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Update place to use scipy.signal.place_poles#176

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Merged
murrayrm merged 6 commits intopython-control:masterfromrabraker:update_place
Jan 5, 2018
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86 changes: 83 additions & 3 deletionscontrol/statefbk.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -45,12 +45,13 @@
from . import statesp
from .exception import ControlSlycot, ControlArgument, ControlDimension

__all__ = ['ctrb', 'obsv', 'gram', 'place', 'lqr', 'acker']
__all__ = ['ctrb', 'obsv', 'gram', 'place', 'place_varga', 'lqr', 'acker']


# Pole placement
def place(A, B, p):
"""Place closed loop eigenvalues

K = place(A, B, p)
Parameters
----------
A : 2-d array
Expand All@@ -63,13 +64,92 @@ def place(A, B, p):
Returns
-------
K : 2-d array
Gains such that A - B K has given eigenvalues
Gain such that A - B K has eigenvalues given in p

Algorithm
---------
This is a wrapper function for scipy.signal.place_poles, which
implements the Tits and Yang algorithm [1]. It will handle SISO,
MISO, and MIMO systems. If you want more control over the algorithm,
use scipy.signal.place_poles directly.

[1] A.L. Tits and Y. Yang, "Globally convergent algorithms for robust
pole assignment by state feedback, IEEE Transactions on Automatic
Control, Vol. 41, pp. 1432-1452, 1996.

Limitations
-----------
The algorithm will not place poles at the same location more
than rank(B) times.

Examples
--------
>>> A = [[-1, -1], [0, 1]]
>>> B = [[0], [1]]
>>> K = place(A, B, [-2, -5])

See Also
--------
place_varga, acker
"""
from scipy.signal import place_poles

# Convert the system inputs to NumPy arrays
A_mat = np.array(A)
B_mat = np.array(B)
if (A_mat.shape[0] != A_mat.shape[1]):
raise ControlDimension("A must be a square matrix")

if (A_mat.shape[0] != B_mat.shape[0]):
err_str = "The number of rows of A must equal the number of rows in B"
raise ControlDimension(err_str)

# Convert desired poles to numpy array
placed_eigs = np.array(p)

result = place_poles(A_mat, B_mat, placed_eigs, method='YT')
K = result.gain_matrix
return K


def place_varga(A, B, p):
"""Place closed loop eigenvalues
K = place_varga(A, B, p)

Parameters
----------
A : 2-d array
Dynamics matrix
B : 2-d array
Input matrix
p : 1-d list
Desired eigenvalue locations
Returns
-------
K : 2-d array
Gain such that A - B K has eigenvalues given in p.


Algorithm
---------
This function is a wrapper for the slycot function sb01bd, which
implements the pole placement algorithm of Varga [1]. In contrast to
the algorithm used by place(), the Varga algorithm can place
multiple poles at the same location. The placement, however, may not
be as robust.

[1] Varga A. "A Schur method for pole assignment."
IEEE Trans. Automatic Control, Vol. AC-26, pp. 517-519, 1981.

Examples
--------
>>> A = [[-1, -1], [0, 1]]
>>> B = [[0], [1]]
>>> K = place(A, B, [-2, -5])

See Also:
--------
place, acker
"""

# Make sure that SLICOT is installed
Expand Down
9 changes: 8 additions & 1 deletioncontrol/tests/matlab_test.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -401,8 +401,15 @@ def testModred(self):
modred(self.siso_ss3, [1], 'truncate')

@unittest.skipIf(not slycot_check(), "slycot not installed")
def testPlace_varga(self):
place_varga(self.siso_ss1.A, self.siso_ss1.B, [-2, -2])

def testPlace(self):
place(self.siso_ss1.A, self.siso_ss1.B, [-2, -2])
place(self.siso_ss1.A, self.siso_ss1.B, [-2, -2.5])

def testAcker(self):
acker(self.siso_ss1.A, self.siso_ss1.B, [-2, -2.5])


@unittest.skipIf(not slycot_check(), "slycot not installed")
def testLQR(self):
Expand Down
47 changes: 46 additions & 1 deletioncontrol/tests/statefbk_test.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -8,7 +8,7 @@
import numpy as np
from control.statefbk import ctrb, obsv, place, lqr, gram, acker
from control.matlab import *
from control.exception import slycot_check
from control.exception import slycot_check, ControlDimension

class TestStatefbk(unittest.TestCase):
"""Test state feedback functions"""
Expand DownExpand Up@@ -157,6 +157,51 @@ def testAcker(self):
np.testing.assert_array_almost_equal(np.sort(poles),
np.sort(placed), decimal=4)

def testPlace(self):
# Matrices shamelessly stolen from scipy example code.
A = np.array([[1.380, -0.2077, 6.715, -5.676],
[-0.5814, -4.290, 0, 0.6750],
[1.067, 4.273, -6.654, 5.893],
[0.0480, 4.273, 1.343, -2.104]])

B = np.array([[0, 5.679],
[1.136, 1.136],
[0, 0,],
[-3.146, 0]])
P = np.array([-0.5+1j, -0.5-1j, -5.0566, -8.6659])
K = place(A, B, P)
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Can we also add some tests forplace_varga andacker here, as a way to increase coverage?

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I thinkacker already has a test(line 125)...

I added a test for place_varga.

P_placed = np.linalg.eigvals(A - B.dot(K))
# No guarantee of the ordering, so sort them
P.sort()
P_placed.sort()
np.testing.assert_array_almost_equal(P, P_placed)

# Test that the dimension checks work.
np.testing.assert_raises(ControlDimension, place, A[1:, :], B, P)
np.testing.assert_raises(ControlDimension, place, A, B[1:, :], P)

# Check that we get an error if we ask for too many poles in the same
# location. Here, rank(B) = 2, so lets place three at the same spot.
P_repeated = np.array([-0.5, -0.5, -0.5, -8.6659])
np.testing.assert_raises(ValueError, place, A, B, P_repeated)

@unittest.skipIf(not slycot_check(), "slycot not installed")
def testPlace_varga(self):
A = np.array([[1., -2.], [3., -4.]])
B = np.array([[5.], [7.]])

P = np.array([-2., -2.])
K = place_varga(A, B, P)
P_placed = np.linalg.eigvals(A - B.dot(K))
# No guarantee of the ordering, so sort them
P.sort()
P_placed.sort()
np.testing.assert_array_almost_equal(P, P_placed)

# Test that the dimension checks work.
np.testing.assert_raises(ControlDimension, place, A[1:, :], B, P)
np.testing.assert_raises(ControlDimension, place, A, B[1:, :], P)

def check_LQR(self, K, S, poles, Q, R):
S_expected = np.array(np.sqrt(Q * R))
K_expected = S_expected / R
Expand Down
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