-
Consider a system shown in the given flgure with
G(s) = K(s + 1) s3 + as2 + 2s + 1
What value of ‘K’ and ‘a’ should be chosen so that the system oscillates?
-
- K = 2, a = 1
- K = 2, a = 0.75
- K = 4, a = 1
- K = 4, a = 0.75
- K = 2, a = 1
Correct Option: B
| G(s) = | ||
| s2 + as2 + 2s + 1 |
The given system is unity negative feedback system. Its characteristic equation is therefore,
s3 + as2 + 2s + 1 + K (s + 1) = 0
or
s3 + as2 + (2 + K) s + (1 + K) = 0 …(i)
R.H.C. of the equation (i)
s3 1 (2 + K)
s2 a (1 + K)
s1 2 + K (1 + K)/a
s0 (1 + K) –
For a system to be stable a > 0.
[(2 + K) – (1 + K)/a] > 0
and
(1 + K) > 0.
For the system just to oscillate (2 + K) – (1 + K)/a = 0
and also a and (1 + K) should not come negative, we see that out of the given set of value K = 2 and a = 0·75 satisfies the equation.
