diff --git a/control/statefbk.py b/control/statefbk.py
index 634922131..e2f02c1a4 100644
--- a/control/statefbk.py
+++ b/control/statefbk.py
@@ -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
@@ -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
diff --git a/control/tests/matlab_test.py b/control/tests/matlab_test.py
index 8c8a1f199..1793dee16 100644
--- a/control/tests/matlab_test.py
+++ b/control/tests/matlab_test.py
@@ -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):
diff --git a/control/tests/statefbk_test.py b/control/tests/statefbk_test.py
index 34070aca7..042bda701 100644
--- a/control/tests/statefbk_test.py
+++ b/control/tests/statefbk_test.py
@@ -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"""
@@ -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)
+ 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
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