-
The open loop transfer function of a unity feedback control system is given by:
G(s) = K s(s + 1)
If the gain K is increased to infinity, then the damping ratio will tend to become—
-
- 1/√2
- 1
- 0
- ∞
- 1/√2
Correct Option: C
Given G(s) = K/s(s + 1)
and
H(s) = 1
C.E. 1 + G(s) H(s) = 0
| 1 + | · 1 = 0 | |
| s(s + 1) |
s2 + s + K = 0 …(i)
on comparing equation (i) with the standard equation
s2 + 2ξωn s + ωn2 = 0,
we get
ωn2 = K
⇒ ωn = ± √K
2ξωn = 1
or ξ = 1 2√K
Now, as K → ∞, then ξ → 0.
Hence alternative (C) is the correct choice.
