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Implement a better algorithm for pole placement #117
Description
Hello!
I've happened to compare pole placement with Matlab's, and found out that returned matrix doesn't make the poles fall in the chosen values.
I made an example script just like python-control/examples/slicot-test.py for matlab and python.
Matlab script:
A = [
[ 0, 0, 0, 1],
[-42.7207306947135, 0, 0, 0],
[ 0, 0, 0, 0],
[ 47.0334901743703, 0, 0, 0]];
C = [[ 1., 0., 0., 0.],
[ 0., 1., 0., 0.],
[ 0., 0., 1., 0.],
[ 0., 0., 0., 1.]];
p = [-31., -21., -20., -30.];
L = place(A',C',p)
eigs(A' - C'*L)
% L= 31.0000 -42.7207 0 47.0335
% 0 21.0000 0 0
% 0 0 20.0000 0
% 1.0000 0 0 30.0000
% eigs = -20, -21, -30, -31
Python script:
import numpy as np # Numerical library
from scipy import * # Load the scipy functions
from control.matlab import * # Load the controls systems library
A = matrix([
[ 0, 0, 0, 1],
[-42.7207306947135, 0, 0, 0],
[ 0, 0, 0, 0],
[ 47.0334901743703, 0, 0, 0]])
C = matrix([[ 1., 0., 0., 0.],
[ 0., 1., 0., 0.],
[ 0., 0., 1., 0.],
[ 0., 0., 0., 1.]])
p = [-31., -21., -20., -30.]
L = place(A.T, C.T, p)
print "Pole place: L = ", L
print "Pole place: eigs = ", np.linalg.eig(A.T - C.T * L)[0]
#Pole place: L = [[ 0.73152698 -1.12180554 -0. 5.01688279]
# [ -1.12180554 22.72030247 -0. -7.69345088]
# [ -0. -0. 20. -0. ]
# [ 5.01688279 -7.69345088 -0. 34.40626723]]
#Pole place: eigs = [ -6.85809669 -30. -21. -20. ]
# >>> control.__version__
# '0.7.0'
Am I using it wrong?
Activity
robertobucher commentedon Oct 11, 2016
The problemis related to the MIMO system: it doesn't have a unique
solution! SW like Matlab or Scilab or Scicoslab use algorithms that are
able to find well conditioned solutions, python not!
For my lab I've implemented a replacement of the usual python "place"
command, in order to implement a wrapper to old fortran functions, able
to solve this problem finding a good solution. The solution is not
exactly the same found in Matlab, but it is well conditioned and usable
in real experiments.
The implemented SW is available at my homepage (robertobucher.dti.supsi.ch)
Roberto
On 10/11/2016 04:44 PM, Vitor Matos wrote:
vmatos commentedon Oct 11, 2016
Thank you Roberto!
Meanwhile I found that scipy already has
scipy.signal.place_poles, which results in the same as Matlab for this system.murrayrm commentedon Oct 11, 2016
I think we should leave this issue open. We should do one of the following:
placefunction with 'scipy.signal.place_poles'placeto provide well-conditioned solutionsI think I prefer the first as long as
scipy.signal.place_polesis compatible. We would just convertcontrol.placeto a wrapper function (we already require scipy as a dependency).[-]Pole placement not right?[/-][+]Implement a better algorithm for pole placement[/+]don4get commentedon Jan 5, 2019
It seems like this issue is already solved as there are now 4 possible ways to make pole placement (2 from scipy, one from slycot and one last without dependency).
murrayrm commentedon Jun 9, 2019
Issue is resolved. Current
placefunction uses SciPy and there are alternatives available (place_varga,acker).