Question

Given the process transfer function \[ G_P = \frac{4}{(\tau s + 1)^2} \] and the disturbance transfer function \[ G_d = \frac{2}{(\tau s + 1)}, \] what is the correct transfer function for the Feed Forward Controller for perfect disturbance rejection? 

• A. \( -2(\tau s + 1) \)
• B. \( -1 \)
• C. \( -0.5(\tau s + 1) \)
• D. \( -(\tau s + 1)^2 \)

Hint:

To achieve perfect disturbance rejection, the feed-forward controller must cancel out the disturbance by taking the negative of the disturbance transfer function.

Answer 1

The Correct Option is A

- To achieve perfect disturbance rejection, the feed-forward controller should cancel out the effect of the disturbance transfer function. 
- The controller transfer function for perfect disturbance rejection is \( G_f = -G_d \), hence the correct transfer function is \( -2(\tau s + 1) \). Conclusion: 
The correct transfer function for the Feed Forward Controller is \( -2(\tau s + 1) \), as given by option (A).