Question

Question 4 (15 points): A robot is used on an airplane assembly line to drill some holes in the airplane body. The robot arm is driven by a servomotor. The block diagram of the control system used to control the drill in one axis is shown in the figure below a. Determine the amplifier gain Ka required to achieve a system damping ratio of 0.7 b. Plot, and on the same axis when is a unit step input c. Calculate maximum percent overshoot and time to peak Note: Submit graph with proper labeling Servomotor Amplifier Error Desired angular position 0in(s) Actual angular position 0out(s) E(s) Servomotor 0.5 Amplifier Ка s(0.33s+ 1)

Answer 1

Input interpretation: 4.6818 :](t) 2+3.03 s 4.6818 Result: (1.51529 e1.5 15-1.54485 i)t ((1 +0)e3.08971)t(- Plots: 1.0 0.8 (t from 0 to 1) 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1.0 y 1.0 0.8 0.6 0.4 0.2 (t from 0 to 6) 1 23 456

Me givee unit deachack Slhisin': Chancterishe eertin der elosed Qoop syrem isdhen 1t ka X o.5 ambliftriy&Seaveincder Slo33SH!) L o.33st St 0 5 ka=o s2+ S+o5ka o-(ii) O.33 a.33 Compare eguation (i ith g2+ans+@n =0, we et 0.5ka v [Combwiy Conghirt tem] 0.33 @ Griven dambig dtio =o+7 = So we get Nau By usig iv) we get ka3.09AS 15 x Ke Ka= O'33 Puttingvalres tn above,e get xO7 !FF=&=7 x {00 -TXO y.Mp= e lMp= OO40 X100 7 Mp= 4.69-Ansae Speak time; ftp= T >So tp= tp 2.031 Seconds An 2 164 1-(072 dunctin isiven yT=c©)_ G{s) HCS) =1 elesed Cot ars RIS) HoUSTHIS Lhe G()= ska So338) So; Tis)= o.5 Ka S(01335H) Sa33st)

Autere O.5X 3.09 339+ S+o'5X3 09 >So TCS)- Cls) R(S) CCs) = 545 0133( s2t S+ S R(S) 033 O'33 Pt Putie Ris)= sunit Ste dunction abrce oarsam Cis)= 4.6818 (S2+ 3.03S +4 (Oslace demain ehesentatian outbut de ande De can 919 elfeom alpha Sfte trvease alace antem falove al belos eCt)=E515 i ) 15-5449s)t6-089it geasily Caloulate He Ans 1