Question

For the given closed loop system, where:

C(s)=  9.43  s+  9.56   

G(s)=  87.84 / ( s2+  2.94 s+  9.00 )

Part A: Obtain the rise time of the step response of the plant transfer function  G(s).

Part B: Obtain the overshoot of the step response of the plant transfer function  G(s).

Part C: Obtain the 1% settling time of the step response of the plant transfer function  G(s).

Part D: Obtain the natural frequency  ωn of the characteristic polynomial of the closed-loop transfer function T(s).

Part E: Obtain the rise time  tr of the characteristic polynomial of the closed-loop transfer function  T(s)

Part F: Obtain the steady-state value of the output  yout(t) for a unit step input of magnitude 8.

Ω. out G(s) C(s) control plant For the given closed loon system, where: C(s)9.43 84 9,56 G(s)= 394 19.0 87.84 Part A Plant Rise Time Obtain the rise time of the step response of the plant transfer function G(s). ΑΣp t 0.0617856 Previous Answers Request Answer Submit X Incorrect ry Again Part B - Plarit Overshoot Obtain the oershoot of the sten respensa of the plant transfer function Glsh M Reguest Angwer Submit Part C Plant 1 % Settling Time Ostain the 1% etting time of the atep reparow of the alart tramafer function Glsl Nth a? Reguest Angwe Submit Part D Closed Loop Natural Frequency OLwin the nurel frauuency y ol the characteriatis pulynomial o e lused loop tranafer funstion 7a). rarl/s Request Answer Suberit Part E Closed Loop Rise Time Obbain the rise time to af the characteristic abenemial oi the clsed-lace tranie functien 7Y Submit Renuest Answer Part F-Steghe-state Value Obtain the steady-state value of the outout .it for a unit step ireut mannieudeu Cu a ? o, Submit Request Answer

Answer 1

Slutian Given Plant are functin G)ay characteistic eatien dthe hen Gls)= derominade Pe Gls) So gs)= S+2.9us+9=0 Compare equation wih tuhs+ To St+2.94S+9) Jet we Comparig >Qun= D.94 2 S-Co CCompari Congent feym] an=3 dael|sec de get 2X-X3= 2.94 PART-A' Plont die time; -Cos By Putiry all knon values get t=3.14-1.058 2.6151 we o49 3XT649 ing PARTB POont oveshed Mps .Ey o) Putigvallueateve, me gt PARTC 1 time is given by ts = _46 -9X 31292 Secng elosed Coop Charartesistic eguatienis given by 1+ C(S) GS) O PART-D 1+.43S+9.50) x 87-24 =0 S+2.94+9+ 828.93 S+ 839.75 0 >S2t 831.27S+ 848-75=0 Cem bare eguationt iv 22Gun Stwn=owe get 2un=9.31127 D48.75 -(iv Q-Teyms

4.267 S dise time |tj= T-Cos (4.2 ecoz ise Hime Cannet Le caleulatel Coverdambel System) PARTE we get 2x29133X 3127