René's URL Explorer Experiment

{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"stability_margins doesn't find gain=1 crossover frequency correctly for DT systems","articleBody":"stability_margins doesn't find gain=1 crossover frequency correctly for DT systems, but it seems to mostly do so for CT systems. I think the probelm may be in how `margins.poly_z_mag1_crossing` is finding roots, but there were a few  steps in that function I couldn't follow, e.g. why H(z)*H(1/z)=1 implies |H(z)| = 1. \r\n\r\nExample: \r\n```python\r\nimport control as ct\r\nomegan = 2*np.pi\r\nzeta = 0.2\r\nplant = 1.1*ct.tf(omegan**2, [1, 2*zeta*omegan, omegan**2])\r\nTs = .05\r\nplantdisc = ct.c2d(plant,Ts,'zoh')\r\n#_ = ct.bode_plot(plant, margins=True) # gives correct gain=1 crossover freq\r\n_ = ct.bode_plot(plantdisc, margins=True) # no gain=1/no phase margin given\r\n```\r\n\u003cimg width=\"407\" alt=\"image\" src=\"https://user-images.githubusercontent.com/58706249/106208565-6f86b100-6178-11eb-874a-809bd05a899b.png\"\u003e\r\n\r\nAs an example of what it should look like, here is Matlab:\r\n```matlab\r\nomegan = 2*pi;\r\nzeta = 0.2;\r\nplant = 1.1*tf(omegan^2, [1, 2*zeta*omegan, omegan^2])\r\nTs = .05;\r\nplantdisc = c2d(plant,Ts,'zoh')\r\nmargin(plantdisc)\r\n```\r\n\u003cimg width=\"476\" alt=\"image\" src=\"https://user-images.githubusercontent.com/58706249/106208756-bb395a80-6178-11eb-8bb2-95ee6d928a3d.png\"\u003e","author":{"url":"https://github.com/sawyerbfuller","@type":"Person","name":"sawyerbfuller"},"datePublished":"2021-01-28T22:52:59.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":15},"url":"https://github.com/523/python-control/issues/523"}