PID Controller Tuner

Compute PID gains from a first-order-plus-dead-time plant using Ziegler-Nichols, Cohen-Coon, or IMC-style rules.

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What This Calculator Does

This calculator tunes a PID controller for a first-order-plus-dead-time plant model using common industrial rules. It reports gains and a compact closed-loop step-response estimate so you can compare aggressive and conservative tuning choices quickly.

It combines Process Gain K, Time Constant τ, Dead Time L, Tuning Method to estimate Kp, Ki, Kd.

Formula & Method

Plant model:

G_p(s)=\frac{K e^{-Ls}}{\tau s+1}

. The controller is

G_c(s)=K_p\left(1+\frac{1}{T_i s}+T_d s\right)

with

K_i=\frac{K_p}{T_i}

and

K_d=K_p T_d

Notation used in the formulas: $R$ = Kp; $x_{1}$ = Process Gain K; $x_{2}$ = Time Constant τ; $x_{3}$ = Dead Time L; $x_{4}$ = Tuning Method; $x_{5}$ = Desired Closed-Loop Time Constant.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when you have a reduced-order plant estimate and need initial PID values before fine tuning on hardware or in a higher-fidelity simulation.

Reference Book

Modern Control Engineering

Katsuhiko Ogata · Pearson

A standard control-systems text for transfer functions, response analysis, and PID-style tuning frameworks.

View Book

Inputs Used

Process Gain K: Used directly in the calculation.
Time Constant τ: Used directly in the calculation.
Dead Time L: Used directly in the calculation.
Tuning Method: Used directly in the calculation.
Desired Closed-Loop Time Constant: Used directly in the calculation.

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