Compare PID settings without losing sight of the plant

Fix one case before changing gains

Comparing PID settings requires the same plant, setpoint, sampling time and output limits. If everything changes at once, a different response does not tell you which decision caused it.

For practice, use K = 1, τ = 1 s, setpoint 1, maximum sampling interval 0.02 s and control output between 0 and 2. The plant starts at zero. These are normalized units and an ideal first-order plant, not values to copy into a real motor controller.

Observe P-only error first

Set Ki = Kd = 0. At equilibrium, y = K·u and u = Kp·(r − y). Without saturation, y/r = K·Kp/(1 + K·Kp). This explains why proportional control can settle below the reference without the simulation being wrong.

Now compare Kp = 2, Ki = 1 and Kd = 0 over 20 s. The integral term accumulates error and model output approaches 1. Record u as well: an apparently good output can require a control effort the actuator cannot deliver.

Identify the problem you are observing

• Slow response: observe how long it takes to approach the target and whether control output remains limited.
• Oscillation: look for repeated setpoint crossings. Compare amplitude and persistence; one crossing does not describe the whole response.
• Saturation: control output stays at its maximum or minimum. Raising Ki does not expand those limits.
• Persistent error: check for missing integral action, a short observation window or a physically unreachable setpoint.

Try setpoint 5 with maximum control output 1 and K = 1: steady output cannot exceed 1. Disabling anti-windup shows I continuing to grow without overcoming that limit. Anti-windup blocks integration when it would push harder against a limit.

OhmPlay’s D term acts on the measurement and uses a Tf filter. Change Kd while holding Tf fixed; do not assume more D always helps. Noise, delay and disturbances are absent, so this test does not prove a physical controller is robust.

One record per comparison

1. Record the plant, sampling interval, setpoint and limits.
2. Change just one gain and observe output, error, control effort and saturation.
3. Repeat with a smaller sampling interval. Similar-looking results help assess simulation resolution; they do not replace a stability analysis.
4. Explain the improvement you want and the trade-off you accept before tuning.