Subtopic: Fundamentals of Downstream processing (chromatography, filtration)
Question Statement:
Which one of the following statements is CORRECT about proportional controllers?
Options:
(A) The initial change in control output signal is relatively slow
(B) The initial corrective action is greater for larger error
(C) They have no offset
(D) There is no corrective action if the error is a constant
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2019 Q.51)**
**1. Governing Concept**:
- **Topic**: Downstream Processing & Centrifugation (Sigma Concept)
- In industrial centrifugal sedimentation:
- The equivalent settling area $\Sigma$ characterizes the clarifying capacity of a centrifuge independently of the broth properties:
$Q = 2 v_g \Sigma$
where $Q$ is volumetric throughput and $v_g$ is terminal settling velocity under gravity ($1g$).
- For a tubular or disk-stack centrifuge, $\Sigma$ is directly proportional to rotational speed squared ($\omega^2$) and centrifuge geometric settling area.
- Matches Option **B**.
**2. Option Analysis**:
- **Option (A) is INCORRECT**: Inverted dependency on rotation speed.
- **Option (B) is CORRECT**: Accurately reflects centrifugal sedimentation scaling relationships.
- **Option (C) is INCORRECT**: Ignores density difference.
- **Option (D) is INCORRECT**: Linear speed dependency is false (quadratic in $\omega$).
**3. Final Answer**:
- **Correct Choice**: **B**
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