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?