Process Controllers - P, PI & PID

Calculator and visualizer for Proportional (P), Integral (I), and Derivative (D) process controller outputs. Analyze controller responses including P-Controller, I-Controller, D-Controller, and combined PID-Controller behavior.

Process Controllers Overview

This tool calculates and visualizes the output responses of different process controller types:

P-Controller (Proportional): Output proportional to error
I-Controller (Integral): Output proportional to accumulated error over time
D-Controller (Derivative): Output proportional to rate of change of error
PID-Controller: Combined proportional, integral, and derivative control

Key Formulas

P-Controller: OP = -kP × Er

I-Controller: OI = -kI × Σ(Er dt)

D-Controller: OD = -kD × dEr/dt

PID-Controller: O = OP + OI + OD

Calculator

Inputs

Error (Er) (%)

Proportional Gain (kP)

Integral Gain (kI)

Derivative Gain (kD)

Error Rate of Change (dEr/dt) (%/s)

Error Integral (Σ Er dt) (% s)

Proportional Band (P) (%)

Results

Proportional Output (OP)-- %

Integral Output (OI)-- %

Derivative Output (OD)-- %

PID Output (Total)-- %

Calculated Gain (kP = 100/P)--