A motor is already on the bench. You know the speed you want and can command voltage, but nobody has given you its resistance, inertia or friction. Do you have to derive every differential equation before touching Kp? No. You do need to know what you can measure and what your actuator can safely deliver.
What ‘without a model’ actually means
Empirical PID tuning uses the plant's observed input–output behavior instead of starting from a complete physical equation. A step test, load change or repeated run gives information about delay, speed, overshoot and steady error. Those measurements are a form of knowledge about the plant, even if you never write A and B matrices.
PID is therefore not ‘only trial and error’. You can also tune it from an identified transfer function, frequency-response data or an autotuning experiment. The choice depends on available data, time, safety and the performance you need.
A bench workflow that produces useful evidence
First record the sensor unit, sample period, voltage or force limit, initial condition and load. Make a small, safe baseline change and save its output and applied input. Change one controller setting at a time, then repeat under the same disturbance. If the requested command and applied input differ, you are studying saturation as much as PID gains.
P reacts to current error; I can remove persistent error but may accumulate during saturation; D responds to measured change and can amplify noise. These are tendencies of a specified loop, not rules that guarantee a result on every plant. Inspect both tracking and control effort, then check another target or load before accepting the tuning.
When a model becomes worth the effort
A model helps you predict behavior outside a single test, examine stability margins and compare design choices before putting hardware at risk. It can come from physics or system identification; it does not have to be a perfect first-principles derivation. If delays, coupled axes, strict constraints or safety requirements dominate, a few successful PID trials are weak evidence of robustness.
In the EIGENROOM motor experiment, compare the dashed requested voltage with the applied voltage capped at ±12 V. Pin the same run with anti-windup on and off. The important explanation is not merely which curve looks better; it is what the integrator did while the actuator could not obey it.
Start from measured behavior when a full model is unavailable; keep limits and test conditions visible. Build or identify a model when prediction and robustness matter more than a quick first loop.