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[python-control-discuss] SF.net SVN: python-control:[27] trunk
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From: <mur...@us...> - 2010-06-18 05:06:36
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Revision: 27
http://python-control.svn.sourceforge.net/python-control/?rev=27&view=rev
Author: murrayrm
Date: 2010-06-18 05:06:29 +0000 (Fri, 18 Jun 2010)
Log Message:
-----------
Extracted Ryan's root locus code to see how things work. Main change
was converting num, den to poly1d's (assumed in Ryan's TF class).
Basic functionality seems to work (!).
Modified Paths:
--------------
trunk/external/controls.py
Added Paths:
-----------
trunk/src/rlocus.py
Modified: trunk/external/controls.py
===================================================================
--- trunk/external/controls.py 2010-06-17 21:29:23 UTC (rev 26)
+++ trunk/external/controls.py 2010-06-18 05:06:29 UTC (rev 27)
@@ -1,5 +1,5 @@
# controls.py - Ryan Krauss's control module
-# $Id$
+# $Id: $
"""This module is for analyzing linear, time-invariant dynamic systems
and feedback control systems using the Laplace transform. The heart
Added: trunk/src/rlocus.py
===================================================================
--- trunk/src/rlocus.py (rev 0)
+++ trunk/src/rlocus.py 2010-06-18 05:06:29 UTC (rev 27)
@@ -0,0 +1,140 @@
+# rlocus.py - code for computing a root locus plot
+# Code contributed by Ryan Krauss, 2010
+#
+# Copyright (c) 2010 by Ryan Krauss
+# All rights reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions
+# are met:
+#
+# 1. Redistributions of source code must retain the above copyright
+# notice, this list of conditions and the following disclaimer.
+#
+# 2. Redistributions in binary form must reproduce the above copyright
+# notice, this list of conditions and the following disclaimer in the
+# documentation and/or other materials provided with the distribution.
+#
+# 3. Neither the name of the California Institute of Technology nor
+# the names of its contributors may be used to endorse or promote
+# products derived from this software without specific prior
+# written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL CALTECH
+# OR THE CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
+# USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+# ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
+# OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+# SUCH DAMAGE.
+#
+# RMM, 17 June 2010: modified to be a standalone piece of code
+# * Added BSD copyright info to file (per Ryan)
+# * Added code to convert (num, den) to poly1d's if they aren't already.
+# This allows Ryan's code to run on a standard signal.ltisys object
+# or a controls.TransferFunction object.
+# * Added some comments to make sure I understand the code
+#
+# $Id: $
+
+# Packages used by this module
+from scipy import *
+
+# Main function: compute a root locus diagram
+def RootLocus(sys, kvect, fig=None, fignum=1, \
+ clear=True, xlim=None, ylim=None, plotstr='-'):
+ """Calculate the root locus by finding the roots of 1+k*TF(s)
+ where TF is self.num(s)/self.den(s) and each k is an element
+ of kvect."""
+
+ # Convert numerator and denominator to polynomials if they aren't
+ (num, den) = _systopoly1d(sys);
+
+ # Set up the figure
+ if fig is None:
+ import pylab
+ fig = pylab.figure(fignum)
+ if clear:
+ fig.clf()
+ ax = fig.add_subplot(111)
+
+ # Compute out the loci
+ mymat = _RLFindRoots(sys, kvect)
+ mymat = _RLSortRoots(sys, mymat)
+
+ # plot open loop poles
+ poles = array(den.r)
+ ax.plot(real(poles), imag(poles), 'x')
+
+ # plot open loop zeros
+ zeros = array(num.r)
+ if zeros.any():
+ ax.plot(real(zeros), imag(zeros), 'o')
+
+ # Now plot the loci
+ for col in mymat.T:
+ ax.plot(real(col), imag(col), plotstr)
+
+ # Set up plot axes and labels
+ if xlim:
+ ax.set_xlim(xlim)
+ if ylim:
+ ax.set_ylim(ylim)
+ ax.set_xlabel('Real')
+ ax.set_ylabel('Imaginary')
+ return mymat
+
+# Utility function to extract numerator and denominator polynomials
+def _systopoly1d(sys):
+ """Extract numerator and denominator polynomails for a system"""
+
+ # Start by extracting the numerator and denominator from system object
+ num = sys.num; den = sys.den;
+
+ # Check to see if num, den are already polynomials; otherwise convert
+ if (not isinstance(num, poly1d)): num = poly1d(num)
+ if (not isinstance(den, poly1d)): den = poly1d(den)
+
+ return (num, den)
+
+def _RLFindRoots(sys, kvect):
+ """Find the roots for the root locus."""
+
+ # Convert numerator and denominator to polynomials if they aren't
+ (num, den) = _systopoly1d(sys);
+
+ roots = []
+ for k in kvect:
+ curpoly = den + k * num
+ curroots = curpoly.r
+ curroots.sort()
+ roots.append(curroots)
+ mymat = row_stack(roots)
+ return mymat
+
+def _RLSortRoots(sys, mymat):
+ """Sort the roots from sys._RLFindRoots, so that the root
+ locus doesn't show weird pseudo-branches as roots jump from
+ one branch to another."""
+
+ sorted = zeros_like(mymat)
+ for n, row in enumerate(mymat):
+ if n==0:
+ sorted[n,:] = row
+ else:
+ # sort the current row by finding the element with the
+ # smallest absolute distance to each root in the
+ # previous row
+ available = range(len(prevrow))
+ for elem in row:
+ evect = elem-prevrow[available]
+ ind1 = abs(evect).argmin()
+ ind = available.pop(ind1)
+ sorted[n,ind] = elem
+ prevrow = sorted[n,:]
+ return sorted
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