Process Gain, Lag, Dead Time, and Control Direction

The Core Idea

A process has its own response to an output change. Gain describes how much the measurement changes, lag describes the gradual response, dead time describes the initial wait, and direction describes which way it moves.

What you will learn

• Distinguish response size, gradual change, and an initial delay.

• Measure those properties from a controlled change in output.

• Choose the controller action that corrects error for heating or cooling.

Why it matters

Those properties determine what a controller has to work with. Recognizing them keeps you from treating every slow or reversed response as the same tuning problem.

Explained like you're five

Turn a tap and watch a bucket fill. How much you turn it affects how much water flows, but water travelling along a hose takes time to arrive. A response that starts late is different from one that starts promptly and changes slowly.

You met that waiting time while controlling the heater by hand. Now you will name and measure the different parts of its response.

The problem

Compare two heater process presets, A and B. Each begins at 20 °C, with a 50 °C target and 0–100% heater output. These are faster process presets than PID02's heater and have no scheduled cooling load.

You still command controller output (CV) in manual mode. For a fair comparison, use the same 0% → 30% output change at the start of each 30 s run and make no further adjustments. Setpoint (SP) is a reference line; it does not adjust the manual command for you.

Measure preset A

Set Manual output (CV %) to 30%, then press Run. Record when process variable (PV) first leaves 20 °C, about when it reaches 39 °C, and its final temperature. Use 1× speed and Pause if you want more time to watch.

The purple reference uses the identical output step on a preset with a different response size. Compare its final change with your live PV. If you try another output, restart with 30% before comparing with either supplied reference.

Repeat on preset B

Make the same 0% → 30% step below. The purple reference is the supplied preset A run. Compare three features: when movement starts, how quickly PV changes after that, and where it ends.

Before you run it, predict whether you would change the output again while waiting for the first response. Then watch what information is available during that wait.

What happened and why

Process gain describes how much the eventual PV changes for a given change in CV. The lower-gain reference makes a smaller temperature change for the same output step. It describes the process, not the controller's P gain, which you will adjust in the next lesson.

Dead time is the interval after the output step before its effect reaches the measurement. Preset B stays at its initial temperature longer than A. During that interval, the unchanged PV cannot yet tell you the result of the command you just made.

Lag describes the gradual approach after the response begins. Its time constant is the time to cover about 63% of the eventual PV change, measured after the dead time. Both live presets have the same lag; B's whole response begins later.

For these runs, find roughly 39 °C, about 63% of the way from 20 °C to 50 °C. Measure the interval from the end of the initial delay to that point. Looking only at total time from the command would combine dead time and lag.

Compare your measurements and show the math

Preset A first moves at about 1.1 s; B first moves at about 6.1 s. With 100 ms samples, these correspond to about 1 s and 6 s of dead time. PV reaches about 39 °C near 5 s in A and 10 s in B: about 4 s of lag after either delay.

Both live runs finish close to 50 °C. Their 30 percentage point CV change produces about a 30 °C PV change, so process gain is about 1 °C per percentage point of output. The lower-gain reference finishes near 35 °C: about 15 °C of change for the same output step, or 0.5 °C per percentage point.

The time constant uses 63.2% of the eventual change. Here that measurement is 20 °C + 0.632 × 30 °C ≈ 39 °C. The simulator's sampled response gives close estimates rather than exact continuous-time timestamps.

Which control direction corrects the error?

Your manual steps show the process direction: increasing heater CV raises PV. When you return that process to automatic control, a rise in PV at fixed SP should make the controller reduce CV. Otherwise the controller reinforces the change it should correct.

Direct and reverse acting describe the controller's response to PV at fixed SP. A cooling actuator has the opposite process effect from a heater, so it needs the opposite controller action.

The manual runs identify the plant's effect; they do not demonstrate an automatic controller switching direction. Choose action from the measured process effect, then verify that the automatic response reduces the error.

Check yourself

• Two runs end at the same temperature, but one stays flat for longer before moving. Which property differs?

• Two runs start moving together and have the same final temperature, but one takes longer to reach 63% of its change. Which property differs?

• The same 30 percentage point output step moves one process by 30 °C and another by 15 °C. Which has greater process gain?

• Increasing a cooling valve's CV lowers PV. If measured temperature rises above SP, should the automatic controller increase CV or decrease it? Name the controller action.

Check your explanations

The later start indicates more dead time. A slower approach after movement starts indicates more lag. The larger final temperature change for the same output step indicates greater process gain.

The cooling controller should increase CV when PV rises at fixed SP: direct acting. On the heater, that same action would add heat as the measured temperature rose, so the heater needs reverse action.

Common mistakes

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