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## Copyright (C) 1996, 2000, 2004, 2005, 2007
## Auburn University. All rights reserved.
##
##
## This program is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or (at
## your option) any later version.
##
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} rldemo (@var{inputs})
## Octave Control toolbox demo: Root Locus demo.
## @end deftypefn
## Author: David Clem
## Created: August 15, 1994
## Updated by John Ingram December 1996
function rldemo ()
while (1)
clc
k = menu("Octave Root Locus Demo", ...
"Display continuous system's open loop poles and zeros (pzmap)", ...
"Display discrete system's open loop poles and zeros (pzmap)", ...
"Display root locus diagram of SISO continuous system (rlocus)", ...
"Display root locus diagram of SISO discrete system (rlocus)", ...
"Return to main demo menu");
if (k == 1)
clc
help pzmap
prompt
clc
disp("Display continuous system's open loop poles and zeros (pzmap)\n");
disp("Example #1, Consider the following continuous transfer function:");
cmd = "sys1 = tf([1.5, 18.5, 6], [1, 4, 155, 302, 5050]);";
disp(cmd);
eval(cmd);
cmd ="sysout(sys1);";
disp(cmd);
eval(cmd);
disp("\nPole-zero form can be obtained as follows:");
cmd = "sysout(sys1,""zp"");";
disp(cmd);
eval(cmd);
disp("View the system's open loop poles and zeros with the command:")
cmd = "pzmap(sys1);";
run_cmd
prompt
clc
disp("Example #2, Consider the following set of poles and zeros:");
cmd = "sys2 = zp([-1, 5, -23],[-1, -10, -7+5i, -7-5i],5);";
disp(cmd);
eval(cmd);
cmd = "sysout(sys2);";
disp(cmd);
eval(cmd);
disp("\nThe pzmap command for the zp form is the same as the tf form:")
cmd = "pzmap(sys2);";
run_cmd;
disp("\nThe internal representation of the system is not important;");
disp("pzmap automatically sorts it out internally.");
prompt;
clc
disp("Example #3, Consider the following state space system:\n");
cmd = "sys3=ss([0, 1; -10, -11], [0; 1], [0, -2], 1);";
disp(cmd);
eval(cmd);
cmd = "sysout(sys3);";
disp(cmd);
eval(cmd);
disp("\nPole-zero form can be obtained as follows:");
cmd = "sysout(sys3,""zp"");";
disp(cmd);
eval(cmd);
disp("\nOnce again, the pzmap command is the same:");
cmd = "pzmap(sys3);";
run_cmd;
prompt;
closeplot
clc
elseif (k == 2)
clc
help pzmap
prompt
clc
disp("\nDisplay discrete system's open loop poles and zeros (pzmap)\n");
disp("First we must define a sampling time, as follows:\n");
cmd = "Tsam = 1;";
run_cmd;
disp("Example #1, Consider the following discrete transfer function:");
cmd = "sys1 = tf([1.05, -0.09048], [1, -2, 1],Tsam);";
disp(cmd);
eval(cmd);
cmd ="sysout(sys1);";
disp(cmd);
eval(cmd);
disp("\nPole-zero form can be obtained as follows:");
cmd = "sysout(sys1,""zp"");";
disp(cmd);
eval(cmd);
disp("View the system's open loop poles and zeros with the command:")
cmd = "pzmap(sys1);";
run_cmd
prompt
clc
disp("Example #2, Consider the following set of discrete poles and zeros:");
cmd = "sys2 = zp(-0.717, [1, -0.368], 3.68, Tsam);";
disp(cmd);
eval(cmd);
cmd = "sysout(sys2);";
disp(cmd);
eval(cmd);
disp("\nThe pzmap command for the zp form is the same as the tf form:")
cmd = "pzmap(sys2);";
run_cmd;
disp("\nThe internal representation of the system is not important;");
disp("pzmap automatically sorts it out internally.");
prompt;
clc
disp("Example #3, Consider the following discrete state space system:\n");
cmd = "sys3=ss([1, 0.0952; 0, 0.905], [0.00484; 0.0952], [1, 0], 0, Tsam);";
disp(cmd);
eval(cmd);
cmd = "sysout(sys3);";
disp(cmd);
eval(cmd);
disp("\nPole-zero form can be obtained as follows:");
cmd = "sysout(sys3,""zp"");";
disp(cmd);
eval(cmd);
disp("\nOnce again, the pzmap command is the same:");
cmd = "pzmap(sys3);";
run_cmd;
prompt;
closeplot
clc
elseif (k == 3)
clc
help rlocus
prompt;
clc
disp("Display root locus of a continuous SISO system (rlocus)\n")
disp("Example #1, Consider the following continuous transfer function:");
cmd = "sys1 = tf([1.5, 18.5, 6],[1, 4, 155, 302, 5050]);";
disp(cmd);
eval(cmd);
cmd ="sysout(sys1);";
disp(cmd);
eval(cmd);
disp("\nPole-zero form can be obtained as follows:");
cmd = "sysout(sys1,""zp"");";
disp(cmd);
eval(cmd);
disp("\nWhen using rlocus, inital system poles are displayed as X's.")
disp("Moving poles are displayed as diamonds. Zeros are displayed as")
disp("boxes. The simplest form of the rlocus command is as follows:")
cmd = "rlocus(sys1);";
run_cmd
disp("\nrlocus automatically selects the minimum and maximum gains based")
disp("on the real-axis locus breakpoints. The plot limits are chosen")
disp("to be no more than 10 times the maximum magnitude of the open")
disp("loop poles/zeros.");
prompt
clc
disp("Example #2, Consider the following set of poles and zeros:");
cmd = "sys2 = zp([],[0, -20, -2, -0.1],5);";
disp(cmd);
eval(cmd);
cmd = "sysout(sys2);";
disp(cmd);
eval(cmd);
disp("\nThe rlocus command for the zp form is the same as the tf form:")
cmd = "rlocus(sys2);";
run_cmd;
disp("\nThe internal representation of the system is not important;");
disp("rlocus automatically sorts it out internally.");
prompt;
clc
disp("Example #3, Consider the following state space system:\n");
cmd = "sys3=ss([0, 1; -10, -11], [0; 1], [0, -2], 0);";
disp(cmd);
eval(cmd);
cmd = "sysout(sys3);";
disp(cmd);
eval(cmd);
disp("\nPole-zero form can be obtained as follows:");
cmd = "sysout(sys3,""zp"");";
disp(cmd);
eval(cmd);
disp("\nOnce again, the rlocus command is the same:");
cmd = "rlocus(sys3);";
run_cmd;
disp("\nNo matter what form the system is in, the rlocus command works the");
disp("the same.");
prompt;
closeplot
clc
elseif (k == 4)
clc
help rlocus
prompt
clc
disp("Display root locus of a discrete SISO system (rlocus)\n")
disp("First we must define a sampling time, as follows:\n");
cmd = "Tsam = 1;";
run_cmd;
disp("Example #1, Consider the following discrete transfer function:");
cmd = "sys1 = tf([1.05, -0.09048],[1, -2, 1],Tsam);";
disp(cmd);
eval(cmd);
cmd ="sysout(sys1);";
disp(cmd);
eval(cmd);
disp("\nPole-zero form can be obtained as follows:");
cmd = "sysout(sys1,""zp"");";
disp(cmd);
eval(cmd);
disp("\nWhen using rlocus, inital system poles are displayed as X's.")
disp("Moving poles are displayed as diamonds. Zeros are displayed as")
disp("boxes. The simplest form of the rlocus command is as follows:")
cmd = "rlocus(sys1);";
run_cmd
disp("\nrlocus automatically selects the minimum and maximum gains based")
disp("on the real-axis locus breakpoints. The plot limits are chosen")
disp("to be no more than 10 times the maximum magnitude of the open")
disp("loop poles/zeros.");
prompt
clc
disp("Example #2, Consider the following set of discrete poles and zeros:");
cmd = "sys2 = zp(-0.717, [1, -0.368], 3.68, Tsam);";
disp(cmd);
eval(cmd);
cmd = "sysout(sys2);";
disp(cmd);
eval(cmd);
disp("\nThe rlocus command for the zp form is the same as the tf form:")
cmd = "rlocus(sys2);";
run_cmd;
disp("\nThe internal representation of the system is not important;");
disp("rlocus automatically sorts it out internally. Also, it does not");
disp("matter if the system is continuous or discrete. rlocus also sorts");
disp("this out automatically");
prompt;
clc
disp("Example #3, Consider the following discrete state space system:\n");
cmd = "sys3=ss([1, 0.0952; 0, 0.905], [0.00484; 0.0952], [1, 0], 0, Tsam);";
disp(cmd);
eval(cmd);
cmd = "sysout(sys3);";
disp(cmd);
eval(cmd);
disp("\nPole-zero form can be obtained as follows:");
cmd = "sysout(sys3,""zp"");";
disp(cmd);
eval(cmd);
disp("\nOnce again, the rlocus command is the same:");
cmd = "rlocus(sys3);";
run_cmd;
disp("\nNo matter what form the system is in, the rlocus command works the");
disp("the same.");
prompt;
closeplot
clc
elseif (k == 5)
return
endif
endwhile
endfunction