Question:

A proportional controller is used to control the temperature of an autoclave from \(60^{\circ}C\) to \(130^{\circ}C\). If the proportional band setting of the controller is 25%, the proportional gain value is ______________.

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Proportional Band (PB) indicates the range of error over which the controller output varies from 0% to 100%.
Proportional Gain (\(K_p\)) is the inverse of PB (in fraction form). Smaller PB \(\Rightarrow\) larger gain.
Typical relation: \(K_p = 100/PB(%)\).
Updated On: Aug 26, 2025
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Correct Answer: 4

Solution and Explanation

Step 1: Proportional Band (PB) and Proportional Gain (\(K_p\)) are related as: \[ K_p = \frac{100}{PB(%)} \] Step 2: Here, proportional band \(PB = 25%\). Substituting: \[ K_p = \frac{100}{25} = 4 \] Step 3: Hence, the proportional gain value is: \[ \boxed{4} \]
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