Derivative Action: Decide Whether It Helps

The Core Idea

Derivative action adds a correction based on how quickly the measurement is changing. It gives a controller information about movement toward or away from the target, alongside the present and accumulated error.

What you will learn

  • Compare a working proportional-integral (PI) response with a modest amount of D.

  • Inspect output movement as well as the temperature trace.

  • Explain why keeping D at zero can be a sound choice.

Why it matters

A useful change to a tune must improve the process response enough to justify its effect on output movement. Derivative needs that same evidence.

Try a clean measurement first

This heater starts at 20 °C and has a 50 °C target, a 15 s lag, and 5 s of dead time. Output is 0–100%. P is 2% output per °C and I is 0.12% output per (°C·s); keep both fixed.

Run the PI starting settings for the full 120 simulated seconds. Record the peak temperature and how the blue controller output (CV) line changes as process variable (PV) approaches setpoint (SP). The purple line is the same PI run for comparison.

Change only D to 3% output·s per °C, use Restart, and run again. Decide whether the change improves the peak and settling enough to be useful.

What D responds to

D responds to how quickly the measured value is changing. In this controller it acts on the measurement: a rising temperature produces a contribution that reduces heating. It can restrain a rapid approach to the target, but it cannot remove the process's dead time.

P responds to present error; I accumulates correction while error persists. D adds a response to the rate of change. It does not supply the lasting correction that holds a heated process at its target.

Optional equation and units

For this site's heating direction, the derivative contribution is −Kd × change in PV / elapsed time. Kd has units of % output·s per °C. The contribution itself has units of percentage points of output.

The derivative uses changes between measurements. Closely spaced noisy measurements can therefore produce a large changing contribution even when the actual process moves smoothly.

Now inspect the output with noise

The next copy has identical process conditions and P/I settings, with measurement noise enabled. It starts at D = 3. Run it, inspect both PV and CV, then restart with D = 0 and compare. Every restart uses the same noise sequence.

The purple reference is PI with the same noisy measurement. Compare noise with noise here; use the first experiment for the clean comparison. Look for repeated output reversals, not just the height of the temperature peak.

Make a decision from both traces

For a heater whose switching device should avoid rapid command changes, would you keep this D setting? State the measured benefit, the output cost, and your choice. A smoother-looking PV alone does not establish that the actuator command is suitable.

If noise is the problem, increasing D is not a general cure. Check the measurement and consider filtering, which the later noise lesson lets you test. A working PI controller can be the appropriate result.

Hint — Compare one change at a time

Keep P, I, the target, and noise condition fixed within each comparison. Finish 120 s from the same 20 °C start before comparing. The blue output line uses its own 0–100% scale.

Worked interpretation after the runs

With a clean measurement, D = 0 peaks near 54.3 °C; D = 3 peaks near 50.9 °C. Here D reduces the first overshoot.

With noise, D = 3 produces much more rapid output movement than PI alone. Over the final 24 s, total absolute command travel divided by time is about 360 percentage points/s, versus 15 percentage points/s for PI. This measures repeated command changes, not the speed of a physical valve.

Keeping D at zero is defensible when that output movement is unacceptable. Keeping a nonzero D requires evidence that its benefit and the available filtering and actuator behavior suit the job. No single gain is required to complete this lesson.

Check your understanding

Record the clean PI and proportional-integral-derivative (PID) peaks, describe the noisy CV difference, and explain your D choice in one sentence. Identify which trace supports each claim, then mark the lesson complete.

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