Question

Identify the correct definition for phase Margin and Gain margin:

• A. I. Gain margin is a factor by which the system gain can be decreased to drive the system to the verse of instability.
  II. Phase margin is the additional phase lead at the gain cross over frequency to bring the system to verge of instability.
• B. I. Gain margin is a factor by which the system gain can be decreased to drive the system to the verse of instability.
  II. Phase margin is the additional phase lag at the gain cross over frequency to bring the system to verge of instability.
• C. I. Gain margin is a factor by which the system gain can be increased to drive the system to the verse of instability.
  II. Phase margin is the additional phase lag at the gain cross over frequency to bring the system to verge of instability.
• D. I. Gain margin is a factor by which the system gain can be increased to drive the system to the verse of instability.
  II. Phase margin is the additional phase lead at the gain cross over frequency to bring the system to verge of instability.

Answer 1

The correct option is C I. Gain margin is a factor by which the system gain can be increased to drive the system to the verse of instability.

II. Phase margin is the additional phase lag at the gain cross over frequency to bring the system to verge of instability.
$\text{Concept:}$
$\text{Gain margin}\left(GM\right):$ The gain margin of the system defines by how much the system gain can be increased so that the system moves on the edge of stability.
$\text{It is determined from the gain at the phase}\text{cross-over frequency.}$

$GM=\frac{1}{|G\left(j\omega \right)H\left(j\omega \right){|}_{\omega ={\omega }_{pc}}}$

$\text{Phase crossover frequency}\left({\omega }_{pc}\right):$ It is the frequency at which the phase angle of G(s) H(s) is $-{180}^{\circ }$.

$\angle G\left(j\omega \right)H\left(j\omega \right){|}_{\omega ={\omega }_{pc}}=-{180}^{\circ }$

$\text{Phase margin (PM):}$ The phase margin of the system defines by how much the phase of the system can increase to make the system unstable.
$PM={180}^{\circ }+\angle G\left(j\omega \right)H\left(j\omega \right){|}_{\omega ={\omega }_{gc}}=-{180}^{\circ }$
$\text{It is determined from the phase at the gain cross over frequency.}$
$\text{Gain crossover frequency}\left({\omega }_{gc}\right):$ It is the frequency at which the magnitude of G(s) H(s) is unity.
${\left|G\right(j\omega \left)H\right(j\omega \left)\right|}_{\omega ={\omega }_{gc}}=1$
$\text{Observation:}$
Option 2 is correct.