PID Gain vs Proportional Band: Units and Examples

Controller gain and proportional band can describe the strength of proportional action using different parameter conventions. A larger gain produces a larger proportional output change for the same normalized error. A smaller proportional band describes stronger action. Copying the number from one field into the other can therefore reverse the intended adjustment.

Begin by identifying whether the controller uses gain or band, how it scales error and output, and which algorithm is selected. Integral and derivative settings require their own checks; this comparison does not convert an entire PID configuration.

For positive gain magnitude Kc expressed as percent output change per percent input-error change, proportional band PB in percent satisfies PB = 100/Kc. Equivalently, Kc = 100/PB. Direct or reverse action is handled separately in this example. A gain expressed in engineering units is not automatically the same normalized Kc.

Yokogawa’s manufacturer material explains proportional-band behavior and gives the reciprocal gain convention. The table above uses our own round-number examples under the explicit normalization.

In a synthetic proportional-only calculation, a 2-percentage-point input error and Kc = 2 produce a 4-percentage-point output contribution. PB = 50% represents the same proportional sensitivity: 100/50 × 2 = 4. An offset, output saturation, integral accumulation and derivative response are excluded from this small calculation.

If someone instead enters 2 in a proportional-band field, the normalized proportional sensitivity becomes 100/2 = 50. The same error would request a much larger proportional contribution before any limits apply. The arithmetic illustrates a parameter-convention mistake; it does not predict the behavior of a complete closed loop.

• Record the measurement span and output span used for normalization.
• Keep controller gain separate from process gain, which describes process response to an input change.
• Check whether integral action is stated as time per repeat, repeats per time or another convention.
• Check algorithm form, direct/reverse action, filters, output limits and implementation documentation before comparing full configurations.

For example, an engineering-unit gain in percent output per degree must be related to the configured temperature span before it can be compared with a normalized percent-per-percent gain. A correct reciprocal calculation cannot repair an incorrect assumption about those units.

The PID tuning guide connects parameter conventions with process dynamics and response evaluation. PID100 primary process control and PID tuning is the course sales page for the published syllabus and prerequisites. If a trend is oscillating, use the stiction-versus-tuning evidence comparison before assuming the proportional setting is the only cause.

Technical definitions are supported by the primary references below. The labelled numerical records, timelines and checklists are original teaching examples for this article. They do not establish site-specific design approval or a new course entitlement.

• Yokogawa: loop monitoring and gain/PB convention
• Yokogawa: proportional-band manual

Browse the process-control learning library for the wider subject guides and course routes.