Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
The transfer function of a process is G(s) =
Kp
p s+1, where Kp is the gain and p is
the time constant. This is a ________ process.
Options:
(A) first order
(B) multi-capacity
(C) purely capacitive
(D) second order
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2024 Q.12)**
**1. Governing Concept**:
- **Topic**: Process Dynamics & Bioprocess Control (Transfer Functions)
- Standard transfer function form for a continuous linear system:
$G(s) = \frac{K_p}{\tau_p s + 1}$
- The highest power of the Laplace variable $s$ in the denominator polynomial (characteristic equation) is 1. Therefore, this represents a **first-order process** with process gain $K_p$ and time constant $\tau_p$.
**2. Option Analysis**:
- **Option (A) [first order] is CORRECT**: Denominator polynomial degree in $s$ is strictly 1.
- **Option (B) [multi-capacity] is INCORRECT**: Multi-capacity processes involve multiple interconnected capacitances resulting in higher-order transfer functions ($n \ge 2$).
- **Option (C) [purely capacitive] is INCORRECT**: Pure capacitive processes have transfer function $G(s) = \frac{1}{As}$ (an integrator with no $+1$ term).
- **Option (D) [second order] is INCORRECT**: Second-order systems have denominator of the form $\tau^2 s^2 + 2\zeta\tau s + 1$.
**3. Final Answer**:
- **Correct Choice**: **A**
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