Control Systems Test 1

Result

Control Systems Test 1

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Question 1
1 / -0

For a given closed loop transfer function \(\frac{{s + 5}}{{{s^2} + 6s + 11}}\) with unity negative feedback, what is the value of open loop DC gain (upto two decimal places) ?

A
0.82-0.84

B
0.824-0.841

C
0.827-0.846

D
0.829-0.842

Solution

For the given closed-loop transfer function we can write:
\(\frac{{G\left( s \right)}}{{1 + G\left( s \right)}} = \frac{{s + 5}}{{{s^2} + 6s + 11}}\)
\(1 + \frac{1}{{G\left( s \right)}} = \frac{{{s^2} + 6s + 11}}{{s + 5}}\)
\(\\ \frac{1}{{G\left( s \right)}} = \frac{{{s^2} + 5s + 6}}{{s + 5}}\)
\(\\ G\left( s \right) = \frac{{s + 5}}{{{s^2} + 5s + 6}} \)
\(G(s)= \frac{{s + 5}}{{\left( {s + 3} \right)\left( {s + 2} \right)}}\)
Open-loop DC gain will be:
\(G\left( 0 \right) = \frac{5}{6}\)
= 0.8333