Control systems miscellaneous Easy Questions and Answers

Control systems miscellaneous

The Laplace transformation of f (t) is

F(s) =	ω	=
	s² + ω²

the final value of f(t) is—

Correct Option: D

The unit step response of a second order linear system with zero initial states is given by
C (t) = 1 + 1.25 exp (– 6t) sin (8t – tan^–1 1.333); t ≥ 0
The damping ratio and the undamped natural frequency of oscillation for the system are respectively—

From the expression for C (t), we get
8 = ω_n√1 – ξ² …(i)
and
√1 – ξ²/ξ = 1.333 …(ii)
solving these two equation, we get
ω_n = 10 rad/sec, and ξ = 0.6

Correct Option: A

From the expression for C (t), we get
8 = ω_n√1 – ξ² …(i)
and
√1 – ξ²/ξ = 1.333 …(ii)
solving these two equation, we get
ω_n = 10 rad/sec, and ξ = 0.6

The number of roots of the equation
2s⁴ + s³ + 3s² + 5s + 7 = 0
that lie in the right half of s plane is—

R.H.C. of the given C.E.
2s⁴ + s³ + 3s² + 5s + 7 = 0
s⁴ 2 3 7
s³ 1 5
s² – 7 7
s¹ 6
s⁰ 7
since there are two sign changes, therefore, two roots in the right half plane.

Correct Option: C

R.H.C. of the given C.E.
2s⁴ + s³ + 3s² + 5s + 7 = 0
s⁴ 2 3 7
s³ 1 5
s² – 7 7
s¹ 6
s⁰ 7
since there are two sign changes, therefore, two roots in the right half plane.

G (s) =	1
	s(1 + 6s)

the system is—

The poles at the origin, the phase angle may extend upto – 180º, limits the stability. Hence the system is marginally stable.

Correct Option: C

The poles at the origin, the phase angle may extend upto – 180º, limits the stability. Hence the system is marginally stable.

The type of a transfer function denotes the number of—

The type of a transfer function denotes the number of poles at origin.

Correct Option: A

The type of a transfer function denotes the number of poles at origin.