Given a controlled transfer function (aka closed-loop transfer function) of the formG(s)1 G(s), sketch the rootlocus for following open-loop transfer functions, G(s). Clearly explain the rationale for your sketch includingthe basic root locus concepts like which part of the root locus lie on the real axis, how many branches of theroot locus goes to infinity, is there a break away point, etc. Furthermore, find the value ofKfor which: i)system is always stable, ii) characteristic equation have repeated real roots (if any) and iii) system will havefastest settling time. Verify your root locus sketch in MATLAB by making use ofrlocuscommand.