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# How To Convert PID Parameters From Gain to Time

Updated May 9, 2019

## Reported In

### Software

• LabVIEW Control Design and Simulation Module
• LabVIEW Base
• LabVIEW Professional
• LabVIEW Full
• LabVIEW PID and Fuzzy Logic Toolkit

## Issue Details

I am using the PID functions in LabVIEW (formerly known as the PID Control Toolkit or the PID and Fuzzy Logic Toolkit). When working with the PID VI, the PID Gains input requires Proportional Gain (Kc), Integral Time (Ti), and Derivative Time (Td).

How are these values related to Proportional Gain (P), Integral Gain (I), and Derivative Gain (D), and how do I convert between them?

## Solution

Three major classifications of PID controller algorithms are: ideal, parallel, and series.
As shown in the equations below, KpKc are gain parameters; Ti and Tare integral and derivative time respectively. where: • Proportional term or Gain
The proportional term make changes to the output that is proportional to the current error value. The proportional gain may also be expressed as proportional band (PB). So a proportional band of 50% is equivalent to a proportional gain of 2.

• Integral term or Reset
The integral term is proportional to both the magnitude and the duration of the error. Increasing integral time makes the output respond slower to an error, which is opposite of the effect of increasing integral gain. The integral gain in the parallel PID is equal to the overall gain divided by integral time in the ideal PID. • Derivative term or Rate
The derivative term demonstrates the rate of change of the process error by determining the slope of the error over time. The derivative gain in the parallel PID is equal to the overall gain times derivative time in the ideal formulation. 