GATE Control Systems 3

Question 1

The characteristic equation of a closed-loop system is 1 + G(s)H(s) = 0. The roots of this equation are:

Accepted Answer

Closed-loop poles

Answer

Open-loop poles

Answer

Open-loop zeros

Answer

Closed-loop zeros

Question 2

Which criterion is used to determine the ABSOLUTE stability of a linear time-invariant system without finding the roots of the characteristic polynomial?

Accepted Answer

Routh-Hurwitz criterion

Answer

Bode criterion

Answer

Nyquist criterion

Answer

Root locus criterion

Question 3

For a unity negative feedback system, if the open-loop transfer function is G(s) = K/[s(s+2)], the system is critically damped when K equals:

Accepted Answer

1

Answer

0.5

Answer

2

Answer

4

Question 4

The phase margin of a system is defined as 180° plus the phase angle of the open-loop transfer function at:

Accepted Answer

Gain crossover frequency

Answer

Phase crossover frequency

Answer

Natural frequency

Answer

Bandwidth frequency

Question 5

State transition matrix Φ(t) = e^(At) satisfies which property?

Accepted Answer

Φ(t1 + t2) = Φ(t1) · Φ(t2)

Answer

Φ(t1 + t2) = Φ(t1) - Φ(t2)

Answer

Φ(-t) = Φ(t)

Answer

Φ(0) = 0

Question 6

In the Nyquist stability criterion, the number of clockwise encirclements N of the (-1, j0) point is related to Z (RHP closed-loop poles) and P (RHP open-loop poles) by:

Accepted Answer

N = Z - P

Answer

N = Z + P

Answer

N = P - Z

Answer

N = Z × P

Question 7

A system is said to be observable if:

Accepted Answer

The initial state can be determined from the output over a finite time interval

Answer

All states can be driven to zero by a suitable input

Answer

The transfer function has no RHP zeros

Answer

All eigenvalues are in the left half-plane