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"scipy.signal.cont2discrete" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "We can transform a continuous state-space system to a discrete one:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.signal import cont2discrete, lti, dlti, dstep\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nDefine a continuous state-space system.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "A = np.array([[0, 1],[-10., -3]])\nB = np.array([[0],[10.]])\nC = np.array([[1., 0]])\nD = np.array([[0.]])\nl_system = lti(A, B, C, D)\nt, x = l_system.step(T=np.linspace(0, 5, 100))\nfig, ax = plt.subplots()\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "ax.plot(t, x, label='Continuous', linewidth=3)\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nTransform it to a discrete state-space system using several methods.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "dt = 0.1\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "for method in ['zoh', 'bilinear', 'euler', 'backward_diff', 'foh', 'impulse']:\n d_system = cont2discrete((A, B, C, D), dt, method=method)\n s, x_d = dstep(d_system)\n ax.step(s, np.squeeze(x_d), label=method, where='post')\nax.axis([t[0], t[-1], x[0], 1.4])\nax.legend(loc='best')\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "fig.tight_layout()\nplt.show()\n", "execution_status": "success" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "1.17.1", "kind": "assets", "path": "fig-54cb4ba363860c13.png" } } ], "title": [], "level": 0, "target": null }, "see_also": [], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 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[1] https://en.wikipedia.org/wiki/Discretization#Discretization_of_linear_state_space_models", "", ".. [2] http://techteach.no/publications/discretetime_signals_systems/discrete.pdf", "", ".. [3] G. Zhang, X. Chen, and T. Chen, Digital redesign via the generalized", " bilinear transformation, Int. J. Control, vol. 82, no. 4, pp. 741-754,", " 2009.", " (https://www.mypolyuweb.hk/~magzhang/Research/ZCC09_IJC.pdf)", "", ".. [4] G. F. Franklin, J. D. Powell, and M. L. Workman, Digital control", " of dynamic systems, 3rd ed. Menlo Park, Calif: Addison-Wesley,", " pp. 204-206, 1998." ], "qa": "scipy.signal._lti_conversion:cont2discrete", "arbitrary": [], "local_refs": [ "alpha", "dt", "method", "sysd", "system" ] }