Question

An open loop control system results in a response of \({e^{ - 2t}}\;\left( {sin5t + cos5t} \right)\) for a unit impulse. The DC gain of the control system is_______________

Answer 1

\( g\left( t \right)\; = \;{e^{ - 2t}}\;\left[ {sin\;5t\; + \;cos\;5t} \right]\)

Taking Laplace transform, we get

\(G\left( s \right) = \frac{5}{{{{\left( {s + 2} \right)}^2} + {5^2}}} + \frac{{s + 2}}{{{{\left( {s + 2} \right)}^2} + {5^2}}} \)

DC gain means:

 \({\left| {G\left( s \right)} \right|_{s=0}}\;\)

\(G\left( 0 \right) = \frac{5}{{{2^2} + {5^2}}} + \frac{2}{{{2^2} + {5^2}}} = \frac{7}{{29}}\)