MCPCalc

PID Controller Tuner

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

Scratchpad (not saved)

s
s
s

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)= rac{K e^{-Ls}}{ au s+1}. The controller is G_c(s)=K_pleft(1+ rac{1}{T_i s}+T_d s ight) with K_i= rac{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.

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.

Related Calculators

  • Transfer Function Analyzer — Analyze poles, zeros, DC gain, Bode samples, and time-domain response data from a polynomial transfer function.
  • Filter Design Calculator — Design a practical biquad-style lowpass, highpass, bandpass, or notch filter and return coefficients plus response samples.
  • Nyquist Sampling Calculator — Compute minimum sampling rate, aliasing behavior, and a simple capture-quality assessment.
  • Percentage Calculator — Perform common percentage operations: find a percentage of a value, calculate what percentage one number is of another, and find percentage change.
  • Fraction Calculator — Add, subtract, multiply, or divide two fractions and simplify the result.
  • Ratio Calculator — Simplify a ratio and compute equivalent forms.
  • Proportion Calculator — Solve proportions of the form a / b = c / x.
  • Average Calculator — Compute mean, median, and mode from up to five values.