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How to solve the following question?

For a unity feedback control system with a forward-path transfer function G(s)=16/s(s+a), design the value of 'a' to yield a closed-loop step response that has 5% overshoot.

It's answer is a=5.52

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  • \$\begingroup\$ does your G(s) include the step input 1/S or not? \$\endgroup\$ – Rrz0 Jan 7 '18 at 10:00
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    \$\begingroup\$ Show your effort first. \$\endgroup\$ – Rohat Kılıç Jan 7 '18 at 10:01
  • \$\begingroup\$ @Rrz0 No it does not. \$\endgroup\$ – Wani Jan 7 '18 at 10:24
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Thanks for help bit I think I have solved it.

System transfer function will be T(s)=16/(s^2+as+16) Therefore, a = 2*damping ratio*natural freq. But natural freq. = 4 Therefore, a = 8*damping ratio Since %OS = 5 Therefore
damping ratio = (-ln(%OS/100)/√((π^2)+(ln(%OS/100))^2) That is, damping ratio = .69 a=8*.69=5.52

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