Hello, I was just wondering if it would be possible to get a solution for this question, and to please show all workings if possible, to help me understand it(transfer function analysis) better:

Given a system with the transfer function:

GP(s) = 20*13*9.8*1/10*(s+10)
(s+20)(s+2+3j)(s+2-3j)(s+9.8)

Evaluate the stability of the system.

(I think it's unstable due to the - in 1 of the brackets on the bottom of the equation) .

If it is required to approximate the given Gp(s) using a 2nd order system, please write down its transfer function (it should have the same system gain as Gp(s)).

Any help with solving and helping me understand this type of equation better, would be greatly appreciated.

Thanks.

 

A system is unstable if the real part of a pole is positive.

For the term (s + 2 - 3j) the pole is -2 + 3j, so it's still stable.
Complex poles always come in conjugate pairs, so if there is a x+jy there will be an x-jy.