In PID terms, what is the relationship between proportional band and gain?

• A. Proportional band is the range of error that yields full-scale output; gain is the inverse of the proportional band; reset time (Ti) is the integral term controlling how quickly accumulated error is corrected.
• B. Proportional band is the integral term; gain is the derivative term; reset time is the setpoint maintenance time.
• C. Proportional band is the derivative term; gain is the integral term; reset time is the sensor response time.
• D. Proportional band is the range of error that yields full-scale output; gain equals the inverse of the proportional band; reset time Ti is the integral time constant.

Answer: (A)

The main idea here is how the proportional action relates to gain. Proportional band defines the error range that drives the controller output up to its full value. In common PID terminology, gain is the inverse of that band: a small proportional band means a large gain (more aggressive corrective action), while a large proportional band means a small gain (gentler action). This inverse relationship is what links how wide the error range is to how strongly the system responds.

The statement also correctly notes the role of the integral term: the reset time Ti is the integral time constant, which determines how quickly accumulated past error is corrected by the integral action. So the proportional band and gain sit together to shape immediate response, while Ti controls the speed of the accumulated-error correction.

Other options mislabel the roles, mixing up proportional band with integral or derivative terms, or mischaracterizing what Ti represents (as a setpoint maintenance time rather than the integral time constant).