Process Control Tool

PID Tuning Calculator

Turn a step test or an ultimate-gain test into PID starting values. Get controller gain, integral time and derivative time from Ziegler-Nichols, Cohen-Coon, Lambda and Tyreus-Luyben, ready to drop into your PLC.

Tuning data
Controller

Output change divided by input change at steady state.

Dead-time ratio theta/tau = 0.1667 (moderate). Balanced (0.1 to 1). PID with derivative helps; Cohen-Coon handles this range well.
PID tunings (ISA form, time in sec)
MethodKcTiTd
Ziegler-NicholsSTART3.6205
Cohen-Coon4.12523.02333.5294
Lambda / SIMC1.5605
Parallel-form equivalents for the first method: Ki = Kc / Ti = 0.18 , Kd = Kc x Td = 18 (per sec).

Results are in the ISA standard (non-interacting) form used by Allen-Bradley PIDE and Siemens PID_Compact: Kc is dimensionless when K is, Ti and Td carry the time units you selected. Ziegler-Nichols gives an aggressive quarter-amplitude response and is a starting point, not a final answer. Cohen-Coon suits larger dead time. Lambda/SIMC is the robust industrial choice for slow loops. Always start with the highlighted row, then trim by watching the real loop. Educational tool; verify on your process.

Questions

Frequently Asked

How do I tune a PID controller?

Characterize the process first, then apply a tuning rule. The easiest path is a step test: bump the output, record the response, and read off the process gain, time constant and dead time. Feed those three numbers into a method like Ziegler-Nichols, Cohen-Coon or Lambda and you get starting values for gain, integral time and derivative time. Load those into the loop, then trim while watching the real response.

What is the difference between Ziegler-Nichols and Cohen-Coon?

Both use the same FOPDT step-test data, but they target different responses. Ziegler-Nichols aims for a quarter-amplitude decay, which is fast but oscillatory and often too aggressive for real plants. Cohen-Coon was designed to handle processes with more dead time and usually gives a tighter result when the dead-time to time-constant ratio is larger. Neither is a final answer; both are starting points you refine on the loop.

When should I use Lambda tuning instead?

Lambda tuning, also called IMC or SIMC tuning, is the robust choice for slow or noisy loops like level, temperature and large flow systems. Instead of chasing speed, you pick a closed-loop time constant and the method delivers a smooth, stable response with good margins. It is the default in many process plants precisely because it rarely oscillates, even if the process model is a little off.

What are Kc, Ti and Td?

They are the three terms of a PID controller in the ISA standard form. Kc is the controller gain, which sets how hard the controller pushes per unit of error. Ti is the integral time, which sets how quickly it removes steady-state offset (a shorter Ti acts faster). Td is the derivative time, which reacts to the rate of change to dampen overshoot. Allen-Bradley PIDE and Siemens PID_Compact both use this form, so the numbers drop straight in.

What is the ultimate gain method?

It is a closed-loop test. With the controller in proportional-only mode, you slowly raise the gain until the loop oscillates with a constant amplitude. The gain at that point is the ultimate gain Ku and the oscillation period is the ultimate period Pu. Ziegler-Nichols and Tyreus-Luyben both turn Ku and Pu directly into PID settings, with Tyreus-Luyben giving a more conservative, less oscillatory result.

Is anything sent to a server?

No. Every calculation runs in your browser. No process data, tuning values or model parameters leave your machine.