PID Output & Bias Calculator: Controller Output

Error

Setpoint minus process variable, using the same units as the controller's proportional calculation.

Proportional Gain (Kp)

Proportional gain applied to the error.

Bias / Manual Reset (%)

Base controller output before proportional, integral, and derivative contributions.

Integral Contribution (%)

Enter the current accumulated integral contribution.

Derivative Contribution (%)

Enter the current derivative contribution.

Output Minimum (%)

Minimum controller output limit.

Output Maximum (%)

Maximum controller output limit.

Controller Output

PID Output Formula

For the simplified calculation used by this calculator, the controller output is:

Output = Bias + (Kp × Error) + Integral Contribution + Derivative Contribution

The calculated output is then limited to the configured minimum and maximum output values.

This calculator treats the integral and derivative terms as already-calculated contributions. A real PID controller calculates those terms from process history and timing.

Example

Example: A temperature controller has:

Bias = 50%
Error = 5
Kp = 2
Integral contribution = 5%
Derivative contribution = 0%

Output = 50 + (2 × 5) + 5 + 0

Controller Output = 65%

What Is PID Bias?

Bias is the controller output around which proportional, integral, and derivative action operates. It is sometimes called manual reset or output bias, depending on the controller.

For example, a modulating heating valve may require approximately 40% output to maintain a particular operating condition. That operating output can serve as a useful starting point for the controller's bias.

Why Bias Matters

Without an appropriate bias or integral contribution, a proportional-only controller may require a persistent error to maintain the output needed by the process.

Integral action can move the controller output until that persistent error is reduced, depending on the controller's configuration and tuning.

Important PID Notes

Different PLCs, DDC controllers, and process controllers implement PID equations differently.
Some controllers use gain while others use proportional band.
Integral and derivative settings may use different time units or calculation conventions.
Direct-acting and reverse-acting controllers can produce different output responses to the same error.
Output limits, anti-reset windup, deadband, filtering, sample time, and setpoint tracking can affect actual controller behavior.
This calculator is intended to illustrate and calculate the controller equation; it is not a substitute for the PID implementation documentation for a particular controller.

PID Output & Bias Calculator