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A#17_Solutions-2

# A#17_Solutions-2 - Assignment#17— Solutions p ECSEQélO...

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Unformatted text preview: Assignment #17— Solutions -- p. / ECSEQélO Signals & Systems ~ Spring 2007 ﬂmﬁéw/ For the DC motor circuit below, the input voltage is v(t) and the output motor angular position is 6(5) . The motor constant is Kt, the back EMF constant is K1,, the torque is 7(t) , and the back EMF voltage is vb (t) i The armature inductance and fm’ction are negligible. Also assume the rotating load on the motor shaft has only inertia and no viscous friction. v(t) 6—) V(S) 69(1) <—> 6(5) 9a) rﬂ) " J (in-em) vbme ms) 1(2) <——> T(s) e.){i§ pts)Finc1 the transfer function 5(3) . Ms M 3 155 9 QM: K; ; 6(5) 9(5) he} {3 fits) Finn the transfer function j . - (a S 8 Z. M 775'} 5 f S 9.(S) mm a cote/94 G f7” e31: % 5; lots) Find the torque developed by the motor, T(s), as a function of the input voltage, V(s), the resistance R, the backemf voltage, Vb (s), and K M) s a M/ K Assignment #17— Solutions -— p. 7/ ECSEQMG Signals & Systems - Spring 2007 2, W Shown below is a DC motor. From the motor data sheet, the resistance of the armature is R = 4 ohms, the moment of inertia of the armature and the armature inductance are negligible, the motor constant is K, a: {£35 Newton-meter/amp, and the motor back-emf constant 18 Kb = 0.8 volt—sec/rad. Assume frictions} tosses are ZCI’OV t 60¢) 328,) v - -> a {3 Now suppose I connect a resistive load, RL == 8 ohms to the motor and a crank at the motor shaft. t" 600) R Crank Rt - ~> Ross {last do 1 have to crank the motor shaft so that the voltage across RL is 4 volts? fies, or)” , the constant angular speed of the motor shaft. The ﬁnal answer should be expressed as a mother in radians/second. 4‘ N M Liv ‘ ‘Zt y ' : V9 if; 1/» r it “5‘ a it} 1/ I j t w, A! 7 7~> M WS) " ‘t/ ’ (9‘, X Assignment #17— Solutions — p. 3 ECSEQQIO Signais & Systems — Spring 2007 Y(S) 3(10). Find {ho zransfer function X(S) . X(s) + Y(s) Assignment #17— Solutions — p. f! ECSEQéiiQ Signals & Systems - Spring 2007 W 53:: (a) \$C, 6AM. r- ,LL- :_ 6‘ 3+0 31s) 3+0; —_= éaké - 6L Jug) 1+ L-M‘ga MN?“ ‘k \ e :[ 6 dc. am -.-. m H.ch l Tc: ACHKQ Assignment #17— Solutions — p. 5/ ECSE—24IQ Signais & Systems — Spring 2007 /M€°« V (Cavﬁévaﬁﬂ W 033 .. Woman?“ 2 3‘3wa {0 4mm} ‘= 2A “:7 #67:! (F — CQDMMVTC': ALI-{\$51} = 2k ) ,._.._. in)“ . 6 4 AC?” Husk = E KAH WQ/CJ Caer/e Assignment #17— Solutions - p. 4 ECSEQéiQ Signals & Systems — Spring 2007 P . X M) 6 / (s) + . For the closed-loop system shown above, ﬁnd the transfer function, . Write it in terms of s the general HCS’) shown in the ﬁgure. / J. g/r/z x8) -—~ #57; ) s s) gm [/ ¢ W0] >4 If the closed—loop transfer function of the system shown above is = m , ﬁnd the open—loop transfer function (i.e., loop gain) H{s) (i.e., %%). s ,Z/[IJ / Assignment #17- Solutions - p. 7 80813342436 Signals & Systems - Spn‘ng 2007 /W Consider the feedback system shown. Find the characteristic equation (express X(s) a geigmmial equation in decreasing powers Y (s) Xe) ' Y (S) sf 3} for the closeddoop transfer function, 5 :0 7L ‘ / KW 3J+2+KI30 ...
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A#17_Solutions-2 - Assignment#17— Solutions p ECSEQélO...

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