Q.64 A proportional controller is used to control the temperature of an autoclave from 60 °C to 130 °C. If the proportional band setting of the controller is 25%, the proportional gain value is ____________.
Proportional Gain Calculation for Autoclave Temperature Controller
The proportional gain for the autoclave temperature control system is 4, computed from a 25% proportional band setting across the temperature span.
Key Concepts
Proportional controllers regulate output based on the error between setpoint and measured value.
- Proportional Band (PB) — the portion of the input error that drives the controller from 0% to 100% output.
- Gain (Kp) — inverse of proportional band.
Gain formulas:
Kp = 100 / PB% = 1 / PB (fraction)
Problem Data
- Temperature range: 60°C → 130°C
- Span = 130 − 60 = 70°C
- PB = 25% = 0.25 (fraction)
Step-by-Step Solution
1. Convert PB to Degrees
PB width = 0.25 × 70°C = 17.5°C
2. Compute Gain
Kp = 100 / 25 = 4
Units are dimensionless.
Final Answer
Proportional controller gain, Kp = 4
Common Pitfalls
- Using PB directly as gain
- Ignoring span (results in incorrect values)
Introduction
In industrial bioprocesses such as sterilization, autoclaves rely on proportional temperature controllers.
This GATE Biotechnology–style problem demonstrates computing controller gain using proportional band theory.
Understanding PB and Kp
- Proportional band (PB) = % of span for full valve movement
- Gain (Kp) = inverse of PB:
Kp = 100 / PB%
Given 25% PB, the controller output spans the full stroke over only one quarter of the error range.
Sample Calculation
Span = 130 − 60 = 70°C
PB = 25% = 0.25
PB width = 0.25 × 70 = 17.5°C
Gain = 100 / 25 = 4
Relevance
Mastering proportional band and gain relationships is essential for PID tuning questions in:
- GATE Biotech
- IIT JAM
- Process control engineering
Takeaway
Kp = 4 for a 25% proportional band controller on a 60–130°C autoclave.
