[bresch]

Fixes to the closed-loop simulation and the stability margins, which could be very optimistic and report comfortable margins for an unstable design, plus warning/crash fixes.

Simulation and margins

• Pad the ARX numerator when building the transfer function. The coefficients are in powers of z⁻¹ but ctrl.TransferFunction reads them in powers of z, so models with more poles than zeros had n − m extra samples of delay.
• Put the identified delay inside the loop. It was only applied to the reference, and not at all in the disturbance simulation, so the step response was only time-shifted and didn't show the loss of damping.
• Compute the margins on the actual loop gain sign · Kp(1 + I + D) · G · z^-(d+1). The "open loop" was built by removing the error junction, but D (and P with PI no-zero) act on the feedback and stayed in the loop. The margins then covered only part of the controller.

Example on a synthetic plant, K = (0.8, 0.3, 0.02):

delay	before	after
d = 1	GM 9.1 dB, PM 132°	GM 4.8 dB, PM 55°
d = 3	GM 7.2 dB, PM 125°	GM 1.1 dB, PM 19°

With K = (1.5, 0.5, 0.08) the old code reported PM 113°. The closed loop actually has a pole at |z| = 1.19, and the new margins are negative.

For all combinations of delay, PI no-zero and negated output, the closed-loop poles contain the roots of 1 + L.

Warnings

• Pass 1-D signals to the identification. The column-vector reshape made every filter assignment convert a 1-element array to a scalar. That is deprecated in NumPy 1.25 and crashes on NumPy 2.x. Fixes Fix crash due to new Numpy 2.x version #48; supersedes the draft fix(autotune): keep u and y in array (row) shape #49, which only covered one of the two call sites.
• Keep the Bode grid below Nyquist. It went up to 1000 rad/s whatever the sample time.
• Always compute the margins from the frequency response, on a dense grid up to Nyquist. python-control fell back to that method, with a warning, for nearly every identified loop. The results match the polynomial method to 4 decimals where that method is accurate.

Testing

• Ran the full pipeline headlessly on the three sample logs in logs/: no warnings, and the identification fit is unchanged.