Question

The loop transfer function of a system is:

\(\frac{K}{{s\left( {s + 1} \right)\left( {s + 5} \right)}}\)

The loop gain K is adjusted for inducing sustained oscillations. What is the value of K for this objective?

1. 16
2. 25
3. 30
4. 45

Answer 1

Correct Answer - Option 3 : 30

Analysis:

Condition for sustained oscillation is given by RH criteria

For RH, Characteristic equation is required

1 + G(s)H(s) = 0

\(1+\frac{K}{{s\left( {s + 1} \right)\left( {s + 5} \right)}}=0\)

s³ + 6s² + 5s + k = 0

s3	1	5
s2	6	k
s1	\(=\frac{30-k}{6}\)	0
s0	k

For sustained oscillations condition put s¹ row = 0

\(\frac{{30 - k}}{6} = 0\)

k = 30