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INSTRUCTIONS for the program SYSAN. SYSAN is a program for the analysis of linear analog and discrete systems with and without feedback. The complete and unrestricted rights of the program belong to the author, M.J. van den Oever, Gregoriusdonk 10, 4707 VA Roosendaal, the Netherlands. Licensees can, in accordance with the licensing agreement, obtain certain rights to the program. Violation of the licensing agreement will void this agreement without any compensation for the licensee. The author reserves the right for compensation from the licensee in case the licensee circulates the program or parts thereof without written permission from the author. The program is not copy protected, but it contains a personal identifica- tion. This identification is shown in every program output. The identifica- tion is stored in code in the file IDENT.FIL. The file IDENT.FIL must be in the same directory as the the program SYSAN.EXE, otherwise SYSAN will not start. SYSAN was specially developed to run on PC's under the operating system MS- DOS. The required memory capacity is 640 Kbyte. A 8087 type numeric coprocessor is recommended. The program will automatic- ally use the coprocessor if it is available. The program is fully driven via menus and is ment to be used without other instructions. The program is multilingual. At the moment Dutch, German and English are available. Via an independant language generator program, other languages can be made available. The selection of the default language is fully automatic. You start the program with SYSAN LANGUAGE, in which LANGUAGE is omitted for the default language. The automatic language selection operates by means of the country number that is given at the startup of the computer in the config.sys file. In case config.sys does not provide a country number, the default language is English. You can also create a default language by preparing a file with the name DEFLANG.TXT and storing this file in the same directory with SYSAN.EXE. As an example the file DEFLANG.TXT for Dutch is prepared with: copy NEDERL.TXT DEFLANG.TXT If you do not use the default language, you start SYSAN with SYSAN NEDERLANDS for Dutch SYSAN DEUTSCH for German SYSAN ENGLISH for English. The program delivers tables, mathematical expressions and graphics. All output parts are complete on one screen. By means of Shift-PrtScr hardcopies of tables and expressions can be obtained. The special command P yields hardcopies of the graphics. The options command lets you choose between half size and full size graphics copies. The program is in color and adjusts itself automatically to the installed graphics card. The source program was written in Borland Pascal 7.0. All graphics cards that can be handled by Borland Pascal 7.0 can also be handled by SYSAN. It is possible to drive the program by mouse. You therefore should have installed a mouse with a MicroSoft mousedriver. The program has an extensive help function. At any place in the program, except in graphics with activated cursor, you can call the dedicated helpfunction with function key F1. At the moment the helpfunction is only available in Dutch and English. Depending on the particular graphic, the graphic can be provided with a grid to facilitate reading or a cursor can be installed. The grid facility is chosen with the options menu. Function key F4 installs the cursor. Hard copies can be made on Epson compatible 9 pins dot matrix printers and on HP laserjet and deskjet printers. The hard copy is a screen copy. Therefore the resolution of the hard copy depends on the graphics card. There are 2 print sizes: A5 (half size) over the width of the paper and A4 (full size) over the length of the paper. The choice is made in the options menus. If you wish, you may switch off all the menu directions in the tables, expressions and graphs. In that case you may also provide the graphics and the tables with a caption. The output is then more suitable for inclusion in reports and other publications. This switching is done in the options menu. Inputs, consisting of only one keystroke (commands), are executed im- mediately. Inputs, consisting of more keystrokes (data), are to be concluded with <Enter>. ┌───────────────┐ │ D O S │ └───────┬───────┘ -------------------------------------│------------------------------------ ┌────────────────────────────────────┴───────────────────────────────────┐ │ │ │ M A I N M E N U │ └────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬──────┬────┘ -----│-------│-------│-------│-------│-------│-------│-------│------│----- ┌────┴─────┐ │ ┌─────┴─────┐ │ ┌─────┴─────┐ │ ┌─────┴─────┐ │ ┌────┴────┐ │ │ │ │ │ │ │ │ │ │ SYSTEM │ │ │ │ │ INPUT │ │ │ ROOTLOCI │ │ │ FEEDBACK │ │ │ DISPLAY │ │ │ END │ └────┬─────┘ │ └─────┬─────┘ │ └───────────┘ │ └─────┬─────┘ │ └─────────┘ │ ┌─────┴─────┐ │ ┌─────┴─────┐ ┌─────┴─────┐ │ ┌─────┴─────┐ │ │ TIME │ │ │FREQUENCY │ │ │ │ │ │ │ │ RESPONSE │ │ │ ANALYSIS │ │ MATRIX │ │ │ OPTIONS │ │ └─────┬─────┘ │ └─────┬─────┘ └─────┬─────┘ │ └───────────┘ -----│-------│-------│-------│---------------│-------│-------------------- │ │ │ │ │ │ │ ┌─────┴─────┐ │ ┌─────┴─────┐ │ ┌─────┴─────┐ │ │ GRAPHICS │ │ │ │ │ │ Save │ │ │ OPTIONS │ │ │ GRAPHICS │ │ │.DFL files │ │ └───────────┘ │ └─────┬─────┘ │ └───────────┘ │ ┌───────────┐ │ ┌─────┴─────┐ ┌─────┴─────┐ │ │ GRAPHICS ├─┤ │ GRAPHICS │ │ Save/Call │ │ │ OPTIONS │ │ │ OPTIONS │ │.STE files │ │ └───────────┘ │ └───────────┘ └───────────┘ -----│---------------│---------------------------------------------------- ┌────┴─────┐ ┌─────┴─────┐ │ Call │ │COMPENSATOR│ │.DFL files│ │ DESIGN │ └──────────┘ └───────────┘ The program starts in the main menu. In the maim menu the various parts of the program may be selected either with the keys for the vertical cursor movement and the <Enter> key or with with the key for the bold letter or with the mouse and the left mouse button. In the same manner you make the selection in the other menus. With the function key F6, system data may be changed from all program parts. The changes concern the location of the poles and zeros, the value of the coefficients of the denominator- and numerator polynomes, the corner frequencies or the gain. The order of the transfer function cannot be changed. After the changes via F6 the program returns to the program part from where the change was initiated but with the new data. The function key F8 reinstalls the menu of the subject program part. The function key F9 directly selects the next menu item. Shift-F9 selects the former menu item. The function key F10 brings you back in the main menu. The system parameters are the common data. The three main parts of the program: TIMERESPONSE, FREQUENCY ANALYSIS and ROOTLOCI each work indepen- dently with the system parameters without changing them (except with F6). Transfer from one main part to another main part always goes via the main menu. Contents MAIN MENU: System Input Time response Root loci Frequency analysis System Matrix Close control loop Display of system / page overview Options Input K or Kpz ? Coord Cart or pol? Program Instruc. ? Grids in Plots ? Print size ? End of program - return to DOS SYSTEM INPUT: With the SYSTEM INPUT menu you may input the system data from the keyboard or from the data files. Also the system may be enlarged by adding poles and/or zeros. Contents SYSTEM INPUT menu: Poles and zeros PoLynomials Corner frequencies Data from File Append system Input of systemdata. The system transfer function can be presented with poles and zeros by s s (── - 1)(── - 1).... z1 z2 (s - z1)(s - z2).... G(s) = K ──────────────────── = Kpz ──────────────────── s s (s - p1)(s - p2).... (── - 1)(── - 1).... p1 p2 or by the polynomial form 3 2 ......b3s + b2s + b1s + b0 G(s) = ──────────────────────────── 3 2 ......a3s + a2s + a1s + a0 In the case of system input with poles and zeros, one has to select in advance via the options menu whether K or Kpz will be input. The default selection is K. The location of the poles and zeros in the complex plane is normally input and shown in Cartesian coordinates. Through the options menu one can opt for polar coordinates. Besides system inputs by means of poles and zeros or polynomials, system inputs may also be made through corner frequencies as is customary with Bode plots. Including the driving function, the system can handle a maximum of 8 poles and 8 zeros. Equal complex poles are not allowed. Up to 4 equal real poles are permitted. System data can also be input by means of state equations. The allowable magnitude of the input poles and zeros depends on the order of the transfer function. For the calculation of the absolute values of complex variables one needs the square of the real and the imaginary parts. Therefore highest power (= the order of the system) of the square of the complex roots must be smaller than 10 to the power 38. If you use a transfer function of the order 8, then the absolute value of poles and zeros must be smaller than 10 to the power 38/16 (237). The real and the imaginary part must then be smaller than 0.5√2 times this value (167). If you exceed this limit, it will result in a runtime error 205. Data from File: With this menu item you may read system data from a disk file. These data are stored through the save function of the 'Display of system/Data overview' item of the main program. There is no difference between data read from disk and data input through the keyboard. TIME RESPONSE: In this part of the program the time response of the system is calculated. The input signal to the system is defined by its poles, zeros and gainfac- tor. In case of an analog system, the Z-transform of the sampled system with zero-order hold may be calculated. This Z-transform may be stored on disk so that it can be read later to perform further calculations with it. This Z-transform is correct only when you start with the response on a unit step. Contents TIME RESPONSE menu: Input signal Laplace - partial fractions or Z-transform - partial fractions Time response - Expression Time response - Table Time response - Plot Plot Options Store plot Fetch plot Verticals - discrete Change main menu options Program Instruc. ? Grids in Plots ? Print size ? Z-transform (analog systems only) ROOT LOCI: Breakaway points and root-locus points as a function of the gain factor may be calculated. The gain factor is considered to be a separate proportional controller with gain Kc. The root-locus plot is drawn by varying Kc from 0 to 10 000. Above 10 000 Kc is considered to be ∞. The original DC system gain remains unaltered. Of each root locus 100 steps are calculated. It may occur that certain root loci are not entirely drawn, because either Kc exceeds 10 000 or the amount of steps is 100. The graphic display of the root loci can be explored by means of a cursor. The root-locus plot can be detailed more by reducing the step magnitude through the options menu. By doing so, there is a fair chance however, that the complete root-locus plot is not visible anymore as the total number of steps is limited to 100. The step magnitude should always be smaller than the smallest distance between any poles and zeros. The cursor location can be adjusted with the + and - keys of the cursor block when the cursor is locked onto the root locus. By default the cursor step is half the step of the root-locus calculation step. The cursor step may be changed via the options menu. A first order lead or lag compensator can be designed with the Compensator design program. First a dominant pole of the closed loop system, outside the excisting root locus, is chosen. Thereafter a choice can be made between a desired zero/pole ratio, a desired DC gain and an optimisation towards a maximum bandwidth. Further details are available in the accompanying help text. Contents ROOT LOCI menu: Breakaway points Root locus - Table Root locus - Plot Root locus plot Options Beginning of horizontal scale End of horizontal scale Step magnitude Cursor Adjustment magnitude Negative imaginary part of plot Maximum gain Constant Damping ratio Unit circle (discrete systems) Change main menu options Program Instruc. ? Grids in Plots ? Print size ? Compensator design Zero/pole ratio DC gain Optimise FREQUENCY ANALYSIS: In this part of the program the system frequency responses are calculated. One can automatically determine phase and gain margins. The 'date line' for the phase is -270°,+90°. This means that angles greater than +90° are continued beyond -270° and vice versa. The calculation of phase and gain margins succeeds only with monotonously climbing or descending functions. If the phase or gain as function of the frequency does not comply with this rule, the calculation may not converge. Non convergence will be mentioned. Bode plots, Nyquist plots and Nichols plots may be drawn. Where applicable, these plots can be provided with a M and a N circle of specified value. Approximation of the amplitude plot by straight lines and corner frequencies can be shown. The phase plot can also be approximated by straight lines. For single poles or zeros the straight line lies between 0.1*corner-frequency and 0° and 10*corner-frequency and ±90°. For complex poles or zeros the straight line approximation runs from -zèta{1+0.35(1-z²)} zèta{1+0.35(1-z²)} wn*10 and 0° to wn*10 and 180°. In case further details, of e.g. a Nyquist plot, are to be shown, the lowest and/or the highest frequency should be adjusted via the Plot Options menu. Contents FREQUENCY ANALYSIS menu: Frequency response Table Single frequency Phase margin Gain at phase Margin Gain margin Bode, Nyquist and Nichols Plot Magnitude-frequency plot (Bode) Phase-frequency plot (Bode) Nyquist plot Nichols Chart Plot Options Lowest frequency - rad/s Highest frequency - rad/s M - Circle N - Circle Unit circle in polar plot Change main menu options Program Instruc. ? Grids in Plots ? Print size ? For instruction purposes you may start Bode plots (frequency-gain and frequency-phase shift) with empty coordinates. In this way you can show the asymptotes first and the real curves afterwards. CLOSE CONTROL LOOP: When closing the control loop, the system output signal is inverted and fed back to the input of the system. Part of the gain, poles and zeros can be relocated from the forward part of the loop to the feedback part of the loop. By doing so, one can for instance determine the controller output signal. WARNING: If the gain choice is K, then relocation of poles or zeros to the feedback part of the loop means relocation of the terms s s (1 - ─) respectively (1 - ─). p z If the gain choice is Kpz, then the relocated terms are (s - p) respectively (s - z). This influences the static gain of the feedback proces. When poles and zeros of a discrete system are relocated, the controller gain and the feedback gain are corrected in such a way that all static gains of the control loop remain as is. MATRIX: In this program part system parameters may be input as state variables. The state equations are shown in the form of matrices. The matrices are defined for one output and one input of the system. Apart from supplying system data in the form of state equations, the system data that are already in the system can be shown as state equations. In that case you have the choice between the controllable canonical form and the observable canonical form. In the matrix menu you input the state data with function key F3. New and modified state equations are transferred to the main program and the system data are stored in the form of poles and zeros and of polynomials. The state equations of an analog system may be transformed to a sampled system with a zero order hold. You then obtain the Z-transform of the sampled system. The state equations may be saved on disk. To do so you select the menu item 'System matrices / page overview' and you save the data with F2. When saving, a filename without extension must be entered. The matrix files automati- cally obtain the extension .STE. The saved matrix files are called with the menu item 'State data from file'. Under the menu item 'Pole placement' you calculate the feedback vector K that causes the selected poles of the feedback system. If you have made this calculation, the calculations of the menu items 'Observer' and 'Reduced observer' are extended to the calculation of an observer-controller. To be able to check the robustness of the feedback system with an observer- controller the program calculates (if possible) the phase and the gain margins. Furthermore the data of the open loop system are saved on the scratch pad, so that it is always possible to perform a frequency analysis. Contents MATRIX menu: Input system matrices System matrices from File System matrices / Page overview Existing state equations Controllable canonical form Observable canonical form View pages Pole placement Observer Reduced observer Z - transform of matrices (analog systems only) SYSTEM DISPLAY / PAGE OVERVIEW In this part of the program all system parameters, both as poles and zeros and as polynomes are shown. Besides the active data, also past data are stored and shown. There are 5 pages available for the storage of past data. Those pages can be shown and made active. Each page has 4 subpages to store system data in the form of coefficients of state equations. The latter may be shown under the matrix menu. With function key F2 you can save system data. For demonstrations and repeated calculations on the same system it is recom- mended to prepare the system data in advance and to store those data on disk. There is no difference between data read from disk and data input through the keyboard. Data files may be stored in and read from any direc- tory. To store or read the data a filename without extension has to be entered. The files with the transfer functions automatically obtain the extension .DFL. The matrix files obtain the extension .STE. Graphics modes supported by SYSAN.EXE. All graphics modes that are supported by SYSAN.EXE have a horizontal resolution of either 640 dots or 720 dots. The supported modes are: CGA 640 x 200 MCGA 640 x 200 MCGA 640 x 480 EGA 640 x 200 EGA 640 x 350 EGA64 640 x 200 EGA64 640 x 350 EGAMono 640 x 350 IBM5814 640 x 480 HERCMono 720 x 348 ATT400 640 x 200 ATT400 640 x 400 VGA 640 x 200 VGA 640 x 350 VGA 640 x 480 PC3270 720 x 350 Only one graphics page is used. It is not possible to automatically select IBM8514 or ATT400. There may also be problems with automatic detection of some other graphics cards. This problem occurs e.g. with the Tulip DGA system. Therefore it is possible to override the automatic selection and to choose a particular graphics driver. This selection can be made with the program INSTGRAF.EXE, that generates a file BGI.SEL with a fixed driver selection. The contents of BGI.SEL is just one line: GraphDriver(number)<space>GraphMode(number)<space>GraphDriver(name) everything in accordance with Borland Pascal code. If the selected driver in BGI.SEL is not equal to the PC video system, the program will hang or show unreadable output. BGI.SEL can be deleted with DOS, thereafter the driver selection is fully automatic again. Monochrome monitors with a grey scale: In computers with a monochrome monitor and a VGA videocard the text mode colors presented in grey may give an unreadable result. In this case you can switch to monochrome with INSTTEXT. Graphics prints: Graphics hardcopies are normally made with an Epson compatible 9 needles matrix printer. If you want to make hardcopies with a monochrome HP printer you need to have an empty file named DESKJET.INS in your working directory. This file can be made with any text editer. Contents of the disk (the demo version has not all these files): SYSAN . EXE IDENT . FIL ATT . BGI STATE . PIC CGA . BGI 16X8 . FON EGAVGA . BGI 14X9X . FON IBM8514 . BGI 4X6 . FON HERC . BGI 8X8X . FON PC3270 . BGI ENGLISH . TXT NEDERLAN . TXT DEUTSCH . TXT DESIGHLP . NED DESIGHLP . ENG FEEDBHLP . NED FEEDBHLP . ENG FREQUHLP . NED FREQUHLP . ENG INPUTHLP . NED INPUTHLP . ENG LOCUSHLP . NED LOCUSHLP . ENG MAINHLP . NED MAINHLP . ENG MATRXHLP . NED MATRXHLP . ENG OPTIHLP . NED OPTIHLP . ENG SYSTHLP . NED SYSTHLP . ENG TIMEHLP . NED TIMEHLP . ENG ZERO1HLP . NED ZERO1HLP . ENG ZERO2HLP . NED ZERO2HLP . ENG INSTGRAF . EXE To be used for non-automatic graphics driver selection. INSTTEXT . EXE To be used with a monochrome monitor and color video card. INSTDIR . EXE Use this when IDENT.FIL is not in the same directory with SYSAN.EXE. INSTMAIN . EXE Use this when you start SYSAN.EXE from a different directory. M.J. van den Oever. October 4 1995