Chapter $9$ Root Locus Analysis

Consider a unity feectback control system with the lollowing characteristic equation:

$(s-1)(s^2+4s+7)+K=0$

a$)$ Find the oper loop transler funcion G$($s$).(5$ Pts$)$

b$)$ Write down the angle and magntude condiors. $(6$ Pts$)$

c$)$ Find number certer, and angle$($s$)$ of asymptotes. $(6.$ Pts$)$

d$)$ Find breakaway point$($s$),$ if exist. $(5$ Pts$)$

e$)$ What is the range of $K$ lor the system to be stable? $(5$ Pts$)$

f$)$ Finc intersection with the maginary axis and the value of K at the intersection. $(6$ Pis$)$

Sketch the root$-$locis showing all details $(12$ Pts$)$

h$)$ Use the magntude condricen to find the value co K at the breakaway point. $(5$ Pts$)$