Question

The transfer function for a PID controller is (where, \( \tau_I \) is the integral (reset) time and \( \tau_D \) is the derivative time.)

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

Hint:

Use PID transfer function to tune controllers effectively.

Answer 1

The Correct Option is D

PID control action = Proportional + Integral + Derivative terms.
Integral term: \( \frac{1}{\tau_I s} \), derivative term: \( \tau_D s \).