Reading a step response

In short. The response to a set-point or disturbance step shows almost everything about the tuning: how fast PV moves to the set point, whether it overshoots, how long it keeps swinging and whether an error remains. To compare settings these features are turned into numbers with explicit definitions.

Metrics and their definitions

Notation: y_init is PV at the start of the interval, y_final the steady-state value, Δ = y_final − y_init. This is how the performance analysis computes them.

Rise time and overshoot follow the definitions of MathWorks stepinfo. Authors measure the settling time against different bases (|Δ| or the final value), so state the band and the base when comparing.

The steady-state value is chosen explicitly. The last sample of a trend is not necessarily steady state: if the record ends too early, the response is reported as "not settled" rather than as settled with an error.

Example: two settings on one process

Process K = 1.8 °C/%, τ = 45 s, θ = 12 s; set-point step.

The second controller rises twice as fast but, because it oscillates, settles almost three times later and has a larger error area. "Faster" in one metric does not mean "better".

In the performance analysis tool the "Example" button builds the second response (set point 55 → 65 °C, interval from the step) — giving the same 9.3 s, 70 % and 201 s.

Reading the shape of the curve

The oscillation period is a useful hint: oscillation caused by a large Kc is close to the loop's ultimate period, "integral" oscillation is noticeably slower.

Set-point step or disturbance step

A controller is judged on two tasks, and they look different:

• a set-point step shows how SP changes are followed;
• a disturbance (load) step shows how the loop holds its operating point — in process plants usually the more important task.

IMC tuning (τI = τ) follows set-point changes well but rejects input disturbances of slow processes more slowly; this is why SIMC limits Ti = min(τ, 4(τc + θ)) — see IMC and SIMC. In the simulator the disturbance is set under "More settings".

Typical mistakes

• Comparing trends with different steps (size or direction) — on non-linear processes the result differs.
• Computing settling time on a noisy signal with a band smaller than the noise — the response "never settles".
• Judging the tuning by the set-point step only without checking a disturbance.

Limits

The metrics describe one experiment at one operating point. If K, τ or θ change with load, evaluate several operating points. Numbers are comparable only under the same conditions: step size, band, interval and the way the steady-state value is chosen.