René's URL Explorer Experiment

{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"td04ad (convert tf to ss) returns incorrect poles","articleBody":"A bug was reported in python-control issue [#935](https://github.com/python-control/python-control/issues/935) in which `tf2ss` returns the incorrect poles.\r\n\r\nIt looks like the underlying problem is in `td04ad`.  The following code illustrates the bug:\r\n```\r\nfrom numpy import array, roots, sort\r\nfrom numpy.linalg import eig\r\nfrom numpy.testing import assert_allclose\r\nfrom slycot import td04ad\r\nfrom scipy.signal import tf2ss\r\n\r\n# Test case #1 (works)\r\n\r\nnum = array([[[1, 1, 1, 1, 1]]])\r\nden = array([[1, 2, 1, 2, 1]])\r\ndenorder = np.array([den.size - 1])\r\n\r\nssout = td04ad('C', 1, 1, denorder, den, num, tol=0)\r\n\r\ntf_poles = sort(roots(den[0]))\r\nss_poles = sort(eig(ssout[1])[0])\r\nassert_allclose(tf_poles, ss_poles)\r\n\r\n# Test case #2 (doesn't work)\r\n\r\nnum = array([[[1.05351324e-02, 2.83623596e-01, 2.44891698e+00, 1.22011448e+01,\r\n               5.34846570e+01, 1.42092310e+02, 2.24627039e+02, 2.54305034e+02,\r\n               2.18224432e+02, 1.24102950e+02, 4.99448809e+01, 1.26651596e+01,\r\n               2.02239050e+00, 1.06681479e-01, 1.56212741e-03, 8.90622718e-06,\r\n               1.77205330e-08]]])\r\nden = array([[1.00000000e+00, 6.41551095e+02, 8.40213016e+03, 5.55121354e+04,\r\n              1.93428590e+05, 1.31800818e+05, 9.20183802e+04, 2.90211403e+04,\r\n              4.54824418e+03, 4.08636727e+02, 1.72367976e+01, 8.91452881e-02,\r\n              1.04426479e-04, 4.32051569e-08, 5.88752872e-12, 3.24913608e-16,\r\n              6.34764375e-21]])\r\ndenorder = np.array([den.size - 1])\r\n\r\n# Try scipy\r\nA, B, C, D = tf2ss(num[0, 0], den[0])\r\ntf_poles = sort(roots(den[0]))\r\nss_poles = sort(eig(A)[0])\r\nassert_allclose(tf_poles, ss_poles)\r\n\r\n# Now try slycot\r\nssout = td04ad('C', 1, 1, denorder, den, num, tol=0)\r\nss_poles = sort(eig(ssout[1])[0])\r\nassert_allclose(tf_poles, ss_poles)\r\n```\r\nFor the second system, the scipy-generated poles match, but some of the the slycot-generated poles are not the same (and one of them is unstable).\r\n\r\nIt's possible this is a numerical issue (the coefficients span 21 orders of magnitude!), but odd the SciPy gets it right and slycot doesn't.  (SciPy uses an observable canonical form-based realization.)","author":{"url":"https://github.com/murrayrm","@type":"Person","name":"murrayrm"},"datePublished":"2023-10-22T20:09:57.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":2},"url":"https://github.com/222/Slycot/issues/222"}