Question

The following are the effects of a phase-lead compensation except

• A. Crossover frequency is increased
• B. Rise time is increased
• C. Settling time is reduced
• D. More damping

Hint:

Effects of phase-lead compensation: \[ \text{Bandwidth} \uparrow \] \[ \text{Phase Margin} \uparrow \] \[ \text{Rise Time} \downarrow \] \[ \text{Settling Time} \downarrow \] \[ \text{Damping Ratio} \uparrow \]

Answer 1

The Correct Option is B

Concept: A phase-lead compensator improves the transient response of a control system by adding positive phase. Its transfer function is generally \[ G_c(s)=K\frac{1+\tau s}{1+\alpha\tau s}, \qquad 0<\alpha<1. \] It increases phase margin and improves system stability.

Step 1: List the effects of phase-lead compensation.
A phase-lead compensator generally:
• Increases bandwidth
• Increases crossover frequency
• Increases phase margin
• Improves damping ratio
• Reduces settling time
• Reduces rise time

Step 2: Examine each option.
Option (A): \[ \text{Crossover frequency increases} \] This is true. Option (C): \[ \text{Settling time decreases} \] This is also true. Option (D): \[ \text{Damping increases} \] This is again true.

Step 3: Check rise time.
A phase-lead compensator speeds up the response. Therefore, \[ t_r \downarrow \] rather than increasing. Hence the statement \[ \text{Rise time is increased} \] is incorrect.

Step 4: Final Answer.
\[ \boxed{\text{Correct Option (B)}} \]