MIDAS(ID:439/mid002)

Digital simulation language 

• Country: us
  • languages for us
  • us/1963
• Began: 1963
  • Languages for 1963
  • 1960s languages
  • Third generation
  • Early Cold War
• Published: 1964
  • 1964
• Type:Expression oriented
  • Expression oriented
• Sammet:SPC
  • SPC
  • SPC/1963
  • SPC/us

Sansom, Harnett, Warshawsky, "MIDAS - How It Works and How It's Worked" view details
External link: Elements of MIDAS External link: Midas Elements - Switching External link: Midas Elements - Arbitrary functions External link: Midas Elements - Iterative External link: Midas Elements - Other External link: Midas Output - Case 1 External link: Midas Output - Case 2 External link: Midas Output - Case 3 Extract: Introduction
Introduction
The possibility of using a digital computer to obtain check solutions for the analog was recognized by many people at the dawn of our 15 year old history. Unfortunately several problems existed then, mainly at the digital end, which made this impracticable. Digital computers of that day were terribly slow, of small capacity and painfully primitive in their programming methods. It was usually the case when a digital check solution was sought for an incoming analog problem, that it was several months after the problem had been solved on the analog computer and the results turned over to the customer before the digital check solution made its appearance. The fact that the two solutions hardly ever agreed was another deterrent to the employment of this system. As we all know, digital computers have made tremendous strides in speed, capacity and programmability. In the area of programming ?and throughout this pa per - we're talking of scientific problems expressible as differential equations; the main effort has been in the construction of languages such as Fortran. Algol, etc. to permit entering the problem in a quasi-mathematical form, with the machine taking over the job of converting these to the individual serial elemental steps. While the progress along this line has been truly awe-inspiring to an analog man (usually all engineer), the resulting language has become quite foreign to him so that if he wishes to avail himself of the digital computer he must normally enjoy an interpreter in the form of a digital programmer (usually a mathematician). This means that he must describe his engineering problem in the required form, detail, and with sufficient technical insight to have the digital programmer develop a workable program on the first try. This doesn't happen very often and it is the consensus of opinion among computing facility managers that a major source of the difficulty lies in the fact that the engineer does not always realize the full mathematical implications of his problem. For example, ill specifying that a displacement is limited, he might not state what happens to the velocity. This can lead to all sorts of errors as an analog programmer would know. It is, of course, possible for an analog programmer to learn to program a digital computer by studying Fortran. This has been attempted here at Wright-Patterson AF Base with little success, mainly because, unless used very often, the knowledge is lost so that each time a considerable relearning period is required. Some computing facilities have even embarked on cross-training programs so that each type of programmer knows the other's methods. While this has much to 1,ecommend it, it is often impracticable.
In March of 1963, Mr. Roger Gaskill of Martin-Orlando explained to us the operation of DAS (Digital Analog Simulator), a block diagram type of digital program which he intended for use by control system engineers who did not have ready access to an analog computer. We immediately recognized in this type of program the possibility of achieving our long-sought goal of a means to obtain digital check solutions to our analog problems by having the analog programmer program the digital computer himself! We found that our analog engineers became quite proficient in the use of DAS after about one hour's training and were obtaining digital solutions that checked those of the analog.
At this point several limitations of this entire method should be acknowledged. First, the idea that obtaining agreement between the digital and analog solutions is very worthwhile is based mainly on an intuitive approach. After all both solutions could be wrong since the same programming error could be made in both. Secondly, the validity of the mathematical model is not checked, merely the computed solution. Finally, it might be argued that the necessity of the analog man communicating the problem to his digital counterpart has the value of making him think clearly and organize his work well. This is lost if he programs the digital computer himself. In spite of these limitations we thought it wise to pursue this idea.
Although DAS triggered our activity in the field of analog-type digital programs, several others preceded it. A partial list of these and other such programs would include:
DEPI     California Institute of Technology
DYSAC    University of Wisconsin
DIDAS    Lockheed-Georgia
PARTNER  Honeywell Aeronautical Division
DYNASAR  General Electric, Jet Engine Division

Almost all of these - with the possible exception of PARTNER (Proof of Analog Results Through a Numerical Equivalent Routine) - had as their prime purpose the avoidance of the analog computer. They merely wished to borrow the beautifully simple programming techniques of the electronic differential analyzer and apply them to the digital computer.
While DAS proved to be very useful to us, certain basic modifications were felt to be necessary to tailor it better to our needs. Principal among these modifications was a rather sophisticated integration routine to replace the simple fixed interval rectangular type of DAS. Other important changes were made but the change in the integration scheme and our wish to acknowledge our debt to DAS, led us to the choice of the name MIDAS, an acronym meaning Modified Integration Digital Analog Simulator. In this paper a brief description of the method of using MIDAS will be given, followed by a summary of our experience in using it in a large analog facility for about 18 months.
Extract: How MIDAS Has Worked
How MIDAS Has Worked
In the following paragraphs, a brief summary of the experiences of the Wright-Patterson AF Base Computation Facility in the use of MIDAS will be given. Actually, at this writing, approximately 100 computing facilities throughout the U.S. are using MIDAS; thus only a small segment of the total experience can be reported on.
The Analog Computation facility at Wright-Patterson has used MIDAS in almost every problem submitted for solution on its large analog computer. Generally the MIDAS solution is attempted prior to the analog in order to achieve the maximum benefits as regards scaling. Another side benefit of MIDAS has been the calculation of Problem Check values. It has been found in many cases that the extra time involved in programming a MIDAS check is saved in checkout time on the analog computer. The increased confidence in the validity of the solutions when a check between MIDAS and the analog solution is obtained is the most important benefit of the program. Another side benefit is the broadened horizons achieved by the analog programmers in giving them the ability to program the digital computer. This should be very valuable when hybrid computers come into their own. Until now the problem of finding people with the required capability in both areas has proven to be the greatest deterrent to the growth of these new devices.
While everything mentioned above is on the positive side, there are quite a few aspects of MIDAS that are annoying and time consuming. One thing that the analog programmer learns is that the digital computer brooks no mistakes. If a "zero" is punched when the letter "0" is required, the problem comes back  - generally the following day - with a diagnostic telling him of an undefined symbol. A little thing like a missing decimal point in numerical data will cause a day to be lost. Another thing that an analog programmer encounters is that when an error exists in a MIDAS program (however not of the type to prevent its running) , the solutions look just as good (as many significant figures of output) as they would if the solution were perfect. On the analog computer errors of the same type would cause overload lights to flash, etc.
The very sophisticated integration routine of MIDAS introduces problems at times. For example,  discontinuities  in  derivatives  some- times make it impossible for the error criterion to be met even though the increment of the independent variable is halved many times. This will cause a solution to "hang up." Provision has been made to overcome this problem by the use of MININT (see Table I) but it usually requires one or more unsatisfactory runs before the programmer is made aware of the difficulty.
One rather interesting discovery was the fact that an operation that was very easy to perform on an analog computer was very bothersome on the digital. Specifically, a rather large missile simulation was performed first on the analog computer and later using MIDAS. Quite a few first order lags were present in  the  mathematical   model   in   the  form   of 1/T(S+1) On the analog computer this offers no problem. For small values of r one way to handle this to parallel the feedback resistor of a summer with a capacitor of r microfarads. In fact, far from creating a difficulty, it generally is beneficial to the analog simulation by reducing some of the high frequency "noise." Using MIDAS, small values of T can cause considerable increase in solution time. For example, in this particular problem, when such transfer functions with  r of ,001  secs.  were included, the solution time was extrapolated to be 5 1/2 hours for 26 seconds of problem time. This was reduced to 1 1/2 minutes for the same length of problem time, simply by neglecting these small delays, and the effect on the results was insignificant. Incidentally, the analog solution was in "real time," i.e., 26 seconds. The subject of solution time is rather important to a digital programmer. We have attempted to gather data on the relative speed of a MIDAS run compared with a Fortran program produced by a skilled programmer. With the conditions of the test equalized, the solution time of the Fortran program was approximately half as long; however, the programming time for MIDAS was much less. The question of solution time is not very important for the typical problem handled with MIDAS because usually we are interested in one or two runs, so whether they take 3 minutes or 5 minutes each is of academic interest only.
There have been a few problems handled by MIDAS alone without recourse to the analog computer. In these cases, program efficiency was of considerable importance since many runs were required. Here, in the present stage of the development of MIDAS, a specially tailored digital program should receive serious consideration.
At this point the question should be considered of whether MIDAS or a similar digital computer program will take over the role of the analog computer in the areas where the latter shines. Since a MIDAS-type program has appropriated one of the best features of the analog computer, viz., simple block diagram programming and the speed and capacity of digital computers have developed so much. there is certainly reason to consider this question.
While anyone would he foolhardy to give an answer to hold for all time, it is our opinion that MIDAS, rather than threatening the existence of analog computers, has reinforced their position by increasing confidence in their output. There are quite a few advantages to the use of an analog computer which MIDAS doesn't touch.    Among these are:
(1) The intimate relationship between the engineer and his problem which enables him to design his system by observing typical outputs and changing parameters as required.
(2)   The ability to tie in physical hardware to the mathematical simulation.
(3)   The ability to use portions of the computer in direct relationship to the size of the problem
(4)   The fact that certain mathematical operations are performed better, e.g., integration.
(5)   The very fact that it is a distinctly different technique of solution, thus making possible a checking means.
While some progress has been and is being achieved in items 1, 2, 3 and 4, item 5 will always remain. Extract: How MIDAS Works
How MIDAS Works
To a large degree, programming in MIDAS closely resembles the methods used in DAS and, therefore, an analog computer. There are usually three steps we go through in obtaining a solution. First we prepare a block diagram very similar to an analog schematic indicating the operational elements required to solve the problem. Next we prepare a listing which is our means of directing the punching of the cards, one for each line. This listing indicates the source of the inputs to each element and defines the values of the required numerical data. After the cards have been punched and checked they are turned in to our IBM 7094 operations group where the information is placed on magnetic tape and this tape, along with the MIDAS subroutine, is used to solve our particular problem. The results are given to us on printed form according to a rather fixed format.
As an illustration of the steps involved in preparing a MIDAS program, let us set up the classical second-order linear differential equation for the mass, spring and damper system.
The equation is:
Mx+ Bx + Kx = 0              (1)
with initial conditions:
x(0)   = A x(0)   = 0
The MIDAS block diagram for this equation is shown In Figure 1. The following points should be noted:
(1)   S1 is a summer which adds the quantities  -Bx and -Kx to yield MY in accordance with equation 1.
(2)   Dl is a divider whose dividend is Mx (the output of S1) and whose divisor is a constant called M. Its output is then +x,
(3)   I1 is an integrator whose input is +x' and output is +x.    Unlike the case of analog integrators and summers, there is no change of sign in the equivalent MIDAS elements. Since no initial value is specified the output of I1 will start at zero.
(4)   12 .i~ another integrator whose input is +x and whose output is +x. The initial value of x is indicated by the dashed line extra input to 12.
(5)   M1 an; M2 are multipliers which multiply +x by  - B and +x by  - K to provide the required inputs to S1.    Unlike on analog computers the same type of multiplier   is   used   whether   two   constants, a variable and a constant, or two variables are being multiplied.
(6)   FIN is a finish element.    This element will stop computation when its A input (in this case t) equals or exceeds its R input (in this case the quantity named STOP).    Computation can be caused to halt by any of several  conditions.    A FIN box is required for each termination criterion.
(7)   When numerical data corresponding to M, B, K, STOP and x(0) are furnished, the problem is completely specified.   No scaling will be required since numerical values ranging between  lo-" and 10*" can be handled.
Next the listing is prepared.    It will contain the following information:
(1)   One card identifying the problem.
(2)   A  few  cards calling out the  MIDAS program.
(3)   Cards  giving  names  to  the  constants and parameters of the problem, including   integrators   with   non-zero   initial values  (up to 6 per card).
(4)   One card for each RfIUAS element in the  block   diagram,   identifying   it   by type  and  number,   and   indicating  the source of  its  inputs   (for  example  S2 meaning summer number 2).
(5)   At least one FIN card specifying a co11dition for finishing a run.
(6)   One or more HUR cards and RO cards specifying   the   header   names   to   be placed on top of the columns of output data to be read out at specified increments of the independent variable.
(7)   An END card indicating the end of the symbolic program and the start of numerical data.
(8)   One or more cards assigning numerical value to the constants, parameters and initial conditions named in  (3)  above.
(9)   Cards  defining  arbitrary  functions,  if any.
An example of a listing is shown in Figure 2 for the mass, spring, and damper system.
Note the use of a comment card by the programmer to identify the problem. Also of significance is the columnar location of various types of entries. For example, comment cards have their first letter in column 1. Operational elements, constant and parameter naming cards, HDR and RO cards all have their first character in column 7. Inputs to these elements are listed starting in column 15. Numerical data is listed starting in columns 1, 11, ... 51.
It should be pointed out that in MIDAS, the programmer need not concern himself with the order in which he prepares the listing since a built-in sorting routine will automatically line up the program properly. This is another important difference from MIDAS' predecessor, DAS.
The particular listing shown will result in three runs being made, each starting with x(0) =20 and terminating when t = 6. The mass M will have a value of 10 for each case since M was named on a constant card. The three runs will have the following values of  - B and  - K, each of which was specified as a parameter.
Run 1 -B=--2.5 , -K = -8.6
Run 2 -B = -3.2 ,  -K = -8.6 Run 3 -B = -2.5 , -K = l5.0
Finally a portion of the printed output of the IBM 7094 is shown in Figure 3. Several points are worthy of note.
(1) The printout of the problem listing including the data for Case 1. Actually some machine mapping and storage information precedes this but has been omitted for clarity.
(2) The format of the output. Note the headers and the spacing of the four columns of output. Provision exists for six columns but only four components were specified to be read out in this simple problem.
(3) The MAXIMA-MINIMA table. This feature, unique to MIDAS, provides the analog programmer with all the information needed to scale his analog schematic, both in amplitude and time. It shows the maximum and minimum values achieved by every component during the course of a run, whether these values occurred at read out intervals or not.
(4) The printout of the parameter and IC data for Cases 2 and 3, followed by their output.
(5) The job accounting summary. The three cases took a total of 44 seconds.
This completes the description of this problem. Although considerable detail has been presented, in retrospect it can be seen that the main idea was simple. An analog-type block diagram was drawn and a listing prepared describing its interconnections. Information providing   numerical   data   was   also   furnished.
This was then converted to punched cards, turned in to the 7094 operators who subsequently supplied the printed output.
Extract: Integration System in MIDAS
Integration System in MIDAS
The integrations in MIDAS are performed by a variable-step, fifth-order, predict-correct integration routine.' This variable-step feature represents the basic departure of MIDAS from its predecessor, DAS. It relieves the programmer from the chore of having to specify a fixed increment of the independent variable, an increment which must be small enough to handle the highest frequency phenomena in a problem but not so small as to cause inordinately long solution times. The step size in the MIDAS integration routine adjusts itself to meet a certain error criterion, a factor which allows it to take large steps for those portions of the solution "when not much is happening" and small steps for those portions when one or more variables are changing at rapid rates.
The net result is that time-scaling, as the analog programmer knows it, is eliminated in MIDAS. However, he must still face the time scaling problem when he prepares his analog schematic, especially when certain variables in the problem drive narrow bandwidth analog components such as servo-multipliers, X-Y plotters, etc. MIDAS helps him here, though, because he can observe the maximum values of the derivatives of these variables from the MAXIMA-MINIMA list and he can then make any necessary time base changes. Fortunately, for every variable appearing at the output of a MIDAS integrator, its derivative must appear at the output of the element feeding the integrator since integrators can accept only a single input.
Miscellaneous Information on MIDAS
The MIDAS program has limitations on the number and characteristics of certain components.   This information may be of value when a very large problem is to be solved on MIDAS.
Maximum Item                          Number
1.   Operational  Elements                       750
2.   Symbols   (operational elements, constants, and header names)       1000
3.   Integrators                                 100
4.    Function Generators                        40
5.   Points  for  each  function  generator      50
6.   Inputs for each summer                       6
Extract: The future of MIDAS and MIMIC
Future of MIDAS
Although MIDAS has proven to be very effective in accomplishing its purpose, certain improvements could be made without materially changing its simple programming rules. Among such improvements would be the following:
(1) Increased efficiency, i.e., shorter solution times without losing programming simplicity.
(2) Additional flexibility in naming outputs.
(3) Permit the use of fixed point literals in the body of the program
(4) A greatly expanded operation list that would include logical operations such as AND, OR, NOT, etc. and others equivalent to the elements found in a hybrid computer.
A new program is being developed at Wright-Patterson AF Base which already includes the improvements listed above. In addition, it is anticipated that the following features will be included:
(1) Ability to add new functions external to the basic program.
(2) Additional controls that would
(a) Allow the results of one run to dictate automatically the conditions for the next.
(b) Permit more "hands on" control of operation of the program as advocated by Mr. R. Brennan in his PACTOLUS program.
It is further hoped that an investigation of various integration routines will result in an integration system that will automatically account for discontinuities and thus prevent the solution from "hanging up."
The new program, MIMIC, is completely different from MIDAS in concept but it retains the programming ease of MIDAS. It will be written as a system to operate under IBJOB control on an IBM 7090/7094 computer.
It is an assembler type program that generates machine language code equivalent to the original problem. The instruction format is very similar to MIDAS but has been designed to appeal to both analog and digital programmers. If and when this occurs and both analog and digital programmers employ MIMIC regularly, a very significant first step in breaking down the communications harrier between the two will have been taken since they will, for the first time, be speaking the same language. Furthermore, just as MIDAS has made the digital computer accessible to the analog man, this new program might serve to educate the digital programmer in analog methods. The day of the omniscient, triple-threat programmer might be on the way!

      in [AFIPS JCC 26] Proceedings of the 1964 Fall Joint Computer Conference FJCC 1964 view details