The Learning Curve

home *** CD-ROM | disk | FTP | other *** search

/ The Learning Curve / The Learning Curve (Weird Science, 1996).iso / electronics / analog_emulator / aces-docs / book < prev

Wrap

Text File | 1995-09-07 | 27.1 KB | 524 lines

The Analog Computer Emulator & Simulator AMIGA - ACES March 10, 1994 (Preliminary Documentation) Robert Berkey ------------------------------------------------------------------------- -Index- Introduction .........................................Page 2 ACES Modules .........................................Page X Data Preparation .....................................Page X Functional Setup......................................Page X Operation ............................................Page X Control Panel ........................................Page x Data Editor ..........................................Page X Plotter Setup ........................................Page X Plot Exporting .......................................Page X ACES Module Definitions ..........................Appendix A Plotter Data Format ..............................Appendix B Macro Collection .................................Appendix C Examples .........................................Appendix D Example 01 --SpringMass----------------------------Page x Example 02 --SineWave------------------------------Page x Example 03 --PHYSBE--------------------------------Page x Example 04 --CurveFit a,b,c -----------------------Page x Example 05 --Splat---------------------------------Page x Example 06 --Plate---------------------------------Page x Example 07 --Algebra-------------------------------Page x Example 08 --PID-----------------------------------Page x Example 09 --Sample--------------------------------Page x Example 10 --Implicit------------------------------Page x Conclusions ..........................................Page x ------------------------------------------------------------------------- -Introduction- Analog computing had it's heyday back in the 1960's, 70's, and 80's. The analog method of simulating physical systems and solving differential equations gave engineers and scientists the power to attack and solve many scientific and engineering problems by using the analog method. Analog computing equipment was and is expensive to buy, maintain, and use. Since analog elements have to be connected with wires plugged into a patching board, programming becomes a somewhat tedious exercise. With the presence of faster and more capable digital computers were being developed, attempts where made to emulate the analog computer functionality on the digital machines. Many of these emulations were run on the large "mainframe" machines, and later implemented on some of the smaller "mini" computers. Emulation languages developed include MIMIC, MIDAS, CSSL, and CSMP to name a few. Most of these programs were run "batch" fashion where data and parameters were entered on punched cards and submitted to the machine room for computation. The output (plots and print-outs) from the computer was received some time later and the results evaluated. This method, while not giving as good of a "feel" for the problem, as with analog methods, did solve problems and reduced or totally eliminated the need for an analog facility. During this period the problems, to be solved, also increased in complexity requiring even larger investments for an analog facility. With the introduction of the "Personal Computer" and the availibility of faster and more capable hardware and software, it is now possible to put analog style computing on your desktop. Analog Computer Emulator System (ACES) is a program for the Amiga computers to do analog-style computation and simulation. ACES doesn't have the capability to do massive simulations and can't replace software packages designed for specific purposes. ACES can solve those everyday smaller problems that could be handled with a medium-sized analog computer. Think of ACES as, sort of, a calculator for differential equations. ACES is designed to run on any current Amiga. The language is easy to learn, contains a rich assortment of emulated analog and hybrid modules, and provides most of the look and feel of an analog computer. ACES has an optional analog Control Panel, Plotter facility, and on-screen Data Editor. With the optional Control Panel, the user can control modes, monitor variables, and vary parameters. A simple plotting window, is included, to show trends in the selected variables. A plot export facility tailors the data for several popular off-line plotting programs. Data (configuration, parameters, outputs etc..) can be prepared "off-line" with any text editor capable of outputing vanilla ASCII characters. (ED is fine.) Optionally the user may take advantage of the Screen Editor facility to enter and modify the input data. ACES, like any analog emulator, computes the independent variable in discrete "steps". Generally, decreasing the step size increases the accuracy of the solution. Internally, ACES uses an "open loop", fourth order, Runga-Kutta scheme of integration and double precision floating variables throughout. Obtaining slightly different solutions, to a given problem, is one thing the user must get used to with open-loop integration. It is common practice to use coarser steps to approach a solution then "tighten down" the step size when higher accuracy is desired. There is always a trade-off between accuracy and speed of calculations. Varying step size gives you this flexibility. Hopefully by the time you work through the given examples you will get a feel for varying the step size and gain confidence in the method. ACES includes a rich assortment of analog and hybrid-type computing modules. Most of the usual analog linear and non-linear functions are included. Currently, up to 75 modules can be programmed in one model. plus the independent variable, denoted block (76). ACES has built-in Proportional + Integral + Derivitive (PID) modules. The PID modules can be used stand alone or in "cascade". The PID module is, in reality, a macro built of ACE modules but uses only one of the available modules for each controller. The PID controller can be used to evaluate control action on simulated processes. ACES expects the dependent variables to be "amplitude-scaled". Scaling is common practice for analog computers, where the operating voltage is fixed and usually ranges from +- 10.0 to +- 100.0 volts. In ACES , scaling helps maintain the solution between reasonable dynamic limits, and as a by-product, increases the accuracy, usability, and forces the user to know more about his problem. ACES uses +-1.0 as the scaled maximum. This is also common analog practice and is known as "unity" scaling. The real-world value of the computed variable can be found simply by multiplying the scaled value by the scale factor. Analog computers must also scale the independent variable (for the analog has a fixed independent variable (seconds) due to the electrical nature of the integration mechanism.) We can use any quantity ,for the independent variable in ACES, as long as all integration scaling is CONSISTENT throughout. -Modules- Computing elements are provided for most of the useful mathematical operations. Elements that add, subtract, multiply, divide, and negate are available. Integrator and mathematical transcedentals, (log, sine cosine, etc.) are supplied. Up to 3 arbitrary function types, each with twenty segments, can be utilized in any number of blocks. There are the so-called "hybrid elements", (digital and analog functions combined) such as sample/hold devices, transport delays, relays, latches and flags., which have both kinds of input and output. There are several digital-only elements such as pulse generator, and "AND" gate. Several special devices are the PID controller and iteration module. Algebraic loops can be handled by the CSMP style wye and vacuous elements. There can be a total of 75 blocks programmed plus the independent variable (block 76) which can be used by any module. The limitations are as follows: 25 integrators, 3 PID controllers, 3 Unit delays, 3 function types. All in all, ACES has at it's disposal a very rich assortment of module type (see the appendix for complete description of the ACES computing elements). -Data Preparation- Having amplitude-scaled the system equations, prepared a suitable flow diagram, and calculated the initial conditions, parameters, and arbitrary function tables, a data set can be prepared using an editor of choice. First the configuration of the modules must be specified. Each configuration statement is on a single line. An, up to 16 character, Identifier, a space, Block number of the module, a space, Block type code, a space Input block 1, a space, Input block 2, a space, and Input block 3. Unused inputs are given Block 0 as a block number. Block number assignments can be arbitrary except for vacuous (V) modules. The efficiency of the computation is increased by giving these modules the highest number in the system.(75 down). A pound sign (#) , after the last configuration statement line, ends the configuration data section. The second part, of the dataset, consists of the initial conditions, parameters, and scaling information. There should be a parameter statement for every module configured. Unused parameters are given a value of 0.0. Scale factor is the actual multiplication factor used for the variable in the scaling process (or 1.0) if un-scaled. Bias factor is generally 0.0... Each parameter statement is on a single line. An, up to 16, character Identifier, a space, Block number, a space, 1st parameter, a space, 2nd parameter, a space, 3rd parameter, a space, Scale factor, and Bias factor. A pound sign (#), on the next line, after the last parameter statement, ends the parameter data section. The third part, of the dataset, is where the parameters for the independent variable are specified. Step size is first followed by a space, then Maximum value, a space, then Frequency of printing. A pound sign (#), on the next line, ends the independent variable specifications. The value of the independent variable always starts at 0.0 and increases to the maximum value. The computation can be interrupted or terminated beforehand through use of a Quit (Q) element or placing the analog into "Hold" mode. The fourth part, of the dataset, is where assignment of the module Block numbers, to be printed, is specified. The independent variable and up to seven dependent variables can be printed in the log. On a single line, seven block numbers are entered separated by single spaces. A pound sign (#), on the next line, ends the print assignment data. Unused variables should be assigned to block 0. The independent variable (Block 76) is always printed. The fifth part, of the dataset, is the plot specification data. The first line is required, the others are optional. The first line specifies the block number for the X axis and up to five Y axis channels, each entry separated by a single space. Unspecified channels must use block 0. If no other data is specified, default values will be used for the plot. A pound sign (#), on the next line, ends the plot specifications. The optional lines contain the plot Title, X and Y axis labels, plot X and Y maximums and minimums, and Y axis identification text, the format and order, of which, can be found in Appendix B. A pound sign (#), on the next line , ends the plot specifications portion of the data set. The last specifications, in the data set, are for the optional arbitrary function tables. There are three different function specifications, Type 1, Type 2, and Type 3. Each Type of function can be assigned to multiple blocks. The functions use equally spaced ordinate values and arbitrary values for the abscissa. The data should also be amplitude-scaled. There are 20 function segments for each function. The ordinate values are entered on four lines, the range of the abscissa is specified in the parameter section for each block using this Type. All 20 abscissa values must be specified, any value, including 0.0, can be specified for unused values. Values,out of range, of the function ordinate extend the endpoints of the function abscicca. A pound sign, on the next line, ends the specifications for up the functions. A pound sign is required, for this section, even if no function tables are used. The function table format will be explained, in detail, later on. A pound sign, on the last line ends the dataset file. -Function Generator Setup- The arbitrary function generator scheme used in ACES consists of fixed divisions of the ordinate and arbitrary points on the abscissa. There are 20 divisions or segments equally spaced. The total range of the ordinate is set by the parameters P1 and P2 for the block assigned. P1 is the maximum value and P2 is the minimum. The value of the ordinate must increase from P2 to P1 (P1 must be more negative than P2). The abscissa can be any arbitrary float value but good scaling practice dictates keeping values between +1.0 and -1.0 . Three different types of function can be stored. Each type function can be re-used as many times as required. Don't forget to set P1 and P2 parameters in all the block parameter specifications. Overrange of the ordinate (P1 and P2 settings) is allowable with the function values above P1 or below P2 equal to the end point of the abscissa (Y) value. The first line of data includes the type # (1, 2, or 3) and first 5 data points, the second line points 6 - 10, third line points 11-15, and the fourth and last line points 16-21. A pound sign (#) follows each type specification. -Operation- After creating a dataset, the dataset may be loaded into ACES and "RUN". Running the data, in this sense, means checking the syntax, legal block assignments, number of allowable modules, ranges, and suitability for operation. There are several datasets in the EXAMPLES drawer, which can be used to gain familiarity with loading data and running ACES. (It is suggested to go through the examples, in order,.) Select the "ARCHIVE" item from the "SYSTEM" menu. Select the desired dataset from any of the available drives. Select "Load" to access the desired file. We can now "RUN" the dataset through ACES to check for legal block numbers, available modules, ranges etc. We do this by selecting the menuitem "RUN" from the "SYSTEM" menu. If there are no syntax or assignment errors ACES will put the emulator in "I/C" mode (applying the initial condition values to all of the integration modules.) The emulator is now ready to operate on the variables and provide a solution. When it is desired to start operation select the "OPERATE" Subitem from the "MODE" Item on the "SYSTEM" Menu. The independent variable, and up to seven, selected dependent variables will be printed on the screen, during the operation. The emulator will be placed in "Hold" at the end of the specified "Operate" period. This is the simplest way to operate ACES, and if a single "answer" is desired this may be all you have to do. ACES, normally, only outputs the log to the screen. The screen only holds output for a few seconds when full, erases, then continues to show the log. A "Screen Pause" feature can be selected during setup which allows the user to view each screen. Select "Continue" to continue operation. The log may, optionally, also be directed to the Preferences printer or a file volume for permanent record. The log documents the initial dataset when the dataset is first run. Subsequent changes are reflected in the log of the sections involved. A Static Test may be printed in the log by selecting "STATIC TEST" Subitem from the "MODE" Item in the "SYSTEM" Menu. The output values, of all currently used blocks, are printed in scaled and unscaled form. A static check can be generated at any time from Initial Condition or Hold modes. A static check of variables can be very helpful in debugging an analog system of equations. Normally, all setup for the system is done before the dataset is "RUN". In "Setup" Mode, you may choose to use the Screen Editor to modify the dataset. The editor must be closed before the dataset can be run. All changes ,at this point, are temporary. The dataset must be "Saved" for the changes to be updated in the dataset file volume. The Control panel may be enabled while in Setup and used to control the operation of the emulated analog computer. The Control panel allows the user to select modes with the mouse, monitor any two blocks continuously, and change parameters in all blocks in any mode. The parameter changes are temporary. The Screen Editor can be used to change the current dataset. If the dataset is re-run the parameters will revert back to the original values. The Plotter window may be enabled in "Setup" Mode. The plot density, annotation, and up to 5 Y axis channels selected for plotting. There is a mode available with the optional Control Panel that is not available from the "MODE" Menu. The name of this mode is "REP/OP", which stands for repeated operation mode. In REP/OP the compute mode of the analog cycles from initial conditions to operate - to hold - back to initial condition - etc. Several of the analog and hybrid modules respond to this mode enabling such things as parameter sweeps and iteration. The REP/OP mode can be canceled by going to "Hold" mode. The last cycle can be completed,if desired, by selecting "Operate" mode. There are several examples included that utilize repetitive operation. The optional QWIK-PLOT window gives a basic, Intuition driven, line plot of up to 5 abscissa (Y axis) variables verses any 1 ordinate (X axis) variable. A sidebar, on the QWIK-PLOT screen shows the current values of the annotation, scale factors, and other information currently in the dataset. From the QWIK-PLOT menu, plot density (the number of points for each variable) can be specified. Lines, tics and grids are optionally put on the plot. Plot data can be "exported" to a off-line plotting program. A plot record can be exported at the end of any operate period while in the hold mode. The pertinent data in the plot section of the dataset, the unscaled ordinate variable and all 5 unscaled abscicca values are included in the plot file. Export files for Multiplot and ListPlot can currently be generated. These data files are ASCII coded text and can be edited, after the fact, to include other plot options which are currently not implemented. -Control Panel Window- The ACES optional Control panel emulates features normally found on an actual analog computer console. The output of any two blocks can be continuously monitored, parameters may be entered in potentiometer devices, and modes can be controlled. The outputs of any of two blocks can be read in any mode. The coefficients for all block parameters can be adjusted while the analog is stopped or running. (Parameters, so adjusted, are changed only while the data is loaded. To make the changes permanent you must resave the dataset back on the volume where stored). The parameters cam be entered on the slide potentiometer gadgets (Range -10. to +10. ) or enter the floating number directly into the text type gadget. The analog mode pushbutton gadgets directly select the Initial condition (IC), Hold(HD), Operate(OP), and Repeated operation(REP/OP) modes on the analog computer. Box indicator gadgets indicate the present mode selected. A spare indicator is energized when a flag(F) element is triggered. This can notify the operator of some event occurring during the solution (sign change, limit, etc.). The Control Panel window can be closed at any time by clicking on the quit box at the upper left corner of the window. -Editor Window- A window-based editor is optionally available to MODIFY, ADD, or DELETE lines from the loaded dataset. You may use the editor to enter a completely new dataset,if you wish. All sections of the dataset [Configuration, Parameters, Timing, Functions, Print and Plot parameters] can be entered. A handy FORMAT display indicates the proper format for each section. One thing to remember... The changes apply only to the dataset loaded. To save changes permanently you must SAVE these changes back to the original storage volume. You can do this from the SYSTEM Menu ARCHIVE. You must close the editor window before re-RUNning the dataset. -Plotter Setup- The QWIK-PLOT Plotter Screen must be enabled while in SETUP mode. Up to 5 variables may be plotted against any module output. Several presentation options are available and may be selected by the screen menu. Plot conditions, on the screen, are sent to the Export plot file. Labeling and annotation information are entered in the dataset. (See Appendix B for data format.) -Plot Export Facility- ACES primary design aim is to provide a system for getting timely and accurate answers to your problem. Every effort has been made to hold down on the frills. There are occasions, however, that documented results, particularly professionally plotted results are required. ACES includes an export facility for several popular shareware plotting programs. Listplot (a subset of PLPLOT) and Multiplot are currently supported. Listplot is available in Fred Fish collection # 391 and a version of Multiplot is available on Fred Fish collection # 572. Either of these programs a can render professional looking plots to a number of different output devices. Every effort is made to export , to each program, all plot data it can accept, such as plot scaling, tic spacing, labels, grids, annotation, etc. Listplot is included with the distribution. Multiplot is available from a number of sources. -Examples- The following example datasets can be found in the Examples folder. They are supplied for informational purposes only. There is no guarantee or implied warranty as to their applicability to any given application. Their main purpose is instructional and as a basis for validating the modules and the emulator. ------------------------------------------------------------------------- EXAMPLE NAME: DESCRIPTION: NOTES: ------------- ------------ ------ SpringMass A spring-mass-damper Basic implementation of oscillatory system. F=MA equation commonly found in engineering. SineWave A basic sine-omega-t Purpose is to show effect and cosine-omega-t of step size upon accuracy linear oscillator. of integration in both frequency and amplitude. Results of integration compared against math trig. functions. PHYSBE Volumetric model of Medium sized simulation the human circulatory uses arbitrary functions system and heart. and discrete logic. A classic example.... CurveFit-1 Minimization of error Purpose is to show between field data and methods using Repetitive a mathematical model. Operation to manually adjust parameters. CurveFit-2 (Same as above) with one Purpose is to show method parameter calculated. of adding automatic iteration of one parameter. Features the Iterative module (?). CurveFit-3 (Same as above) with two Purpose is to show method parameters calculated. of adding additional automatic iteration of multiple parameters. Splat Study of pilot eject- Shows use of hybrid logic ion from an airplane. to control solution of differential equations containing limits. Plate Unsteady-state heat A practical diffusion transfer in a steel model of a solid with variable surface boundary conditions. Algebra Algebraic loop Method for solving calculation. algebraic loops involved in analog models. Pid Control of an first- Demonstrates use of the order process with an use in PID controller analog controller. (%) module to control a simulated process. Sample (Same as above) with Shows use of hybrid / built-up digital-type analog modules. sampling controller. Zero-order-hold (Z) and unit delay (U) modules are implemented. Implicit Computing the inverse Shows use of the Vacuous of log e function (V) and Wye (Y) modules (limited range). to simulate the calculations normally done with the high-gain analog operational amplifier. ------------------------------------------------------------------------ -Conclusions- ACES has been designed as a very basic but capable analog computer system emulator. Every effort has been made to hold down the frills, in this program, so that it may be run on any AMIGA computer system. ACES is very usable to solve those small to medium-sized problems that have a way of cropping up. ACES has not been designed as a production tool. You would hardly use ACES to generate any volumeous amount of data on any particular model. That's the purpose of all the great packages tailored to a specific application. Think of ACES as more of a universal calculator for systems of linear and non-linear differential equations. Through the use of ACES, you will gain a feel of the problem, be able to interact, intuitively make changes, and possibly solve that problem. Good Luck!; I hope you enjoy using ACES... ------------------------------------------------------------------------- [end]