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For a discrete-time system, describing_function_response found limit cycles with about the right amplitude but reported the wrong frequency: it took the oscillation frequency as the imaginary part of the Nyquist contour, which for a discrete system lies on the unit circle exp(1j*w*dt), so it reported about sin(w*dt) - the same number whatever dt is. The refinement cost function and the returned positions also evaluated H at z = 1j*w rather than on the unit circle, and refinement typically failed with "not able to refine result; returning estimate". For example, H(z) = 0.5/(z^2 - 0.5z) with dt = 1 crosses the negative real axis at w = 1.3181, but the reported frequency was 0.9703, and dt = 0.5 gave the same 0.9703 instead of 2.6362. When H.isdtime(strict=True) - matching the timebase semantics used by nyquist_response - take the frequencies as np.angle(contour) / dt and evaluate H at exp(1j*w*dt) in the refinement cost function and for the returned positions. The strict check keeps dt=None (unspecified timebase) on the continuous-time path; dt=True (discrete, unspecified sample time) reports rad/sample. Adds regression tests: a known unit-circle crossing for dt = 1 and dt = 0.5, plus dt=None continuous-equivalence and dt=True coverage. The discrete tests fail at baseline; continuous-time behavior is unchanged. Fixes python-control#1269
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@RoboX2020 Please add AI tool disclosures, ensuring consistency with https://numpy.org/doc/stable/dev/ai_policy.html ? (Given how long and verbose your responses are and how quickly you are committing, I assume you used a chat bot for most or all of this...) |
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@gimballock This PR supposedly fixes the issue you opened. I guess @RoboX2020 is a bot who simply closed the PR in response to my request... If you want, @gimballock , feel free to review this or open a PR that re-uses the code for this PR. I assume @RoboX2020 did not author any of it, so you can just claim authorship. |
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Hi, |
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Fixes #1269.
For discrete-time systems,
describing_function_responsetakes the imaginary part of the Nyquist contour as the frequency. That issin(omega * dt), not the angular frequency. Refinement and returned positions also evaluate the transfer function atj * omegainstead of on the unit circle.This uses
angle(contour) / dtfor discrete-time frequencies and evaluates the response atexp(j * omega * dt)during refinement and when returning positions. The strict timebase check leaves continuous and unspecified (dt=None) systems on the existing path;dt=Trueuses radians per sample.Regression tests cover sample times 1 and 0.5, unspecified discrete time, and continuous-compatible
dt=None. For the issue's sign-nonlinearity example, the reported frequencies change from about 0.9703 for both sample times to 1.3265 and 2.6530. The analytic crossings are 1.3181 and 2.6362; the tests allow 2% numerical error rather than claiming exact refinement.Validation:
refine=Falseandrefine=Truewith an analytic relay nonlinearity at sample times 0.01, 0.5, 1 and 2.