Test: Stability Analysis of Linear Control Systems - 1

Question 1

The presence of non-linearities in a control system tends to introduce

Accepted Answer

all of these

Answer

instability

Answer

steady state error

Answer

transient error

Question 2

Which one of the following is not a property of the Liapunov function?

Accepted Answer

It is a unique function for a given system.

Answer

It is positive definite, atleast in the neighbourhood of the origin.

Answer

It is a scalar function.

Answer

It’s time derivative is non-positive.

Question 3

The number of sign changes in the Routh’s array indicates the number of roots lying in the

Accepted Answer

right half of s-piane

Answer

origin of s-plane

Answer

left half of s-plane

Answer

centre of the s-plane

Question 4

Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.
Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstable

Accepted Answer

Both A and R are true but R is not a correct explanation of A.

Answer

Both A and R are true and R is a correct explanation of A.

Answer

A is true but R is false.

Answer

A is false but R is true.

Question 5

The open loop transfer function of a unity feedback system is
What is the range of value of K so that the closed loop system is absolutely stable?

Accepted Answer

0 < K < 6.5

Answer

K > 6.5

Answer

0 < K < 4.25

Answer

0 < K < 9.8

Question 6

Assertion (A): If the system is stable we can determine the relative stability by the settling time of the system.
Reason (R): If the settling time is less than that of the other system then the system is said to be relatively more stable.

Accepted Answer

Both A and R are true and R is a correct explanation of A.

Answer

Both A and R are true but R is not a correct explanation of A.

Answer

A is true but R is false.

Answer

A is false but R is true.

Question 7

If the unit step response of a system is given by c(t) = -1.5 + e^t + 0.5e^-2f, then the system will be

Accepted Answer

unstable

Answer

stable

Answer

relatively stable

Answer

marginally stable

Question 8

The characteristic equation of a servo system is given by
a₀s4 + a₁s³ + a₂s² + a₃s + a₄ = 0
Now, consider the following conditions required to be satisfied by the coefficient of the above characteristic equation for the system to be stable:
1. a₁ > 0 and a₄ > 0
2. a₁ < 0 and a₄ > 0
3. a₁a₂< a₀a₃
4. a₁a₂ > a₀a₃
5.
6.
Which of the above conditions holds true for the given system to be stable?

Accepted Answer

1,4 and 5

Answer

2, 3 and 6

Answer

1,3 and 5

Answer

2 and 4

Question 9

The open loop transfer function of a unity feedback control system is given by

The oscillating frequency of the given system is

Accepted Answer

4.06 rad/sec

Answer

2.25 rad/sec

Answer

6.60 rad/sec

Answer

3.82 rad/sec

Question 10

The characteristic equation of a system is given by s³ + s + 2 - 0.

What are the number of roots in the right half s-plane and on the jω-axis respectively?

Accepted Answer

2,0

Answer

3, 0

Answer

2, 1

Answer

1,2

GATE Electrical Engineering (EE) Test: Stability Analysis of Linear Control

MCQ Practice Test & Solutions: Test: Stability Analysis of Linear Control Systems - 1 (10 Questions)

The presence of non-linearities in a control system tends to introduce

Which one of the following is not a property of the Liapunov function?

The number of sign changes in the Routh’s array indicates the number of roots lying in the

Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.
Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstable

The open loop transfer function of a unity feedback system is
What is the range of value of K so that the closed loop system is absolutely stable?

Assertion (A): If the system is stable we can determine the relative stability by the settling time of the system.
Reason (R): If the settling time is less than that of the other system then the system is said to be relatively more stable.

If the unit step response of a system is given by c(t) = -1.5 + e^t + 0.5e^-2f, then the system will be

The open loop transfer function of a unity feedback control system is given by

The oscillating frequency of the given system is

The characteristic equation of a system is given by s³ + s + 2 - 0.
What are the number of roots in the right half s-plane and on the jω-axis respectively?

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GATE Electrical Engineering (EE) Test: Stability Analysis of Linear Control

MCQ Practice Test & Solutions: Test: Stability Analysis of Linear Control Systems - 1 (10 Questions)

The presence of non-linearities in a control system tends to introduce

Which one of the following is not a property of the Liapunov function?

The number of sign changes in the Routh’s array indicates the number of roots lying in the

Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time. Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstable

The open loop transfer function of a unity feedback system is What is the range of value of K so that the closed loop system is absolutely stable?

Assertion (A): If the system is stable we can determine the relative stability by the settling time of the system. Reason (R): If the settling time is less than that of the other system then the system is said to be relatively more stable.

If the unit step response of a system is given by c(t) = -1.5 + et + 0.5e-2f, then the system will be

The open loop transfer function of a unity feedback control system is given by ​The oscillating frequency of the given system is

The characteristic equation of a system is given by s3 + s + 2 - 0.What are the number of roots in the right half s-plane and on the jω-axis respectively?

GATE Electrical Engineering (EE) Mock Test Series 2027

GATE Electrical Engineering (EE) Mock Test Series 2027

Top Courses for Electrical Engineering (EE)

About this Electrical Engineering (EE) Practice Test

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Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.
Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstable

The open loop transfer function of a unity feedback system is
What is the range of value of K so that the closed loop system is absolutely stable?

Assertion (A): If the system is stable we can determine the relative stability by the settling time of the system.
Reason (R): If the settling time is less than that of the other system then the system is said to be relatively more stable.

If the unit step response of a system is given by c(t) = -1.5 + e^t + 0.5e^-2f, then the system will be

The open loop transfer function of a unity feedback control system is given by

The oscillating frequency of the given system is

The characteristic equation of a system is given by s³ + s + 2 - 0.
What are the number of roots in the right half s-plane and on the jω-axis respectively?