How To Convert PID Parameters From Gain to Time

Updated Oct 27, 2023

Reported In


  • 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?


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.
  • 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.

Additional Information

  • For a complete explanation of the implementation to the PID algorithm in the PID Control Toolkit see Chapter 2 of the PID Control Toolkit User Manual.
  • There are no industry wide standards for PID algorithms as different manufacturers use different PID algorithms. 
  • The ideal and the parallel forms are most relevant and flexible for tuning algorithms and are both widely used in the industry.
  • The series representation essentially consists of a PI and PD controller in series and made early analog controllers easier to build.