Question

The transfer function of a PID controller is:

• A. $K_c(1 + \tau_I s + \tau_D s)$
• B. $K_c(1 + \frac{1}{\tau_I s} + \tau_D s)$
• C. $K_c(1 + \tau_I s + \frac{1}{\tau_D s})$
• D. $K_c(1 + \frac{1}{\tau_I s} + \frac{1}{\tau_D s})$

Hint:

PID controllers are widely used in control systems because they combine proportional action (fast response), integral action (zero steady-state error), and derivative action (anticipatory correction).

Answer 1

The Correct Option is B

Step 1: PID Controller Definition.
A Proportional-Integral-Derivative (PID) controller's transfer function integrates three components: proportional, integral, and derivative.

Step 2: Standard Transfer Function.
The generalized transfer function is represented as: \[G_c(s) = K_c \left( 1 + \frac{1}{\tau_I s} + \tau_D s \right)\]

Step 3: Option Comparison.
Option (B) is the sole selection that aligns with this standard structure.

Step 4: Final Determination.
Consequently, option (B) accurately represents the PID controller's transfer function.