Question
Download Solution PDFA unity feedback system has an open-loop transfer function \(G\left( s \right) = \frac{K}{{s\left( {s + 10} \right)}}\) If the damping ratio is 0.5, then what is the value of K?A unity feedback system has an open-loop transfer function If the damping ratio is 0-5, then what is the value of K?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Open loop transfer function is given by:
G(s)H(s)
Characteristic equation is given by:
1 + G(s)H(s) = 0
The characteristic equation for second order system is given by:
s2 + 2ζωns + ω2n = 0
TB Solution:
Given ζ = 0.5
\(G\left( s \right) = \frac{K}{{s\left( {s + 10} \right)}}\)
Characteristic equation is given by:
1 + G(s)H(s) = 0
\(1+ \frac{K}{{s\left( {s + 10} \right)}}=0\)
s2 + 10s + k = 0
Comparing the above equation with s2 + 2ζωns + ω2n = 0
2ζωn = 10 and k = ω2n
2(0.5)√k = 10
√k = 10
k = 102
k = 100
Last updated on Jul 2, 2025
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