Question

Feedback control systems are:

• A. Insensitive to both forward and feedback path parameter changes
• B. Less sensitive to feedback path parameter changes than to forward path parameter changes
• C. Less sensitive to forward path parameter changes that to feedback path parameter changes
• D. Equally sensitive to forward feedback path parameter changes % Typo: "forward and feedback"

Hint:

Feedback Sensitivity. Negative feedback significantly reduces the sensitivity of the overall system performance to variations in the forward path gain (G). However, the system remains sensitive (sensitivity approaches -1) to variations in the feedback path gain (H).

Answer 1

The Correct Option is C

One of the primary advantages of using negative feedback in control systems is the reduction of sensitivity to variations in the parameters of the forward path (e
g
, the plant or amplifier gain)
The closed-loop gain or transfer function \( T(s) = \frac{G(s)}{1 + G(s)H(s)} \), where G(s) is the forward path transfer function and H(s) is the feedback path transfer function
The sensitivity of the closed-loop transfer function T to changes in G (\( S^T_G \)) is approximately \( \frac{1}{1 + G(s)H(s)} \)
If the loop gain \(G(s)H(s)\) is large, this sensitivity is significantly reduced
The sensitivity of T to changes in H (\( S^T_H \)) is approximately \( \frac{-G(s)H(s)}{1 + G(s)H(s)} \), which approaches -1 for large loop gain
This means the closed-loop system's performance is much less sensitive to variations in the forward path elements (G) compared to variations in the feedback path elements (H)
Changes in the feedback path have a more direct and pronounced effect on the overall performance
Therefore, feedback control systems are less sensitive to forward path parameter changes than to feedback path parameter changes