Physical vs equivalent parameters

Learning goals¶

• Define physical vs equivalent (effective) fitted parameters

• Give examples of mismatch that force equivalence

• Require recovery checks beyond trajectory NRMSE

Reading¶

• Model structure and parameter interpretation Ljung, 1999

• Identifiability

Definitions¶

• Physical: coefficient matches a device/control constant under a consistent model map and informative data.

• Equivalent: coefficient mainly absorbs unmodeled dynamics, bad excitation, or residual mismatch — even if waveforms look good.

Practical checks¶

1. Loss-surface / sensitivity along each parameter

2. Bound activity (clamped estimates are suspicious)

3. Predict a held-out disturbance with frozen $\hat{\theta}$

4. Optional: synthetic recovery with known true $\theta$ before real data

Converter elective note¶

Reduced-order GFM/GFL parameters are a different estimand family from classical $(H,D)$. If you introduce them, document the simulator map explicitly — do not relabel foreign block constants as if they were identical.

Lab¶

• Required discussion prompt in Lab 3

Common misconceptions¶

• “We estimated $D$, therefore we know machine damping.”

• Treating bound-saturated values as interior physical optima