This section of **Control Systems **Multiple Choice **Questions and Answers **(MCQs) focuses on **“ Gain margin and Phase margin of a system ”. **These **MCQs** are very helpful for the preparation of **University exams, Engineering exams,** and various **competitive exams**.

**CONTROL SYSTEM – GAIN MARGIN AND PHASE MARGIN MCQs**

1. A system is said to be stable if:

Explanation:- For a

**stable system**: The gain crossover frequency is less than the phase crossover frequency. For

**Unstable system:**The gain crossover frequency is greater than the phase crossover frequency. For a

**Marginally stable or critically stable system:**The gain crossover frequency is equal to the phase crossover frequency.

2. If any one of the gain margin and phase margin is negative then the system is :

Explanation:- In a

**stable system:**Both gain margin and phase margin are positive. In

**unstable system:**Any one of the gain margin and phase margin is negative. In

**Marginally or critically stable:**Both gain margin and phase margin are zero.

3. Gain crossover frequency is the frequency where the gain curve crosses the

Explanation:- Gain crossover frequency is the frequency where gain curve crosses the 0dB axis that means at gain cross over frequency the magnitude of open loop transfer function |G(jw)H(jw)|=1 and in dB |G(jw)H(jw)|= 1 can be written as 20log|G(jw)H(jw)|=20log1= 0dB.

4. Phase crossover is the frequency where the phase curve crosses the :

Explanation:-The frequency at which phase angle of open loop transfer function G(jw)H(jw)is -180° is called phase crossover frequency.

5. Gain crossover frequency is one at which |G(jw)H(jw)| is:

Explanation:- Gain crossover frequency is the frequency where magnitude of the openloop transfer function is equal to 1 i.e |G(jw)H(jw)|=1 or magnitude in dB is given as |G(jw)H(jw)|in dB= 20log|G(jw)H(jw)| = 20log1 = 0dB.

6.Mathematically Gain margin can be given as:

Explanation:- Gain margin is defined as the margin in gain allowable by which gain can be increased till the system reaches on the verge of instability. Mathematically gain margin is defined as the reciprocal of the magnitude of G(jw)H(jw)at Phase crossover frequency.

7.Mathematically phase margin can be given as:

Explanation:- The amount of additional phase lag that can be introduced in the system till the system reaches the verge of instability is called phase margin. Mathematically PM=angle of G(jw)H(jw) at gain crossover frequency-(-180°)= 180° + angle of G(jw)H(jw) at the gain crossover frequency.

8.If both gain crossover frequency and phase crossover frequency of a transfer function is equal to 100 rad/sec then the system is

Explanation:- If Gain crossover frequency = Phase crossover frequency then Gain margin =Phase margin =0 and the system is marginally stable.

9. A system has Gain margin(GM)= -2dB and phase margin (PM)= -8° then the system is said to :be

Explanation:- If any of the gain margin and phase margin are negative then the system is unstable. For the system to be stable both gain margin and phase margin must be positive.

10. The larger the gain margin and phase margin, the better the stability of a system.

Explanation:- Gain margin is that gain dB which can be increased in the system without making it unstable while phase margin is the phase in a degree that can be raised in the system without making it unstable. So larger the gain margin and phase margin, the better the stability of a system.

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