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A feedback control system employing output- rate damping is shown in figure below.

What is the steady state error (in radian) for the above system resulting from an unit ramp input if the damping ratio is 0.6?
  • a)
    0.16 rad
  • b)
    0.38 rad
  • c)
    0.22 rad
  • d)
    0.45 rad
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A feedback control system employing output- rate damping is shown in f...
The characteristic equation of the given system is
1+G(s) H(s) = 0
Here,


∴ Characteristic equation is
10

or, s2 + (K0 + 2)s +10 = 0
Comparing with s2 + 2ξωns + ωn2 = 0 we have 
ωn = √10 rad/s
and 2ξωn = K0 + 2
Given, ξ = 0.6
∴ 2 x 0.6 x √10 = K0 + 2
or, K0 = 1.792
For a unit ramp input, ess = 1/Kv
where,


∴ 
= 0.3792 ≈ 0.38 radian
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A feedback control system employing output- rate damping is shown in figure below.What is the steady state error (in radian) for the above system resulting from an unit ramp input if the damping ratio is 0.6?a)0.16 radb)0.38 radc)0.22 radd)0.45 radCorrect answer is option 'B'. Can you explain this answer?
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