 0 5 5 . 3 0 7 . 0 0 9 . 0 0 1 0 . 5 0

S A M P L E D O N C H A N N E L13


75

U N I V E R S I T Y O F A R I Z O N A C O L L E G E O F M I N E S C H R O M A T O G R A M A N A L Y S I S P R O G R A M

T H I S P R O G R A M W I L L A C C E P T U P T O 1 0 C O M P O N E N T S A N D U P T O 1 0 0 u D A T A P O I N T S

E N T E R R U N D U R A T I O N ( M I N ) , I 2

E N T E R D U M P I N T E R V A L I N T E N T H S OF S E C ( 1 3 ) E N T E R U T O S U P R E S S R A W D A T A O U T P U T

E N T E R 1 I F A A R G R A P H I S D E S I R E DE N T E R 1 I F R E S P O N S E F A C T O R S W I L L O E P R O V I D E D

E N T E R I N P U T C H A N N E L ( 1 2 )

Figure 12. User Output for Chromatograph Example.

76

R U N N O . 1

T I M E R A W D A T A( S E C ) ( V O L T S X i Q C O ) B A R G R A P H4 2 . 6 1 1 6 . 5 04 5 . 6 1 8 5 . 0 04 6 . 6 2 7 7 . 0 05 1 . 6 3 9 9 . 3 05 4 . 6 5 5 9 . 8 0 05 7 . 6 7 5 2 . 6 0 0 06 0 . 6 9 9 7 . 2 0 0 0 36 3 . 6 1 2 9 5 . 1 0 0 0 0 06 6 . 6 1 4 8 1 . 1 0 0 0 3 0 06 9 . 6 1 3 0 5 . 1 0 0 0 0 0 0 u 07 2 . 6 2 0 8 5 . 9 0 0 C 0 0 0 G G 07 5 . 6 2 2 6 9 . 9 a o c o o o o o o u7 8 . 6 2 3 5 9 . 7 3 0 0 0 0 0 0 9 0 08 1 . 6 2 3 9 5 . 9 3 0 0 0 0 0 -3 C 0 08 4 . 6 2 3 6 9 . 5 o n c c o n o o o o8 7 . 6 2 3 2 3 . 6 3 0 0 0 0 0 0 0 0 09 ? . 6 2 2 0 3 . 1 3 0 0 0 0 0 3 0 09 3 . 6 2 0 1 0 . 2 3 0 0 3 G C 0 C9 6 . 6 1 8 3 9 . 0 0 C 0 Q 0 Q C C9 9 . 6 1 6 0 9 . 9 0 0 0 0 0 0 31 0 2 . 6 1 5 3 0 . 0 3 0 G 0 0 C1 0 5 . 6 1 1 6 2 . 9 3 0 0 0 01 0 8 . 6 9 4 6 . 8 0 0 0 01 1 1 . 6 7 6 0 . 7 0 0 01 1 4 . 6 6 0 2 . 8 3 01 1 7 . 6 4 6 0 . 2 0 01 2 0 . 6 3 0 6 . 7 Cl1 2 3 . 6 2 6 2 . 0 01 2 6 . 6 2 3 2 . 2 01 2 9 . 6 2 0 3 . 9 31 3 2 . 6 1 8 4 . 0 31 3 5 . 6 1 6 6 . 1 , 01 3 8 . 6 1 6 2 . 1 01 4 1 . 6 1 5 6 . 3 01 4 4 . 6 1 5 6 . 3 31 4 7 , 6 1 5 7 . 8 3

Figure 12. User Output for Chromatograph Example.— Continued

77

1 5 0 . 6 1 7 5 . 0 01 5 3 . 6 2 6 1 . 7 01 5 6 . 6 4 3 3 . 9 01 5 9 . 6 595.3 301 6 2 . 6 7 7 1 . 4 I C O1 6 5 . 6 1011.9 3 C O G1 6 6 . 6 1 3 0 8 . 2 0 G G O G1 7 1 . 6 1 7 1 1 . 5 3000000174.6 2 3 1 3 . 8 3 0 0 0 0 0 0 G O O1 7 7 . 6 3 1 8 8 . 2 3 0 C 0 0 0 3 0 0 0 0 0 0 01 8 C . 6 4 0 7 2 . 7 Q O G O C G I U O C O O G C G O O O1 8 3 . 6 4 9 0 7 . 1 000500 3 0 03000 0 0 0 0 0 30 01 8 6 . 6 5287.3 O O G G O u G O O O C O G C u Q D O O C O O O1 8 9 . 6 5264.5 0 C G 0 C 0 0 C 0 0 0 0 3 0 0 0 0 J 3 L G G 31 9 2 . 6 4 9 9 8 . 3 1 0 G 3 C 0 3 0 G G 0 C 0 0 0 0 3 0 0 G O O1 9 5 . 6 4 5 6 7 . 3 O O C O G O O C u O O C O C G G Q O O O1 9 8 , 6 4262.6 n O G O G O O C O O G O G O G G O O201.6 4 0 7 0 . 4 G C G O J 0 0 C 0 G 0 D 3 G 0 C C G2 0 4 . 6 4 0 7 1 . 3 0 0 0 0 C G 0 G 0 0 0 0 0 0 G 0 >3 G207.6 4 2 0 1 . 2 O C G n O D O C C O C G O C O G C O210.6 4 6 0 1 . 1 0 0 0 0 0 0 3 0 3 0 0 0 0 0 3 0 0 0 3 02 1 3 . 6 5 5 1 0 . 2 0 C C 3 0 C u 0 3 G 0 0 0 0 G G 0 0 C C 0 O u 02 1 6 . 6 6 8 1 4 . 9 3 G C 0 0 O O r G G O G G G Q Q 0 3 3 0 0 0 0 0 0219.6 7 7 0 4 . 1 0 0 0 G 0 0 0 0 0 0 0 0 C G 0 U 0 0 0 0 0 G 0 0 0222.6 8 3 7 9 . 5 O C ' O G G C O C O O O C O u G C O G G G O O a C u225.6 8 8 4 6 . 0 O C G O G O 0 0 0 0 0 0 0 0 0 0 0 0 0 C J 0 3 0 32 2 8 . 6 9 0 2 3 . 1 0 0 C 0 0 0 0 0 0 u 0 C 3 0 C G 0 3 3 0 0 D 0 0 02 3 1 . 6 8 8 6 5 . 3 aeooooseoGOGOOoooaocoooco2 3 4 . 6 8139.5 Q G C 3 0 0 3 C 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 3 7 . 6 6973.3 O O C 3 G G O C a C D C O O C G G O Q G 0 3 0 3 02 4 C . 6 5856.2 0 0 0 0 G 0 3 C 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 32 4 3 . 6 4659.9 a O G O O G O C O G O C G O C O O D O O2 4 6 . 6 3 4 5 3 . 6 occocooojoooaoo2 4 9 . 6 2277.7 3 C 0 0 G Q 0 C 0 02 5 2 . 6 1 2 9 5 . 9 Q 0 G O O255.6 806 .7 ODD2 5 8 . 6 592.4 3 0261.6 4 3 1 . 9 3264.6 2 9 1 . 0 02 6 7 . 6 2 6 5 . 4 02 7 0 . 6 2 4 6 . 1 02 7 3 . 6 226.7 02 7 6 . 6 2 0 7 . 4 32 7 9 . 6 1 8 9 . 0 0

000

OvC

3 O G 0 G G C 0 0 J O O O Q 3 0 0 0 0 C C 3 0 3 0 0 0 QGOGOOOGGG O G u G


C O M P O U N D A C T U A L A R E A

1 .3656+36

2 . 5 G 2 E + 0 6

3 . 1 0 4 5 + 0 7E N T E R R E S P O N S E F A C T O R F O R E A C H C O M P O N E N T ( F 4 . 0 , I X )C O M P O U N D E L U T I O N T I M E ( S E C ) P E R C E N T C O M P O S I T I O N

1 8 1 . 3 0 2 0 . 9 52 1 8 7 . 5 0 2 7 . 7 83 2 2 8 . 6 0 . 5 1 . 2 7


S U B R O U T I N E A P P G MD I M E N S I O N I D A T A ( 2 5 ) , L D A T A ( 1 8 ) , N C H A N ( 2 5 ) S E T C O U N T E R F O R C O N C E N T R A T I O N K C O N C = 5C A L L W A I T ( K C O N C , 2 , M O D E )O B T A I N C O N C E N T R A T I O N O F T A N K 2 E F F L U E N T C A L L A I S Q W ( 1 , 2 0 , I O A T A , M O D E )C O N V E R T V O L T S M C O O T O E N G I N E E R I N G U N I T S C V A R = 0 . 0 1 + 0 . O O G 4 * F L O A T ( I D A T A ( i > ) / 1 G 0 C C A L C U L A T E N E W V A L V E P O S I T I O N C A L L P O S I N ( C V A R , V A L P O S )C O N V E R T V A L V E P O S I T I O N T O V O L T S M G u O . I O A T A ( 1 ) = V A L P O S * ! J G O .O U T P U T N E W V A L V E P O S I T I O N N C H A N ( 1 ) = 8C A L L A O W ( l , N C H A N , I O A T A , M O D E )G O T O 5 E N D

Figure 13. Application Program for Stirred-Tank Reactor

80

S U B R O U T I N E P O S I N ( C V A R , V A L P O S )D I M E N S I O N E R R 0 R ( 4 )D A T A X K C , T I , T O , X M I D / 1 2 0 . 0 , 0 . 1 , 1 0 . 0 , 7 2 . 0 /D A T A S E T P T , S A M I N T , S U M , N O I N T / C . 0 2 4 4 , 5 . 0 , 0 . 0 , 0 /N O I N T = N O I N T + 1 E R R O R ( 4 ) = S E T P T - C V A P I F ( N O I N T . G T . 4 ) G O T O 7 D E L = 0 . 0 G O T O 97 D E L = ( E R R O R ( 4 ) - E R R O R ( l ) + 3 . G * E R R O R ( 3 ) - 3 • J * E R R O R ( 2 ) ) / 1 ( 6 . 0 + S A M I N T )9 S U M = S U M + E R R O R ( 4 )V A L P O S = X M I D 4 X K C * ( E R R O R ( 4 ) + S U M / T I + T D * D E L )D O 1 0 1 = 1 , 3 K = 5 - I L = 4 - I 1 0 E R R O R ( L ) = E R R O R ( K )R E T U R NE N D

Figure 14. A Position Algorithm for DDC.

TITLE1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

S L T I P. D T A N K L A C T O P. S L rv)

IDENTIFICATION41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 53 59 60 61 62 63 64 65 66 67 63 69 70 71 72 73 74 75 76 77 78 79 60

X — !i 2- O * o 7 yjx 1 I |f 1 lo . 1/ L !t Id | !=! h lo . °i ...L.l. ! ! i

Figure 15. MINIF0R Data for Stirred-Tank Reactor.

82

ITEM VARIABLENO. MODE_____________________ INPUT____________________COLUMN


IB INTEGER SIMULATION MINUTES« 5

7

1C REAL TIME SECONDS 8 9 10 11


OUTPUT, SECONDS1 O . o


NUMERIC OUTPUT VARIABLES?(YES) Y £ S

INTEGER NUMBER OF OUTPUT VARIABLES25 26

3 3

INTEGER NUMBER OF STATE/ ALGEBRAIC VARIABLES

29 304 2r: INTEGER NUMBER OF STATE/ALGEBRAIC 33 34 1J STORED FOR DEAD TIME

1 1

6 INTEGER NUMBER OF INPUT VARIABLES

—h




I


MEASURED BY ADC 1


MEASURED BY ADC

11 INTEGER NUMBER OF CONTACT SENSORS/ 57 58

ON-OFF DEVICES


NUMERIC (RK2, RK4, CAL, DUM) R

12B REAL INTEGRATION STEP SIZE, SECONDS66 67 68 69

O . O

Figure 15. MINIF^R Data for Stirred-Tank Reactor.— Continued

83ITEM VARIABLENO._____ MODE_____________ INPUT COLUMN

OBJECT MACHINEi 2

1A INTEGER NUMBER BITS PER WORD I8IB REAL BASIC SYSTEM CLOCK 5 6 7 8 9 10

COUNT MILLISECONDS 1 G b &

ANALOG-TO-DIGITAL CONVERTER

2 REAL ADC SCALE FACTOR, 17 18 19 20 21 22

HARDWARE UNITS

DIGITAL INPUT

3A INTEGER NUMBER OF DIGITAL INPUTS29 30

3B INTEGER NUMBER BITS PER REGISTER33 34

DIGITAL-TO-ANALOG CONVERTER

4A INTEGER NUMBER OF CHANNELS UTILIZED37 38

“Til4B REAL DAC SCALE FACTOR, HARDWARE UNITS

41 42 43 44 45 46

LATCHING DIGITAL OUTPUT

5A INTEGER NUMBER DIGITAL OUTPUTS49 50


• MOMENTARY DIGITAL OUTPUT

6A INTEGER NUMBER BITS PER REGISTER57 58

6B INTEGER NUMBER PULSE OUTPUTS 61 62

6C INTEGER NUMBER PULSES PER CLOCK COUNT 65 66

Figure 15. MINIF0R Data for Stirred-Tank Reactor.— Continued

84

INPUT VARIABLE COLUMN

A(l)

A(2)

1 2 5 4 3 6 7 8 9 10

O . I O

11 12 13 14 15 16 17 18 19 20

9 . 3 5

A(3) 21 22 23 24 25 26 27 20 29 30

A (4 ) 31 32 33 34 35 36 37 30 39 40

A(5) 41 42 43 44 45 46 47 43 49 SO

A (6 ) 51 52 53 54 55 56 57 53 59 60

A(7) 61 62 63 64 65 66 67 68 69 70

A(8) 71 72 73 74 75 76 77 76 79 60


85

STATE/ALGEBRAIC VARIABLE COLUMN

Y (l)

Y(2)

Y(3)

1 2 3 4 5 6 7 8 9 10

o o 7 3

11 12 13 14 15 16 17 18 19 20

0 . 0 2 4 - 4 -

21 27. 23 24 25 26 27 28 29 30

Y(4) 31 32 33 34 35 36 37 38 39 40

Y(5)

Y (6 )

41 42 43 44 45 46 47 46 49 50

i n51 52 53 54 55 56 57 58 59 60

Y(7)

Y(8)

61 62 63 64 65 66 67 63 69 70

71 72 73 74 75 76 77 75 79 60


8 6

VARIABLEMODE INPUT COLUMN

I N T E G E R I N P U T V A R I A B L E D I S T U R B E D

i 2

1

R E A L T I M E T O E N T E R , S E C O N D S

4 5 6 7 6 9 104- O , O

R E A L D I S T U R B A N C E V A L U E

11 12 13 14 15 16 17 16 19 20

O , 1 o 5 1

IN T E G E R I N P U T V A R I A B L E D I S T U R B E D

21 22


24 25 26 27 20 29 30


31 32 33 34 35 36 37 33 39 40


41 42


44 45 46 47 48 49 50


51 52 53 54 55 56 57 13 59 60

1 I ;

H


61 62


64 65 66 67 60 69 70


71 72 73 74 75 76 77 78 79 to

llll.Figure 15. MINIF0R Data for Stirred-Tank Reactor.— Continued


OUTPUT VARIABLE MEASURED SAMPLED ON CHANNELENG.UNITS

MINIMUMMEASURAND

MAXIMUMMEASURAND

SIGNAL READ BY ADC FOR DESIGNATED LEVEL OF MEASURAND, HARDWARE UNITS

F i g u r e 1 5 . M I N I F 0 R D a t a f o r S t i r r e d - T a n k R e a c t o r . — C o n t i n u e d

ENG. UNITS


SIGNAL OUTPUT ON CHANNEL

MINIMUM QAC SIC TO FCE

MAXIMUM DAC SIG. TO FCE

. 00

INPUT VARIABLE MANIPULATED

VALUE OF MANIPULATED VARIABLE FOR DESIGNATED LEVEL OF DAC OUTPUT

10 30 50 70 90 1006 7 a 9»0 H 12 >3 U !S 16 17 18 )9 20 21 72 73 ?4 25 a* 2? » 30 31 3? 33 34 35 36 37 38 40 41 4? 43 44 45 46 47 Ag A? 50 51 52 53 54 55 56 57 58 SO 60 67 63 6* 65

0.0

- 1 j

Sifi

! !J_ L

us.-I—LLLl •

- H -

On

6 7 8 9 10 II 12 13 1 4 15 16 17 18 1 9 20 21 ?2 23 74 2} 26 ?7 ?8 W 30 31 32 33 3< 35 36 37 38 39 40 41 4? *3 44 45 4* 47 46 4» 50 51 52 S3 54 55 56 57 56 5» 60 61 62 63 64 65 66 67 66 69 70 71 72

F i g u r e 1 5 . M I N I F 0 R D a t a f o r S t i r r e d - T a n k R e a c t o r . — C o n t i n u e d

oooo

M I N I F C R * * * * * * * * * * * * * * * * * * * * * * * * *

V E F S I O N 1 S E P T E M B E R 2 5 , 1 9 7 2 * * * * * * * * * * * * *

A N A L Y S I S O F S I M U L A T I O N A N D H A R D W A R E S P E C I F I C A T I O N S F R O M I N P U T C A R O S 1 - 3T I T L E - S T I R R E D T A N K R E A C T O R P R O B L E M I D E N T I F I C A T I O N - X K C = 1 2 0 . C, T I = 0 . 1 , T D = 1 0 . 0S P E C I F I C A T I O N S F O R S I M U L A T E D E N V I R O N M E N T E R R O R C O N D I T I O N / C O M M E N T S E V E R I T Y

T Y P E S I M U L A T I O N D Y N A M I C M O D E LS I M U L A T I O N T I M E - 0 H O U R S , 7 M I N U T E S , - C . C C S E C O N D SF R E Q U E N C Y OF M I N I F O R O U T P U T , S E C O N D S 1 0 . CON U M B E R O F O U T P U T V A R I A B L E S 3N U M B E R O F I N P U T V A R I A B L E S 2N U M B E R O F I N P U T V A R I A B L E S D E L A Y E D -0N U M B E R O F S T A T E / A L G E B R A I C V A R I A B L E S 2N U M B E R OF S T A T E / A L G E B R A I C V A R I A B L E S D E L A Y E D 1N U M B E R O F D I S T U R B A N C E S 1N U M B E R O F C O N T A C T S E N S O R S / O N - O F F D E V I C E S -0I N T E G R A T I O N R U L E S P E C I F I E D F O U R T H O R D E R R U N G E - K U T T AI N T E G R A T I O N S T E p S I Z E , S E C O N D S . 0 1 0

S P E C I F I C A T I O N S F O P O B J E C T M A C H I N E A N D I / O H A R D W A R EO B J E C T M A C H I N E

N U M B E R O F B I T S P E R W O R D C L O C K C O U N T . M I L L I S E C O N D S

181 6 . 6 6 0

A N A L O G T O D I G I T A L C O N V E R T E R N U M B E R O F C H A N N E L S U T I L I Z E D S C A L E F A C T O R , H A R D W A R E U N I T S

11000.0 N O T S P E C I F I E D D E F A U L T

D I G I T A L I N P U T N O T U T I L I Z E D

D I G I T A L T O A N A L O G C O N V E R T E R N U M B E R O F C H A N N E L S U T I L I Z E D S C A L E F A C T O R , H A R D W A R E U N I T S

11000 .0 N O T S P E C I F I E D D E F A U L TD I G I T A L O U T P U T

N O T U T I L I Z E DP U L S E O U T P U T S

N U M B E R O F P U L S E O U T P U T S -0N O F A T A L E R R O R S F O U N D

A S S U M E D

A S S U M E D

F i g u r e 1 6 . M I N I F 0 R O u t p u t f o r S t i r r e d - T a n k R e a c t o r . 00

STIRRED TANK REACTOR PROBLEM

XKC = 120.0, II = G.l, TO = 10.0

P R O G R A M E X P E C T S F O L L O W I N G C A R O I N V E N T O R YC A R O ( S ) F O R S P E C I F I E D I N P U T N U M B E R O F C A R O S

I N P U T V A R I A B L E S N O T P U L S E D 1S T A T E / A L G E B R A I C V A R I A B L E S 1N U M B E R O F D I G I T A L I N P U T S - 0N U M B E R OF D I G I T A L O U T P U T S - 0D I S T U R B A N C E S 1I N P U T V A R I A B L E S D E L A Y E D 3S T A T E / A L G E B R A I C V A R I A B L E S D E L A Y E D 1O U T P U T V A R I A B L E S T O B E M E A S U R E D B Y A D C 1I N P U T V A R I A B L E S T O B E M E A S U R E D B Y A D C - 0I N P U T V A R I A B L E S T O B E M A N I P U L A T E D B Y O A C , 1I N P U T V A R I A B L E S T O B E M A N I P U L A T E D B Y P U L S E S C

\

F i g u r e 1 6 . M I N I F 0 R O u t p u t f o r S t i r r e d - T a n k R e a c t o r . — C o n t i n u e d

vOo


XKC = 120.0, TI = 0.1, TO = 10.0

I N P U T V A R I A B L E S N O T R E C E I V I N G P U L S E S I G N A L S

I N P U T V A R I A B L E I N I T I A L V A L U EA ( 1 ) . 1 0 0A ( 2 ) 9 . 3 5 0

Figure 16. MINIFgfR Output for Stirred-Tank Reactor.— Continued

S T I R R E D T A N K R E A C T O R P R O B L E MX K C = 1 2 0 . 0 , T I = 3 . 1 , T O = 1 0 . 0

S T A T E / A L G E B R A I CV A R I A B L E I N I T I A L C O N D I T I O N SY ( 1 ) . C 7 3Y ( 2 ) . 1 2 4

Figure 16. MXNIF0R Output for Stirred-Tank Reactor.— Continued


XKC = 120.0, TI = 0.1, TO = 10.0

I N P U T V A R I A B L E D I S T U R B A N C E T I M E T O E N T E RD I S T U R B E D V A L U E S I M U L A T I O N , S E C .A ( 1 ) . 1 0 5 4 0 . 0 0

Figure 16. MINIF0R Output for Stirred-Tank Reactor.— Continued


XKC = 120.0, TI - 0.1, TO = 10.0

S T A T E / A L G E O R A I C D E A D T I M EV A R I A B L E S D E L A Y E D S E C O N D SY C 2 ) 3 0 . 0 0 0


S T I R R E D T A N K R E A C T O R P R O B L E MXK C = 120.0, TI = 0.1, TO = 10. 0

S P E C I F I E D P R O C E S S / M O d E L " O U T P U T V A R I A B L E S T O BE M E A S U R E D BY A N A L O G T O D I G I T A L C O N V E R T E RP R O C E S S S P E C I F I C A T I O N S A N A L O G S I G N A L T O A Q C F O R D E S I G N A T E D L E V E L O F M E A S U R A N O , H O W E U N I T S

V A R I A B L E M I N I M U M M A X I M U M 0 10 30 50 7C 90 ICOM E A S U R E D U N I T S M E A S U F A N O M E A S U R A N O P E R C E N T . P E R C E N T P E R C E N T P E R C E N T P E R C E N T P E R C E N T P E R C E N TC < 3) C O N C . 0 1 . 0 5 0. 00 10 . 0 0 30 . 00 50 . 00 7 0 . CO 93. 00 1 0 0 . CO

S A M P L E D ON C H A N N E L23


S T I R R E D T A N K R E A C T O R P R O B L E MXK C — 120*3? TI — G • 1 ? TO — 1C•0

S P E C I F I E D P R O C E S S / M O D E L I N P U T V A R I A B L E S T O B E M A N I P U L A T E D BY S I G N A L S F R O M D I G I T A L T O A N A L O G C O N V E R T E RP R O C E S S S P E C I F I C A T I O N S

I N P U TV A R I A B L EM A N I P U L A T E D U N I T S

V A L U E O F M A N I P U L A T E D V A R I A B L E F O R D E S I G N A T E D L E V E L O F O A C O U T P U T

AC 2) G P M

0P E R C E N T

O.CiO

1GP E R C E N T

.50

3CP E R C E N T

2.20

50P E R C E N T

4 . 5 U

70P E R C E N T

8 . 6 0P E R C E N T

1 5 . 8 0

ICCP E R C E N T

20.00

H A R D W A R E S P E C I F I C A T I O N SM I N I M U M M A X I M U M S I G N A LS I G N A L S I G N A L O U T P U T ON T O F C E TO F C E C H A N N E L

1.03 1 0 3 . 0 0 8


97

* * M I N I F O R ♦ * * ** * * * * * * * * * * * * * VE RSI ON 1 SEPTEMBER 2 5 , 1 9 7 2 + * + * * 4

S T I R R E D TANK REACTOR PROBLEM

XKC = 1 2 0 . 0 , T I = 0 . 1 , TO = 10 . 9

HRS . MI N . SEC. C( 1 ) C ( 2 ) C< 3 )0 3 0 . 0 C . 7 3 0 9 0 G E - 0 1 . 2 4 4 0 0 C E - 0 1 . 2 4 4 C C CE- 013 0 1 0 . 0 0 . 7 3 C 3 1 3 E - 0 1 . 2 4 3 7 2 2 5 - 0 1 . 2 4 4 CL v E - 9 10 0 2 3 . 0 3 . 7 3 0 - 6 4 BE- 0 1 . 2 4 3 5 2 2 E - 91 • 2 4 4 C 0 C E - C 10 0 3 3 . 0 0 . 7 3 C 9 4 6 E - 0 1 . 2 4 3 3 8 2 5 - 0 1 . 2 4 4 0 0 C E - 0 10 3 4 0 . 0 0 . 7 3 1 2 1 9 E - 01 . 2 4 3 2 8 9 5 - 0 1 . 2 4 3 7 2 2 E - 3 10 3 5 0 . 9 0 . 7 3 4 9 8 C E - C 1 . 2 4 3 3 5 5 E - 01 . 24 35 2 2 5 - 0 10 1 O.OC . 7 3 5 3 7 7 E - 0 1 . 2 4 3 6 4 3 5 - 0 1 . 2 4 3 3 8 2 5 - 9 10 1 1 0 . 0 0 . 7 4 1 4 5 5 2 - 0 1 . 2 4 4 ( 6 6 5 - 0 1 . 2 4 3 2 8 9 5 - 0 10 i 2 0 . 0 0 • 7 4 4 2 5 4 E - 0 1 . 2 4 4 6 3 9 E - 3 1 . 2 4 3 3 5 5 5 - 0 10 i 3 0 . 0 0 . 7 4 6 7 9 B E - 31 . 2 4 5 2 5 6 E - G 1 . 2 4 3 6 4 3 5 - 3 10 i 4 3 . 00 • 7 4 9 0 9 5 E - 01 . 2 4 5 9 1 0 5 - 0 1 . 2 4 4 0 8 8 5 - 9 10 1 5 0 . 0 0 . 7 5 1 1 4 2 E - 0 1 . 2 4 6 5 7 7 5 - 0 1 . 2 4 4 6 3 9 5 - 0 10 2 3 . 0 0 . 7 5 2 9 3 2 E - 0 1 . 2 4 7 2 3 8 5 - 0 1 . 2 4 5 2 5 6 5 - 0 10 2 1 0 . 0 0 . 7 5 4 4 5 2 5 - 3 1 . 2 4 7 8 7 6 5 - 9 1 • 2 4 5 9 1 C E - 0 10 2 2 0 . 0 0 . 7 5 5 6 9 0 E - 0 1 . 2 4 8 4 7 9 5 - 0 1 . 2 4 6 5 7 7 5 - 3 10 2 3 0 . 0 0 . 7 5 6 6 3 3 5 - 0 1 . 2 4 9 0 3 3 5 - 0 1 . 2 4 7 2 3 8 5 - 9 13 2 4 3 . 0 2 * 7 5 7 2 7 C E - C 1 . 2 4 9 5 2 9 E - 0 1 . 2 4 7 8 7 6 5 - 0 10 2 5 0 . 0 0 . 7 5 7 6 5 3 5 - 3 1 . 2 4 9 9 5 9 5 - 0 1 • 2 4 8 4 7 9 E - 310 3 O.CO . 7 5 7 8 2 1 5 - 0 1 . 2 5 0 3 2 1 5 - 0 1 . 2 4 9 0 3 3 5 - 9 10 3 1 0 . 0 0 . 7 5 7 7 7 5 E - 0 1 . 2 5 3 6 1 5 E - 0 1 . 2 4 9 5 2 9 5 - 3 10 3 2 0 . 0 0 . 7 5 7 5 1 9 5 - 9 1 . 2 5 0 8 4 C E - 0 1 . 2 4 9 9 5 9 5 - 3 10 3 3 0 . 0 0 . 7 5 7 0 6 C E - 3 1 . 2 5 0 9 9 6 5 - 0 1 . 2 5 0 3 2 1 5 - 0 10 3 4 0 . 0 0 . 7 5 6 4 3 3 5 - 0 1 . 2 5 1 C 8 4 E - 0 1 . 2 5 0 6 1 5 5 - 3 10 3 5 0 . 0 0 . 7 5 5 5 6 0 5 - 0 1 . 2 5 1 1 0 4 5 - 0 1 . 2 5 0 6 4 0 5 - 0 10 4 3 . 0 0 . 7 5 4 5 4 0 5 - 0 1 . 2 5 1 C 5 8 E - 9 1 . 2 5 C 9 9 6 E - 0 13 4 1 3 . 3 0 . 7 5 3 3 5 8 5 - 0 1 . 2 5 0 9 4 9 5 - 0 1 . 2 5 1 0 6 4 5 - 0 10 4 2 0 . 0 0 . 7 5 2 3 2 5 5 - 0 1 . 2 5 0 7 7 7 5 - 0 1 . 2 5 1 1 3 4 5 - 3 10 4 3 3 . CO . 7 5 0 5 5 9 5 - 0 1 . 2 5 C 5 4 7 E - 9 1 . 2 5 1 9 5 8 5 - 0 10 4 4 0 . 0 0 . 7 4 8 9 7 4 5 - 9 1 . 2 5 9 2 6 2 5 - 9 1 . 2 5 0 9 4 9 5 - 3 10 4 5 3 . 3 0 . 7 4 7 2 3 8 5 - 3 1 . 2 4 9 9 2 5 5 - 0 1 . 2 5 0 7 7 7 5 - 3 10 5 0 . 0 0 . 7 4 5 5 5 C E - 0 1 . 2 4 9 5 4 1 5 - 0 1 . 2 5 0 5 4 7 5 - 3 10 5 1 0 . 0 0 . 7 4 3 6 5 6 5 - 0 1 . 2 4 9 1 2 C 5 - 9 1 . 2 5 0 2 6 2 5 - 3 10 5 2 0 . 0 0 • 7 4 2 2 1 I E - 01 . 2 4 6 6 7 2 5 - 0 1 . 2 4 9 9 2 5 5 - 0 10 5 3 3 . 0 0 . 7 4 0 6 1 6 5 - 0 1 . 2 4 8 2 0 7 5 - 0 1 . 2 4 9 5 4 1 5 - 9 10 5 4 3 . 0 0 . 7 3 9 0 7 7 5 - 0 1 . 2 4 7 7 3 C E - D 1 • 2 4 9 1 2 ' . 5 - 0 1Q 5 5 0 . 3 0 . 7 3 7 5 9 4 5 - 0 1 . 2 4 7 2 4 8 5 - 0 1 . 2 4 8 6 7 2 5 - 3 10 6 O.CO • 7 3 6 1 7 C E - 0 1 . 2 4 6 7 6 6 5 - 0 1 . 2 4 8 2 3 7 5 - 3 10 6 1 0 . OC . 7 3 4 8 1 0 5 - 0 1 . 2 4 6 2 8 9 5 - 0 1 . 2 4 7 7 3 0 5 - 9 16 6 2 3 . 0 0 • 7 3 3 5 1 6 E - 0 1 . 2 4 5 6 1 8 5 - 3 1 . 2 4 7 2 4 8 5 - 3 10 6 3 0 . 0 0 . 7 3 2 2 9 2 E - 0 1 . 2 4 5 3 5 8 5 - 0 1 . 2 4 6 7 6 6 5 - 0 10 6 4 3 . 0 0 • 7 3 1 1 4 C E - 0 1 . 2 4 4 9 1 1 5 - 0 1 . 2 4 6 2 6 9 5 - 9 10 6 5 0 . 0 0 . 7 3 0 0 6 2 5 - 0 1 . 2 4 4 4 7 9 5 - 9 1 . 2 4 5 8 1 8 5 - 3 10 7 O.CO . 7 2 9 0 6 1 5 - 0 1 . 2 4 4 0 6 5 5 - 0 1 . 2 4 5 3 5 8 5 - 0 1

Figure 16. MXNIF0R Output for Stirred-Tank Reactor.— Continued

000000000Gc00000e0000000000000000J0000cG

98


XKC = 120.0, TI = 0.1, TD = 10.0

MIN. SEC. AC 1) AC 2)0 0.00 .1C00G0E+00 . 93500 0E + 010 10. oc .100 3JCE+0 0 .950C30E+010 20.00 .lOGOOOE+OO . 950 0 35E+ 310 30. 30 .100C 00E + O0 •950 07CE+010 40.00 .10500CE+00 .953840E+010 50.00 .1050 3 0E+00 .953745E+011 0.00 . 1C5C0GE + CD .956225E+011 10.00 .105000E+00 .963685E+011 20.00 . 10503CE + 00 . 96967 CE+011 30.00 • 1G5G-0CE + 00 .97 4465E+ C11 40.00 .1Q503CE+0G .976355E+011 50.00 .1050 30E+00 .974153E+012 0. 00 .10500CE+00 .967115E+012 10. OC .1050CCE+00 .954763E+312 20.00 .10530OE+OC .936640E+312 30.00 . 105000E + 00 .91332CE+012 40.00 •105C3CE+GC . 88427 CE+012 50.00 . 1050 0CE4 00 .861531E+013 0.00 •1C590GE+03 .8374362+013 10.00 .10500CE+00 .810512E+013 20.00 .1G503CE+03 .781164E+013 30.00 .105 0 OCE + OO .749731E+C13 40.00 .10509CE+03 .716535E+G13 50.00 .1050 0CE+00 .681963E+014 0.00 . 10530CE+00 •646359E+014 10.00 . 135070E4-00 .610067E+014 20.0 0 .105C0CE+CD .573453E+014 30.00 .10533CE+00 .536860E+014 4C.00 . 10503CE + 00 .500632E+014 50.00 .105300E+00 .465G93E+315 0.00 .105GODE+0 0 .439604E+015 10.00 .10500GE+03 .421825E+015 ' 2 3.00 . 1050 J0E + 0 0 .4046972+315 30.00 .105000E+00 .388958E+015 40.00 .1053005+30 .374123E+315 53.00 .105000E+00 . 363484E + 016 0.00 .1353J0E+00 . 348C 982+016 13.30 . 1350 3CE + 00 .337035E+316 23.00 .10530CE+C3 .327283E+016 33.0 0 .105 03CE+00 .318665E+016 40.00 .105000E+30 .311793E+J16 50.00 • 1G50 0PE+ 0 0 .3060202+317 c. 00 •135C0 0E+00 .301546E+31

MINIF0R Output for Stirred-Tank Reactor.— Continued

CHAPTER 4

SUMMARY AND SUGGESTED FUTURE DEVELOPMENT

MINIF0R is designed to facilitate minicomputer real-time

FORTRAN IV program development, debugging, and updating on a large

general purpose computere The system should aid program development

for minimum configuration dedicated minicomputer data acquisition and

process control applicationsc System real-time structure is built

around standard executive and process input/output interfaces estab

lished by the Fifth Workshop on Standardization of Industrial Computer

Languages* Paper tape FORTRAN IV source programs for processing on

the actual minicomputer application are produced by a card-to-tape

conversion program*

It is the authorr s opinion that MINIFgfR can be a productive

tool for debugging, developing, and updating real-time FORTRAN programs

used in industrial applications* Further, the system has potential for

wide usage in an academic environment for unit operation exercises and

studies in process control theory* Industrial acceptance of such

methodology depends upon vendor implementation of the standard inter

face calls soon to be published as ISA standards. It is this writerr s

opinion that users will recognize the advantages of standardized proc

ess calls and demand such vendor implementation.

If wide industrial usage is achieved, then the utility of the

system should be increased through further development. The following

99

100

discussion suggests areas where the program can be improved to increase

user utility. <

Simulation of several levels of process interrupts should be

explored* This will necessitate addressing the problem of reentrant

programming* Reentrancy is currently implemented on minicomputer sys

tems by duplicate common subroutines for each interrupt service routine

and by storing intermediate results using stack points.

Additional standard executive interfaces, START and TRNON, must

be incorporated in the system. These interfaces allow a designated

program to be executed after a specified time delay or at a specified

time of day. The designated program can be called from the program

clock, SUBROUTINE CLOCK, with minor modification.

MINIF0R can be made available to smaller systems through over

lays. Minor modifications could be made as follows: The MINIF0R

executive and common block would be core resident at all times. Since

subroutines INITAL and INCK are executed only at the beginning of a

simulation run, these subroutines can be overlayed by the remaining

system components.

Position and velocity control algorithms for conventional three

mode controllers using single set point, cascade, or ratio control

schemes could easily be included. These algorithms would be available

to the user for implementing DDC and SSP loops.

Variable step size integration routines, such as the Runge-

Kutta-Merson method as implemented by Wait (17), should be incorporated

into the system. This will require only minor modification of the

101

calling sequence in SUBROUTINE UPDATE. The system is presently struc

tured to implement dead time simulation using a variable step size in

tegration rule without modification of system routines for storing and

recalling values of delayed variables.

APPENDIX A

ANSI

ASCII

Cycle stealing

Data acquisition

DDC

Dead time

Disturbance

Final control element

Interrupt

ISA

Manipulated variable

Measurand

GLOSSARY OF TERMS

American National Standards Institute.

American Standard Code for Information Interchange.

Processor operation is suspended for one memory cycle to permit input/output.

Collection and operation on data to produce relevant information about a process.

Manipulated variables, such as a valve position, are calculated from set points, controlled variables, and other measurements on the process. These calculations are applied directly to the process.

Synonymous with transportation lag or velocity lag. Represents the time to travel from one point to another in a process.

Variables whose value affect the operation of the process but which are not subject to adjustment by a control system.

A device which produces corrective action on a process.

Diverts processor operation from normal execution sequence in order to service the computer system needs or to service process emergencies.

Instrument Society of America.

Variables whose value can be adjusted by a control system.

A process variable which is measured by a measuring element.

102

103

Overlay

Process control

Position algorithm

Reentrant programming

Set point

SSP

State variable;

Step change

Transducer

Velocity algorithm

Organization of a program into sections which can be swapped in and out of core memory to conserve program field length.

An automated strategy of maintaining a controlled variable near its set point by adjusting a manipulated variable.

A programmed statement which calculates an actual position for a final control element.

Allows a subroutine to be interrupted and called again by the interrupt service routine without destroying intermediate results.

Target value for a controlled variable.

Set points are determined to optimize operating strategy within process constraints. These set points are output by the process computer to analog hardware.

A dynamic variable whose change is described by a first-order ordinary differential equation.

A step change produces an instantaneous change in a variable.

A device used to transfer a measurement into a signal suitable for transmission.

A programmed statement which calculates a change in position for a final control element.

APPENDIX B

MINIF0R CODING FORMS

104

TITLE1 2 3 4 5 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

-V

IDENTIFICATION41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

UNIVERSITY OF ARIZONA TUCSON, ARIZONA 85721

Figure 17. Card 1 - Title and Identification

MINIF0R - A REAL-TIME SIMULATION PROGRAM FOR MINICOMPUTER DATA ACQUISITION AND PROCESS CONTROL APPLICATIONS.

106

ITEM VARIABLENO. MODE_____________________ INPUT________________ COLUNN


IB INTEGER SIMULATION MINUTES 4 5

1C REAL TIME SECONDS S 9 10 11


OUTPUT, SECONDS


NUMERIC OUTPUT VARIABLES?(YES)

INTEGER NUMBER OF OUTPUT VARIABLES25 26

3

INTEGER NUMBER OF STATE/ 29 304 ALGEBRAIC VARIABLES

5 INTEGER NUMBER OF STATE/ALGEBRAIC 33 34


6 INTEGER NUMBER OF INPUT VARIABLES37 38





MEASURED BY ADC

10 INTEGER NUMBER OF INPUT VARIABLES MEASURED BY ADC

53 54

Tl11 INTEGER NUMBER OF CONTACT SENSORS/ 57 58

ON-OFF DEVICES


NUMERIC (RK2, RK4, CAL, DUM)

12B REAL INTEGRATION STEP SIZE, SECONDS66 67 68 69

Figure 18. Card 2 - Simulation Specifications.

107

ITEM VARIABLENO. MODE INPUT COLUMN

OBJECT MACHINE

1A INTEGER NUMBER BITS PER WORDi 2

IB REAL BASIC SYSTEM CLOCK 3 6 7 8 9 10

COUNT MILLISECONDSANALOG-TO-DIGITAL CONVERTER

2 REAL ADC SCALE FACTOR, 17 18 19 20 21 22

HARDWARE UNITS

DIGITAL INPUT

3A INTEGER NUMBER OF DIGITAL INPUTS29 30


DIGITAL-TO-ANALOG CONVERTER

4A INTEGER NUMBER OF CHANNELS UTILIZED37 38

4B REAL DAC SCALE FACTOR, HARDWARE UNITS41 42 43 44 45 46

LATCHING DIGITAL OUTPUT

5A INTEGER NUMBER DIGITAL OUTPUTS49 50


MOMENTARY DIGITAL OUTPUT

6A INTEGER NUMBER BITS PER REGISTER57 58

6B INTEGER NUMBER PULSE OUTPUTS 61 62

6C INTEGER NUMBER PULSES PER CLOCK COUNT6! 66

Figure 19. Card 3 - Hardware Specifications.

108

INPUT VARIABLE COLUMN

A (I ) 1 2 3 4 5 6 7 8 9 10

A(2) 11 12 13 14 15 16 17 18 19 20

A(3) 21 22 23 24 25 26 27 28 29 30

A(4) 31 32 33 34 35 36 37 38 39 40

A(5) 41 42 43 44 45 46 47 48 49 50

A(6) 51 52 53 54 55 56 57 58 59 60

A(7)

A(8)

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 CO

Figure 20. Card(s) 4 - Input Variables.

Instructions: Code this card to describe initialconditions for input variables. Include constants, manipulated variables, and set points. These inputs cannot receive pulse signals. If more than eight inputs are needed, code additional card(s). Variable mode is REAL.

109

STATE/ALGEBRAIC VARIABLE COLUMN

Y (l) i 2 3 4 5 6 7 8 9 10

Y(2) n 12 13 14 15 16 17 18 19 20

Y (3 ) 21 22 23 24 25 26 27 28 29 30

Y(4) 31 32 33 34 35 36 37 38 39 40

Y(5) 41 42 43 44 45 46 47 48 49 50

Y(6) 51 52 53 54 55 56 57 58 59 60

Y( 7 ) 61 62 63 64 65 66 67 68 69 70

Y(8) 71 72 73 74 75 76 77 78 79 80

Figure 21. Card(s) 5 - State/Algebraic Variables.

Instructions: Code this card to describe initial conditionsfor state/algebraic variables. If more than eight variables are needed, code additional card(s). Variable mode is REAL.

110

CONTACT SENSOR/ON-OFF DEVICE COLUMN

RELAYS 1-161 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

RELAYS 17-3217 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

RELAYS 33-4833 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

RELAYS 49-6449 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

Figure 22. Card(s) 6 - Contact Sensors/On-Off Devices.

Instructions: Code this card to describe the initial statefor digital inputs represented by elements 1 through 64 of IRELAY. Code an additional card to specify initial state of latching digital outputs represented by elements 65 through 128 of IRELAY.

Ill


INTEGER INPUT VARIABLE DISTURBEDi 2

REAL TIME TO ENTER, SECONDS4 5 6 7 6 9 10

REAL DISTURBANCE VALUE11 12 13 14 15 16 17 18 19 20

INTEGER INPUT VARIABLE DISTURBED21 22





51 52 53 54 55 56 57 58 59 60

REAL DISTURBANCE VALUE




Figure 23. Card (s ) 7 - Disturbances.

Instructions: Code this card to program disturbances intothe simulation. Disturbances are in the form of step changes and are applicable to input variables only. If more than four disturbances are needed, code an additional card.

112


INTEGER INPUT VARIABLE DELAYED i 2

REAL DEAD TIME, SECONDS3 4 5 6 7 8 9 10

INTEGER INPUT VARIABLE DELAYED 11 12


INTEGER INPUT VARIABLE DELAYED21 22

23 24 25 26 27 28 29 30

REAL DEAD TIME, SECONDS




REAL DEAD TIME, SECONDS 43 44 45 46 47 48 49 50







Figure 24. Card(s) 8 - Input Variables Delayed.

Instructions: Code this card to describe input variablesstored for dead time simulation. If more than eight input variables are needed, code additional card(s).

113


INTEGER STATE/ALGEBRAIC VARIABLE DELAYED i 2


INTEGER STATE/ALGEBRAIC VARIABLE DELAYED 11 12














Figure 25. Card(s) 9 - State/Algebraic Variables Delayed.

Instructions: Code this card to describe state/algebraicvariables stored for dead time simulation. If more than eight variables are needed, code additional card(s).


frOUTPUT VARIABLE MEASURED SAMPLED ON CHANNEL

1ENG.UNITS

MINIMUMMEASURAND

MAXIMUMMEASURAND

SIGNAL READ BY ADC FOR DESIGNATED LEVEL OF MEASURAND, HARDWARE UNITS10 1 30 1 50 1 70 1 90 100 NO.

7 8 * to II 17 13 H 11 16 17 IS l» 20 21 22 23 24 25 26 27 28 2? 30 31 32 33 34 35 36 37 38 39 40 41 47 43 44 45 46 47 48 49 SO 51 52 53 54 55 56 57 58 >9 60 61 6? 63 64 65 66 6? 68 » 70 71 77t— n

' M '

TT

i I

1—r-i—L

TTT' I

-r-M-

l I

I 2J 4 5 6 7 8 9 10 II 1? 13 14 15 16 17 18 19 20 21 72 23 24 25 26 27 28 79 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 5 7 58 59 60 61 6? 63 64 65 66 67 68 69 70 71 77 173 74 73 76 77 7| 79 80

73 74 75 76 77 78 79 80

F i g u r e 2 6 . C a r d ( s ) 1 0 - T r a n s d u c e r C h a r a c t e r i s t i c s f o r O u t p u t V a r i a b l e s M e a s u r e d ,I n s t r u c t i o n s : C o d e t h i s c a r d t o d e s c r i b e t r a n s d u c e rc h a r a c t e r i s t i c s f o r o u t p u t v a r i a b l e s m e a s u r e d . I f c h a r a c t e r i s t i c s a r e l i n e a r , c o d e o n l y s i g n a l l e v e l s 0 a n d 1 0 0 p e r c e n t . I f m o r e t h a n 1 8 t r a n s d u c e r s a r e n e e d e d , c o d e a n a d d i t i o n a l f o r m .

PKOCESS SPECIFICATIONS HAMVAEE SPECIFICATIONS

INPUT VARIABLE MEASURED SAMPLED ON CHANNEL

ENG. MINIMUM MAXIMUM SIGNAL BEAD BY ADC FOB DESIGNATED LEVEL OF MEASUBAND, HARDWARE UNITSUNITS MEASUBAND MEASUBAND 0 1 io 1 30 _ J . 50 _ _ 1 70 1 90 1 100 - NO.

1 } i i 6 > « f 10 111? 13 14 ts 14 17 H H 30 ?t » a M a I* « W 30 ]l I? 13 34 35 W 3» W 40 «l g 43 44 4t 47 « 49 SO SI 52 i3 54 S5 S6 >7 S« S» tO 61 6? tJ M tS 6t 67 70 71 72 73 74 7j 7« 77 7» lu

1 I

! i

1 : :i ' i 1

I !i i i i i

i i .

i 1 1 j i !

! i 1 1

:! i i j i

i 1 ! ; • 1 ! !! i • i ! i i ■ !

—

i i!

, ' i j

ii I 1 !

i 1 1 1 !

! 1 ! I I ii

| iI 7 3 4 3 4 7 6 9 >0 II 17 13 14 15 16 17 16 19 20 21 22 23 24 23 74 27 26 29 30 31 32 33 34 33 36 37 36 39 40 41 42 43 44 4} 46 47 46 49 30 51 52 S3 34 33 56 37 36 39 60 61 62 63 >4 65 66 67 66 69 70 71 72 1 73 74 73 76 77 71 79 W

F i g u r e 2 7 . C a r d ( s ) 1 1 - T r a n s d u c e r C h a r a c t e r i s t i c s f o r I n p u t V a r i a b l e s M e a s u r e d ,I n s t r u c t i o n s : C o d e t h i s c a r d t o d e s c r i b e t r a n s d u c e rc h a r a c t e r i s t i c s f o r i n p u t v a r i a b l e s m e a s u r e d . I f c h a r a c t e r i s t i c s a r e l i n e a r , c o d e o n l y s i g n a l l e v e l s 0 a n d 1 0 0 p e r c e n t . I f m o r e t h a n 1 8 t r a n s d u c e r s a r e n e e d e d , c o d e a n a d d i t i o n a l f o r m . 115


INPUT VARIABLE MANIPULATED SIGNAL OUTPUT ON CHANNEL

ENG.UNITS

VALUE OF MANIPULATED VARIABLE FOR DESIGNATED LEVEL OF DAC OUTPUT MINIMUM DAC SIC.

MAXIMUM DAC SIG.

0 10 30 50 70 90 100TO FCE TO FCE

N0.- 7 ; T ' T -

1 11 .

! ' 1 | ! 1 ■ i i i 1 i j -' | ;■ ;

; 1 1 ! ! I • ' ; ! ; : : ' 1 ! ! M 1I |

; ! I j j 1 : ! i 11 ' • ; I

; . • i ! r~ i : l} ’ [ "! . | 1

i l l ! I 1 : i i ; ! I : ! 1 I : 1 | ! ! !! : i i 1 ; i i i ! ! ! , ■ ;

i1 . ! ' i : : 11 ■ ; : , ' 1

i • ■ ' ; . , i ; : : . j ; ■ ' '

61 62 W M 66 f S8 70 71 7?

-l—l-

I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 16 20 21 2 2 2 3 24 25 2 6 2 ? 28 29 30 31 33 33 34 35 36 3 7 38 3 9 40 41 42 43 44 45 46 47 48 46 50 51 5) 53 54 55 56 57 5* 5« 60 61 62 63 64 65 6 6 67 68 66 "O 71 72 1 73 74 75 76 77 7» 79 80

73 74 74 7 6 7 7 78 7 9 80

I I

F i g u r e 2 8 . C a r d ( s ) 1 2 - F i n a l C o n t r o l E l e m e n t C h a r a c t e r i s t i c s .I n s t r u c t i o n s : C o d e t h i s c a r d t o d e s c r i b e f i n a l c o n t r o le l e m e n t c h a r a c t e r i s t i c s f o r i n p u t v a r i a b l e s m a n i p u l a t e d b y D A C o u t p u t s . I f c h a r a c t e r i s t i c s a r e l i n e a r , c o d e 0 a n d 1 0 0 p e r c e n t l e v e l . I f m o r e t h a n 1 6 f i n a l c o n t r o l e l e m e n t s a r e n e e d e d , c o d e a n a d d i t i o n a l f o r m .

117


REAL INITIAL CONDITION OF INPUT VARIABLEi 2 3 4 5 6 7

ALPHA ENGINEERING UNITS10 11 12 13

NUMERIC

REALCHANGE IN INPUT VARIABLE 16 17 18 19 20 21 22

PER POSITIVE PULSE

REAL INITIAL CONDITION OF INPUT VARIABLE 25 26 27 28 29 30 31

ALPHA ENGINEERING UNITS 34 35 36 37

NUMERIC

REAL CHANGE IN INPUT VARIABLE 40 41 42 43 44 45 46

PER POSITIVE PULSE

REAL INITIAL CONDITION OF INPUT VARIABLE 49 50 51 52 53 54 55

n t . JALPHA ENGINEERING UNITS 58 59 60 61

NUMERIC

REAL CHANGE IN INPUT VARIABLE 64 65 66 67 68 69 70

PER POSITIVE PULSE I

Figure 29. Card(s) 13 - Pulse Outputs.

Instructions: Code this card to describe input variablesmanipulated by stepping motors or integrating amplifiers receiving pulse signals. If more than three input variables are manipulated by pulse outputs, code additional card(s).

APPENDIX C

INTEGRATION ROUTINES

MINTFjZfR provides three £ixed~step size integration routines for

dynamic simulationse The simulation time is advanced for algebraic

simulations by a dummy integration method. This appendix describes in

tegration methods for dynamic simulations.

The first method is a second-order explicit Runge-Rutta method

described by Gear (6) and implemented by Wait (17). This method is

frequently referenced as the modified trapezoidal or Heun method. The

method is described by

w - v ^ Wand

h = h f(V tn)

kg = h f(yn+ t^+ h)

where

y = current value of y atn time t n

y - = next value of y atn+l time t ,n+l

' . f(y, t) = dy/dt

This method should be used for trivial problems.

118

119

The second routine available is the classical fourth-order ex

plicit. Runge-Kutta method described by Gear (6) and implemented by Wait

(17), The method corresponds to

yn+l = V ? (kl+ 2k2+ 2k3+ k4) ■

where

kl = h f(yn’ tn )

k2 = h f(yn+ % k l» tn+ T )

k 3 = h f(yn + % k 2 , tn + |-) '

k, " h f (y + k0, t + h)4 n 3’ n

This method should be used when greater accuracy is required and the

MODEL differential equations are linear.

The third routine is. a third-order implicit method described by

Calahan (3). This method is based on knowledge of f/ y as defined by

the Jacobian J, The method is described by

and

where

'n+l = yn + 4 kl + 4 k2

kl = h[I - haL J (yn )]~1 f Cyn )

kg = h[I - ha1 J (yn)] 1 f (yn-f )

= identity matrix

■= h (1 + j)bj- = ~2 Vl/3

120

Galatian1s method is recommended by Gear (6) for solution of systems of

nonlinear stiff differential equations. Since it is an implicit method.,

a simultaneous system of equations is solved at each step. Moler's

(13) matrix triangularization by Gaussian elimination and linear equa

tion solver routines are utilized. The method fails if the coefficient

matrix formed by [I.-ha^ J_ (y )] is singular. MINIF0R prints a diagnos

tic when this occurs; the user should then select another integration

method.

When using Galatian's method in the time varying case, a change

of variable should, be used. For example, let

YD0T(1) = 1.0

which has the solution Y(l) = T. Then substitute Y(l) for T in other

state equations where T appears.

REFERENCES

1e Buckley, Page S. 1964. Techniques of Process Control, John Wiley and Sons, Inc., New York City, New York.

2. Butler, J. L. 1970. Comparative Criteria for Minicomputers,Instrum. Technol. 17:67-82.

3C Calahan, D. A. 1968. A Stable Accurate Method of Numerical Integration for Non-linear Systems, Proc. IEEE ‘56:744.

4. Coughanowr, D. R., and Koppel, L. B. 1965. Process Systems Analysis and Control, McGraw-Hill Co., New York City, New York.

5. Digital Equipment Corporation Advertisement.' 1972. Electron. 45:29.

6. Gear, C. W„ 1971. Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Inc., Englewood Cliffs,N. J.

7. Jarvis, P. H. 1968. Some Experiences with Process Control Languages, IEEE Trans, on Indust. Electron, and Control Instrum. 15: 54-56.

8. Kaenel, Reg. A. 1970. Minicomputers - A Profile of Tomorrow’s Component, IEEE Trans, Audio Electroacoust. 18:354-379.

9. Marks, C. H., and Skillern, J. A. 1964. Transmitters for Computer Information Systems, ISA J. 11:73-76.

10. Mensh, M. , and Diehl, W,. 1968. Extended FORTRAN for Process Control, IEEE Trans, on Indust. Electron, and Control Instrum. 15:75- 79.

11.» Minutes, Fifth Workshop on Standardization of Industrial Computer Languages. 1971. Purdue Laboratory for Applied Industrial Control , Purdue University, Lafayette, Indiana.

12o Minutes, Sixth Workshop on Standardization of Industrial ComputerLanguages. 1972. Purdue Laboratory for Applied Industrial Control, Purdue University, Lafayette, Indiana.

13. Moler, Cleve B. 1972. Algorithm 423, Linear Equation Solver (F4),Comm, of the ACM 15:274.

121

122

14, Murphy, John A, 1971, Minicomputers, Modern Data 5_: 58-72.

15, Roberts, Bert C. 1968. FORTRAN IV in a Process Control Environment, IEEE rans, on Indust. Electron, and Control Instrum. 15: 61-63.

16. Spencer, Henry W., Shepardson, Harlon P., and McGowan, Larry M. 1970. Small Computer Software, IEEE Comput. Group News 3j15^20.

17. Wait, John V. 1971. FORTRAN Subroutines for Continuous System Simulation, IfCSRL Memo 223, n Department of Electrical Engineering, University of Arizona, Tucson, Arizona.

.18. White, James Wm. Private communication, Department of Chemical Engineering, University of Arizona, Tucson, Arizona. 1972.

19. Williams, Theodore J. (ed.). 1970. Emulator, Simulator, andTranslator Programs for the Small Digital Computers Necessary for Medical Laboratory Automation, Purdue Laboratory for Applied Industrial Control, Purdue University, Lafayette, Indiana.

mmm m *

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