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{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"place function fails for simple case","articleBody":"### The pole placement function `place` fails in some simple situations. \r\nThis bug is related to the *current* implementation of `place`, which is a wrapper for slicot sb01bd. If PR [176](https://github.com/python-control/python-control/pull/176) is accepted, this bug report will refer to `place_varga` instead.\r\n\r\nExample of failure:\r\n```\r\nimport numpy as np\r\nimport control as pc\r\nA = np.array([[0, 1],[100, 0]])\r\nB = np.array([[0],[1]])\r\nPdes = np.array([-20 + 10*1j, -20 - 10*1j])\r\nK = pc.place(A, B, Pdes)\r\n```\r\nThis raises the error (with python 2.7)\r\n\"ValueError: an attempt was made to place a complex conjugate pair on the location of a real eigenvalue\"\r\n\r\nThe problem is related to how the `alpha` parameter is computed when calling `sb01bd`, which is calculated as \r\n```\r\nsystem_eigs = np.linalg.eig(A_mat)[0]\r\nalpha = min(system_eigs.real);\r\n```\r\nClearly, A has eigenvalues [-10, +10]. But np.lingalg.eigvals(A) reports \r\neigvals = [10.000000000000002, -9.9999999999999982], and so we have set\r\n```\r\nalpha = -9.9999999999999982\r\n```\r\n\r\n`sb01bd` will only move eigenvalues that are greater than `alpha`. It seems that `sb01bd` must calculate the eigenvalues slightly differently than scipy, so it thinks it has only one eigenvalue to move (namely, the one at +10). This evidently corresponds to [error 4](http://slicot.org/objects/software/shared/doc/SB01BD.html).\r\n\r\nIf we fudge the `alpha` parameter, and call the sb01bd wrapper directly, this works as expected\r\n```\r\nimport numpy as np\r\nfrom slycot import sb01bd\r\nA = np.array([[0, 1],[100, 0]])\r\nB = np.array([[0],[1]])\r\nPdes = np.array([-20 + 10*1j, -20 - 10*1j])\r\n\r\nalpha = min(np.linalg.eigvals(A).real)*2;\r\nA_z,w,nfp,nap,nup,K,Z = sb01bd(B.shape[0], B.shape[1],\r\n                               len(Pdes), alpha, A, B, Pdes, 'C')\r\nprint 'Placed Poles: %s'%np.linalg.eigvals(A + B.dot(K))\r\n# yields on my system:\r\n# Placed Poles: [-20.+10.j -20.-10.j]\r\n````\r\n\r\n\r\n\r\n### place() is not implemented for discrete time\r\n`sb01bd` can place poles for discrete time systems. However, the current wrapper assumes a continuous time system, both in how `alpha` is calculated (it should be based on `abs(eigvals)` for discrete systems) and by passing `C` as the dico parameter. This is undocumented in the doc string.\r\n","author":{"url":"https://github.com/rabraker","@type":"Person","name":"rabraker"},"datePublished":"2018-01-03T20:42:25.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":2},"url":"https://github.com/177/python-control/issues/177"}