%msdemo1 % Copyright 1991-2004 MUSYN Inc. and The MathWorks, Inc. % $Revision: 1.1.6.1 $ echo on clc % ************* DATA TYPES ************** % A 1-output, 2-input, 2-state linear % system is described by the following % four matrices a=[ -.15 .5 ; -.5 -.15] pause % strike any key to continue clc b = [.2 4;-.4 0] pause % strike any key to continue c=[5 5] pause % strike any key to continue clc d=[ .1 -.1 ] pause % strike any key to continue clc % The command % PCK % will pack this data into a system matrix % which we will call SYS pause % strike any key to continue sys = pck(a,b,c,d); % Simply printing out the MATLAB matrix SYS % reveals the extra information embedded in % this matrix pause % strike any key to continue clc sys % The matrix SYS is 4 by 5, and contains the % state space matrices a, b, c, and d. these % appear in the upper left, 3 by 4 corner of % the matrix, arranged as [a b; c d]. the matrix % SYS also has an extra row and column to indicate % that it is a system matrix. The -INF in the % (4,5) entry indicates system matrix, and the % 2 in the (1,5) entry indicates 2 STATES. pause % strike any key to continue clc % The command % MINFO, % which stands for matrix_information, gives % STATE, OUTPUT and INPUT information pause; % strike any key to continue minfo(sys) pause % strike any key to continue clc % the command % SPOLES % will print the poles of this system pause; % strike any key to continue spoles(sys) pause % strike any key to continue % That gives an idea of the SYSTEM MATRIX % data type. A VARYING MATRIX can be created % by calculating a frequency response or time % response of the system - first, a frequency % response. Make a frequency vector of 4 % logarithmically spaced points from 0.1 to 1, % using the MATLAB command LOGSPACE pause; % strike any key to continue omega = logspace(-1,0,4) pause; % strike any key to continue clc % The frequency response is computed with % the command FRSP. In particular % SYS_G = FRSP(SYS,OMEGA) % produces a VARYING matrix SYS_G, that is % the frequency response of SYS at the four % frequencies of OMEGA. pause; % strike any key to continue sys_g = frsp(sys,omega); pause; % strike any key to continue clc % If we print out the matrix SYS_G as a MATLAB % matrix, we can see that the frequency information % is embedded there pause; % strike any key to continue clc sys_g pause; % strike any key to continue % SYS_G is a 5 by 3 matrix. the INF in the (5,3) entry % implies VARYING matrix. the 4.00 in the (5,2) entry % indicates 4 data points are represented, and the first 4 % entries in the last (3rd) column are the frequencies. % the 4 by 2 block in upper left corner are the frequency % response matrices (each 1 by 2 - since SYS had 1 output % and 2 inputs) stacked upon each other. pause; % strike any key to continue clc % run the matrix_information command MINFO % on SYS_G to see that it is indeed a VARYING % matrix. pause; % strike any key to continue minfo(sys_g) pause; % strike any key to continue % note that SYS_G is a VARYING MATRIX as % expected. it consists of 4 points, and % each matrix has 1 row and 2 columns. the % command % SEE % is useful for displaying a varying matrix. it % prints out the matrix at each independent % variable value (here, interpreted as frequency) pause; % strike any key to continue see(sys_g) pause; % strike any key to continue clc % in this case, the frequencies at which the % frequency response has been computed are % called the INDEPENDENT VARIABLES of sys_g. % the command % SEEIV % displays the independent variables of a % of a varying matrix without showing all % of the varying matrix data. pause; % strike any key to continue seeiv(sys_g) pause; % strike any key to continue clc % VARYING matrices can be plotted versus % the independent variable with the command % VPLOT, which stands for MATRIX PLOT. VPLOT % plots each element of the varying matrix % versus the independent variable. In this % case, SYS_G has 1 row, and 2 columns, so % the command % VPLOT('liv,lm',SYS_G') % plots a log-magnitude plot (lm means log-magnitude) % of the 2 elements, with log axis for the % independent variable (liv) pause; % strike any key to continue echo off foobar = figure; vplot('liv,lm',sys_g) xlabel('Strike any key to continue') pause; echo on clc % VPLOT can also be used to plot Nyquist % plots. let's calculate a much finer % frequency response, over a larger range, % 100 points from 0.1 to 10. pause; % strike any key to continue omega = logspace(-1,1,100); sys_g = frsp(sys,omega); pause; % strike any key to continue clc % % check the frequencies with SEEIV(SYS_G). % it should be 100 points, from 0.1 to 10. % pause; % strike any key to continue seeiv(sys_g) pause; % strike any key to continue clc % now plot the 2 Nyquist plots of SYS_G with % % VPLOT('NYQ',SYS_G) % % the 'NYQ' stands for REAL versus IMAGINARY, and % the curves are parametrized by the independent % variable pause; % strike any key to continue echo off vplot('nyq',sys_g) xlabel('Strike any key to continue') pause; echo on clc % portions of the varying matrix sys_g can % be extracted out using XTRACT % XTRACT(SYS_G,0.4,2.1) % will extract from SYS_G those points with % independent variable (frequency) values % between 0.4 and 2.1 pause; % strike any key to continue clc some = xtract(sys_g,0.4,2.1); pause; % strike any key to continue % check that only a portion of the original % independent variables are in SOME pause; % strike any key to continue seeiv(some) pause; % strike any key to continue % generate a Nyquist plot of some using % VPLOT('NYQ',SOME) pause; % strike any key to continue echo off vplot('nyq',some) xlabel('Strike any key to conclude the demo') % That is an introduction to generating frequency % responses from system matrices, and plotting the % results. % % pause % strike any key to conclude the demo close(foobar); clc