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: Lag Compensator Pole-Zero Placement AnalysisA lag compensator's transfer function is given by \(G_c(s) = K_c \frac{s+z_c}{s+p_c}\). In a lag compensator, the pole is closer to the origin than the zero (\(p_c<z_c\)), improving steady-state error. Thus, Statement A is correct, and Statement B is incorrect.
Step 2: Lag Compensator Bandwidth Impact AnalysisA lag compensator primarily attenuates higher frequencies, reducing the gain crossover frequency and improving the phase margin. This reduction slows down the system's response, resulting in a reduced bandwidth. Therefore, Statement C is correct, and Statement D is incorrect.
Step 3: ConclusionThe correct statements are A and C.