Question

Choose the correct statements from the following
A. The lag-compensation has a pole nearer to the origin.
B. The lag-compensation has a zero nearer to the origin.
C. The lag-compensator decreases the bandwidth.
D. The lag-compensator increases the bandwidth.

• A. A and D
• B. A and C
• C. B and D
• D. B and C

Hint:

Remember the key characteristics: - \textbf{Lag Compensator:} Pole is closer to the origin (\(p_c<z_c\)). Improves steady-state error, decreases bandwidth (slower response). - \textbf{Lead Compensator:} Zero is closer to the origin (\(z_c<p_c\)). Improves transient response and stability, increases bandwidth (faster response).

Answer 1

The Correct Option is B

Step 1: Analyze the pole-zero placement of a lag compensator. A lag compensator has a transfer function of the form \(G_c(s) = K_c \frac{s+z_c}{s+p_c}\). For a lag compensator, the pole is placed closer to the origin than the zero (\(p_c<z_c\)). This configuration is used to improve steady-state error. Therefore, Statement A is correct and Statement B is incorrect.
Step 2: Analyze the effect of a lag compensator on bandwidth. The primary effect of a lag compensator is to add attenuation at higher frequencies, which brings the gain crossover frequency down to a point where the phase margin is better. Bringing the gain crossover frequency down means the system's response becomes slower. A slower system response corresponds to a reduced bandwidth. Therefore, Statement C is correct and Statement D is incorrect.
Step 3: Combine the correct statements. The correct statements are A and C.