[bresch]

Adds a Robustness tab next to the existing plots, which move to a General tab. The new tab has three plots, all computed from the identified model and the current gains.

• Nyquist (top left) of the loop gain. It shows the gain, phase and modulus margins, and a shaded disc where the modulus margin is below 0.5 (|S| above 6 dB). Two new margins are added:
  • Delay margin: the extra loop delay that destabilizes the loop, in ms and in samples. It is the minimum over all gain crossovers, not only the one the phase margin comes from.
  • Disk margin: stability against simultaneous gain and phase changes. It is also drawn as the exclusion disk that the Nyquist curve touches.
• Root locus in Kp (bottom left). The closed-loop poles in the z-plane as Kp is scaled with I and D fixed; this is an exact root locus because the PID is in ideal form. It marks the current poles and the poles at the stability limit (Kp × gain margin), on a grid of constant damping ratio and natural frequency.
• Sensitivity functions (right): the gang of four (S, T, PS, CS) plus setpoint → control (C_r·S). The peak of |S| is checked against the same 6 dB limit.

When the closed loop is unstable, all three plots show "unstable closed loop" instead of margins, which are meaningless in that case.

Extended presets with initial gains

Initial gains can be set from parameters. When the reference signal is also set, the identification can provide a closed-loop identification fit quality

Gains can now be tuned in standard/ideal or parallel form

Refactor

The closed loop now lives in a new loop_model.py, as a two-degree-of-freedom controller u = C_r r − C_y y around the plant. The time simulation, the loop gain, the margins and the sensitivities all come from this single block diagram. It reproduces the previous step/disturbance responses and margins to machine precision.

Testing

• New test_loop_model.py (28 tests, no Qt needed). It checks:
  • the loop gain for every P/D placement;
  • that the closed-loop poles are the roots of 1 + L;
  • stability detection, S + T = 1, and max |S| = 1 / modulus margin;
  • that scaling the loop by the gain margin puts a pole on the unit circle;
  • that adding ⌊delay margin⌋ samples of delay keeps the loop stable and one more destabilizes it;
  • that the Nyquist curve touches the disk-margin exclusion disk.
• The full pipeline runs on the three sample logs in logs/ with no warnings.
• Checked stable and unstable renders, and small window sizes. The layout no longer collapses in small windows; the in-axes legends and texts are excluded from matplotlib's constrained layout.