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: Recall the definition of PID controller.
A Proportional-Integral-Derivative (PID) controller combines three terms: proportional, integral, and derivative, in its transfer function.

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

Step 3: Match with options.
Among the given options, only (B) matches this standard form.

Step 4: Conclusion.
Hence, the correct transfer function of a PID controller is option (B).