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PID tuning

Process control

Understand PID, watch the loop respond live and learn how to get the values of your loop.

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What PID does

The controller compares the desired value (SP, setpoint) with the measured value (PV) and adjusts the output (MV) — the valve, the heater or the drive — to remove the difference.

P

Proportional

Reacts to the error right now. More gain responds faster but may oscillate and, on its own, leaves a gap between SP and PV.

I

Integral

Adds up the error over time until the remaining gap is gone. A shorter Ti corrects sooner and increases overshoot.

D

Derivative

Looks at how fast the PV moves and brakes the response before the target. It amplifies noise; many flow and pressure loops use PI only.

Live simulation

Study process

Electrically heated furnace: the output sets the power, and the temperature reacts slowly and with delay.

Model: K 1.2 °C/% · θ 30 s · τ 180 s. Initial conservative IMC/Lambda tuning: Kp 0.5 %/°C · Ti 180 s.

t = 0 s · 70× real time
TIC-101AUTO
SP
100 °C
PV
80 °C
MV
50 %
Error
20 °C
SPPVMV
708090100110050100050010001500s°CMV %

Press Play: the SP changes to 100 °C and the controller reacts.

Setpoint (SP)100 °C

Door open: heat loss: -10 % at the process input.

Change the tuning while the loop runs

Kp · proportional gain0.5 %/°C

More gain reacts harder to the error: faster, but it may oscillate.

Ti · integral time180 s

A shorter Ti removes the remaining gap sooner, with more overshoot. Without integral, an error remains.

Td · derivative timeoff

Td brakes the PV when it moves fast. Zero turns it off; too much amplifies noise.

Equivalent parallel form: Kp 0.5 · Ki 0.002778 %/°C/s · Kd —

Assumptions: first-order process with dead time (FOPDT), PID controller in the ideal form with gain in engineering units, reverse action, output limited from 0 % to 100 % with anti-windup and derivative on the PV. It does not include noise, valve stiction or backlash, nonlinearity or interlocks. The simulation is for learning and comparing settings; final validation happens on the real loop, with authorisation.

Teaching values, chosen to resemble real loops of this kind; they do not represent a specific plant or device.

How to get the values of your loop

Without K, θ and τ, tuning is guesswork. A step test in manual gives you those three numbers.

  1. With authorisation, put the loop in manual and wait for the process to settle.
  2. Change the output in one go (a step) and record the PV over time until it stops at a new value.
  3. Enter the output and the PV before and after, and the times at which the PV covered 28.3 % and 63.2 % of its change, counted from the step.

What to check in the field

  • Get authorisation and agree the test with operations.
  • Put the loop in manual with the process steady.
  • Apply a small, safe step to the output, larger than the PV noise, and record PV and output over time.
  • Wait for the PV to settle at the new value. If it does not settle (like a level with a pump on the outlet), the process is integrating and this method does not apply.
  • Start with the conservative tuning, watch the response and adjust gradually.

Taking it to the controller

Every controller has its own convention. Before entering the values, check the manual of the PID block in use:

  • Algorithm form: ideal (ISA), series or parallel. The same Kp, Ti and Td give different responses in different forms.
  • Gain: in engineering units, dimensionless (%/%) or proportional band (PB = 100 ÷ Kp in %/%).
  • Integral: Ti in seconds or minutes, repeats per minute, or Ki in the parallel form.
  • Derivative: Td in seconds or minutes, or Kd in the parallel form, with or without a filter.
  • Direct or reverse action and the block execution period (Ts).

There is no universal default per manufacturer: models, blocks and versions change the convention. The tool does not invent manufacturer numbers.