Question

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. Determine the amplifier gain Ka required to achieve a system damping ratio of 0.7. a. b. Plot int), eout(t), and E(t) on the same axis when ein(t) is a unit step input Calculate maximum percent overshoot and time to peak C. Note: Submit graph with proper labeling. Error Desired angular Actual angular E(s) position 0in(s) position out(s) Servomotor Amplifier 0.5 Ka s(0.33s1

Answer 1

(ANS) (5) out O.5 EC5) Ka 5(0335+) Oin(5) O.5Ka Oout (S) 7 0.3352 5+0.5 ka Ein (5) O.5 ka X Oout C3) 0-33 5+ 3.033+515 ka Oin(5) I-515 Ka Oout(5) 52-3.035+ 515 Ka Oin (5)

(a) §0.7 |55 ka 5 42Econs+on = S+3.035+)-515 ka Gn 3.03 2& Con 3.03 .515 ta XCO-7)X 3.092 ka Jn matlab

0.5 3,092 0.33s2+s Step Gain Transfer Fcn Scope

1 0.8 theta out (S) 0.6 E(s) theta in (S) 0.4 0.2 0 4 0.5 1 1.5 2 2.5 3 3.5 4.5 5 LO

(c) OVer shoot TT CO 7) V-o 7 4.599 .

Peat m TT TT J.515 X 3.09L X 2.164 X 6-7) 4 2.033 Sec