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{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"unexpected behaviour of `feedback` combined with `step_response`","articleBody":"Hi,\n\n\nHere is unexpected behaviour when I create an LTI system with `ct.zpk`, put it in unity feedback using `ct.feedback`, and compute the `ct.step_response` of the resulting feedback system. For the tested system, the result should be stable, but it is not.\n\nHere's the code:\n\n```\nimport control as ct\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n# the system\nG = ct.zpk([],[0,-5,-10],1)\nprint(G)\n\nK = 500\nct.root_locus_plot(G,initial_gain = 500)\n```\n\nThis generates the root locus, indicating the result for the gain 500, which shows that the system is **stable** in closed loop, for this gain value.\n\n![Image](https://github.com/user-attachments/assets/d5b7ee04-5abd-4c54-9935-36d291a2fd91)\n\nHere's the code where unexpected behaviour occurs:\n\n```\n# put the system in unity feedback, with gain of 500\nGc = ct.feedback(G,K)\nprint(Gc)\n\n# plot the step response\nstepresp = ct.step_response(Gc)\nstepresp.plot()\n\n# check the pole locations\npzmap = ct.pole_zero_map(Gc)\nprint(pzmap.poles)\n```\n\nThe response is clearly **unstable**, while the poles have negative real parts (i.e. stable)!\n\n![Image](https://github.com/user-attachments/assets/3aff3efe-d20a-4445-bfa9-802d76c61757)\n\nOn the other hand, creating the feedback system directly with `ct.tf` (as was computed higher up, so theoretically the same feedback system), results in a stable step response.\n\n```\n# create the feed\nGcexpl = ct.tf([],[1,15,50,500])\nprint(Gcexpl)\n\nsteprespexpl = ct.step_response(Gcexpl)\nsteprespexpl.plot()\n```\n\nThis step response is stable, as expected.\n\n![Image](https://github.com/user-attachments/assets/d06ad7a5-7751-460c-a833-052081a1ab8b)\n\nThis indicates that the system generated by `ct.feedback` is not valid.\n\nAny clue?  \nThanks in advance!","author":{"url":"https://github.com/johnlataire","@type":"Person","name":"johnlataire"},"datePublished":"2025-01-19T13:34:42.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":1},"url":"https://github.com/1102/python-control/issues/1102"}