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: Review the key functions and effects of a phase-lead compensator.A phase-lead compensator enhances a control system's transient response and stability by introducing positive phase shift within a specific frequency range.
Step 2: Assess each statement.

(A) Velocity constant increased: A lead compensator can be designed to raise the low-frequency gain, thus increasing the velocity error constant \(K_v\) and diminishing steady-state error. This statement is correct.
(B) Slope reduced... stability improves: The lead compensator introduces a zero and a pole (the zero being nearer to the origin). This flattens the magnitude plot around the gain crossover frequency, leading to improved stability. This statement is correct.
(C) Phase margin increased: This is the main function of a lead compensator. It adds positive phase, directly increasing the phase margin. This statement is correct.
(D) The bandwidth decreased: A lead compensator accelerates the system's response (reduces rise time). A faster response equates to a larger bandwidth. Therefore, a phase-lead compensator \textit{increases} the bandwidth, it does not decrease it. This statement is not correct.