Question

1. (10 points) o Consider the unity feedback system with open loop transfer function Ко L(s) = s(s+ 7) (s+ 3) Let Tf = 0.15 and Tm = 0.3. What value(s) of Ko produce a marginally stable system? Should K, be pushed larger or samller than those value(s) to stabilize the closed-loop system?

Answer 1

sمل giren cinity feedback System ie., Hes)=1 given LCD = s(s+ + + (8 + 7 m) T4=0.15 and Im=0.3 » L(S)= to 6.66780 sest is) (stá ) s(s+6.667)65+3-33) - The Characteristic equation is 0 1+ Ls) HCS) =) it 6.667ko -o SCS76.667) (5+3.33 -) SCS+6.667)(8+333)+6.6676= 0 ») s($710s + 22.992] +6.667 kovo => $37165 +22.228+6.667k6=0 R.H. Costerion? - RH-Tale! - Row calculation it 53 1 22.22 ř 10 6.667ko & Row! 10x 2.22-16 66760) 222.22-6-66 S TO =) 222.22-6.667to 91 o 6.667ko

CO for the system to be Marginally stables we have to get a Row of All Beroes i.e., 222.22-6-66760 -0 (Rowo elemente 10 =) Ko=222-22 = 33.33 6.667 ko=33.33) v and also 6.667kožo ko=0 koso and Ko=33.33 Values Produce a Marginally stable system .. of Koso means, total 105)-0 : Sytem will becomes afko=33.33 soole to be pushed smaller than those tatues to stabilize the closed loop system. . ..