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

The roots of the characteristic equation 1 + G(s)H(s) = 0 are the closed-loop poles of the system.

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

The Routh-Hurwitz criterion uses an array of coefficients to determine the number of RHP roots without solving the polynomial.

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

Closed-loop characteristic equation is s² + 2s + K = 0; critical damping requires ζ = 1, so (2/(2√K)) = 1, giving K = 1.

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 margin = 180° + ∠G(jωgc)H(jωgc), where ωgc is the gain crossover frequency where |GH| = 1 (0 dB).

Question 5

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

Accepted Answer

Φ(t1 + t2) = Φ(t1) · Φ(t2)

Answer

The state transition matrix satisfies the semigroup property: Φ(t1 + t2) = Φ(t1)·Φ(t2), analogous to the scalar exponential.

(GATE) Graduate Aptitude Test in Engineering Practice Test

(GATE) Graduate Aptitude Test in Engineering Practice Test

GATE Control Systems 3