Question

Which one of the following statements regarding the effect of the phase lead network is not correct?

• A. The velocity constant is usually increased.
• B. The slope of the magnitude curve is reduced at the gain crossover frequency, as a result relative stability improves.
• C. Phase margin increased.
• D. The bandwidth decreased.

Hint:

Remember the key trade-offs: Phase Lead improves speed (faster rise time, more bandwidth) and stability (more phase margin) at the cost of amplifying high-frequency noise. Phase Lag improves steady-state error but slows down the response.

Answer 1

The Correct Option is D

Step 1: Recall the primary functions and effects of a phase-lead compensator. A phase-lead network is added to a control system to improve its transient response and stability margin. It adds positive phase shift over a certain frequency range.
Step 2: Evaluate each statement.

(A) Velocity constant increased: A lead compensator can be designed to increase the low-frequency gain, which increases the velocity error constant \(K_v\), thereby reducing steady-state error. This statement is correct.
(B) Slope reduced... stability improves: The lead network adds a zero and a pole (with the zero being closer to the origin). This has the effect of flattening (reducing the slope of) the magnitude plot around the gain crossover frequency, which is associated with improved stability. This statement is correct.
(C) Phase margin increased: This is the primary purpose of a lead compensator. It adds positive phase, which directly increases the phase margin. This statement is correct.
(D) The bandwidth decreased: A lead compensator makes the system respond faster (reduces rise time). A faster response corresponds to a larger bandwidth. Therefore, a phase-lead network \textit{increases}, not decreases, the bandwidth. This statement is not correct.