Proportional Action

The Core Idea

Proportional action makes a correction from the size of the error right now. The proportional gain sets how strongly the controller reacts to the difference between the target and the measurement.

What you will learn

• Relate proportional output to the current error.

• Compare weak, useful, and excessive P settings under the same conditions.

• Recognize the remaining offset that P-only control can leave.

Why it matters

Changing gain changes the controller's response to the same error. You need to judge the resulting process behavior, not just the size of the setting.

Explained like you're five

Think about pushing a swing toward a chosen position. A very gentle push may not get it far enough; a strong push can carry it past where you wanted it. The amount of push matters, and the swing takes time to respond.

A proportional controller chooses its push from the size of the error right now. You will change how strongly it reacts and watch the result.

The problem

Bring a heater from 20 °C toward 50 °C using automatic proportional control. Controller output (CV) commands 0–100% heater power. I and D stay at zero throughout this lesson, so you change only Controller P.

This is the same physical heater model used in the integral-action lesson. Here the controller updates its command once every 1 s and holds it between updates. That interval stays fixed in every trial; Simulator speed only changes how fast you watch. The integral-action lesson uses 100 ms updates, so compare gain trials within this lesson rather than treating traces from the two lessons as identical experiments.

See it: how strong a response?

The prepared controller below uses P = 40% output per °C of error. Before running, predict whether a strong correction will hold process variable (PV) steadily near setpoint (SP). Press Run and watch all 60 simulated seconds: inspect the temperature and whether the output becomes steady or keeps changing sharply.

Find a useful P setting

In the experiment below, first run the starting P = 0.5% output per °C. Compare its PV and CV with the prepared run above. The purple curve supplies that prepared run for comparison.

After the low-P run finishes, press Save this trace. Then increase P, press Restart, and run the full 60 s again. The saved low-P curve stays visible, so you can compare the ending gap and the movement around SP. Clear saved trace restores the supplied high-P reference.

Try a setting between the two extremes. Change only P and restart after each change; a mid-run gain edit begins with a different temperature and does not make a fair comparison.

What happened and why

At low P, the same temperature error produces a small output command. The heater approaches a temperature well below the target. The prepared high-P controller reacts strongly, but its command is held until the next update; PV cycles around SP while CV swings sharply.

A useful middle setting improves the approach without that repeated cycling. These effects depend on the process and its controller interval: increasing P does not make every process oscillate, and a larger number is not automatically better.

P responds to current error. As PV approaches SP, error shrinks and the proportional command shrinks with it. This heater needs continuing power to remain above its starting temperature, so P alone balances heat loss while some error remains. That lasting gap is offset.

Check your response

The hands-on check accepts a full 60 s run whose average absolute error over the final 12 s is at most 3 °C, with at most one counted reversal between opposite sides of the 49.4–50.6 °C target band after PV first crosses SP. A response that stays a little below SP can pass; reaching the target exactly is not required in this P-only lesson.

The error limit is 10% of the 30 °C start-to-target change. The run also exceeds the heater's 40 s minimum observation window. This checks the response rather than a particular gain value. Retry as often as you like, and keep a note of the gain and trace evidence for your best run.

Hint 1 — What does the trace need?

If PV becomes steady far below SP, is the present error producing enough output? If it repeatedly swings across SP, is another increase in P likely to help?

Hint 2 — Change one thing fairly

Keep I and D at zero. Increase a weak P in steps, restarting each time. If you see repeated cycling, reduce P and compare the full run with your saved trace.

Hint 3 — Try a middle range

Try P around 10–16% output per °C, then restart. Check the final gap and any crossings of SP; do not judge the run only by its first few seconds.

Compare useful responses

With P = 0.5% output per °C, PV ends near 30 °C, leaving about 20 °C of offset. With P = 10% output per °C, it ends near 47.3 °C, with a remaining gap of about 2.7 °C and no oscillation reversals. Settings such as 12% or 16% output per °C also pass.

The prepared P = 40% output per °C run repeatedly crosses the target band and fails the cycling check even though its average ending error is fairly small. A good final average can hide an output that keeps swinging.

Show the proportional math

For this reverse-acting heater, error = SP − PV, and P-only output is P × error, limited to 0–100%. For example, P = 5% output per °C and 5 °C of positive error give 25% output. At zero error, the proportional contribution is zero; there is no stored contribution from past error.

The process gain from the previous lesson describes how the process responds to CV. The P gain here describes how the controller responds to error. They are different quantities, even though both influence the final trace.

Common mistakes

Next, Integral Action and PI Control explores an output contribution that can build while error persists.

Enable JavaScript to run the embedded simulator and complete the interactive exercises.