OE-5.3 Process Controllers & Controller Hardware

What this is and why it exists

Proportional-integral-derivative control is the most deployed control algorithm on Earth. Its three terms answer three questions, and putting it that way is the fastest route to understanding it.

How wrong am I now? How long have I been wrong? How fast is it changing?

One of the three deserves respect rather than enthusiasm. Derivative action amplifies noise, which is why a great many industrial loops run with only the first two terms.

The vocabulary

• Controller — the device deciding what adjustment to make.
• Setpoint — the value you want.
• Error — setpoint minus what is actually measured.
• Open loop — the output does not depend on the result.
• Closed loop — the measurement feeds back into the decision.
• Proportional action — output in proportion to the present error.
• Integral action — output growing with accumulated past error.
• Derivative action — output responding to how fast the error is changing.
• Offset — a steady error that proportional action alone will not remove.

The mental model

Open loop means acting without looking at the result: turn the heater on for ten minutes and hope. Closed loop means measuring, comparing against the setpoint, and adjusting. Everything useful is closed loop, and the cost is that the measurement now matters as much as the actuator.

Proportional action responds to the present error, with output proportional to how wrong things are. On its own it has a characteristic weakness: it leaves a steady offset. Some error must remain, because the output is proportional to the error. Zero error would mean zero output, which is generally not what holds the process where you want it.

Integral action fixes exactly that. It accumulates error over time, so a small persistent error keeps building output until the error is gone. That is why proportional and integral together is the standard pairing: one responds quickly, the other removes the residue.

Derivative action responds to the rate of change, so it anticipates. In principle it damps overshoot by pulling back as the error closes quickly. In practice it has a serious problem: differentiating amplifies noise. A measurement with a little high-frequency noise on it produces a derivative term that is mostly noise, and the actuator is asked to chase it. That is why many real loops run as proportional-and-integral only, and why derivative action, when used, is filtered.

On the hardware side, analog controllers implement this with circuits and digital controllers with arithmetic on samples. Pneumatic controllers look archaic and are still installed where electrical equipment would be a hazard. In a flammable atmosphere, an air-driven controller cannot produce a spark. That is a real engineering reason and not nostalgia.

What you should now be able to explain or do

Distinguish open- from closed-loop control and say what closed loop costs you. State the question each of the three terms answers. Explain why proportional action alone leaves an offset. Say what integral action removes and how. Explain why derivative action amplifies noise and what is done about it. Say why pneumatic controllers are still installed.

Check yourself