Fall1998_Exam2 - Namcaarim) 50LUT/0N- Section (circle one)...

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Unformatted text preview: Namcaarim) 50LUT/0N- Section (circle one) 9 am 10 am ECE330 B&C EXAM #2 Fall 98 Problem 1 (30) An electromechanical system with three electrical ports and one rotational mechanical port (6) has the following equations for flux linkages ,2. = £1|II+(Mcose)iJ ,17 = 1,225 + (M sin6)i, A: = (M c059)!“l + (M sin 0):} + 1131', where M, L; ., L2; and L3; are constants. (15) a) Compute the co-energy W;. (15) b) Compute the torque of electric origin 7;(i,,i2.ij.0}. ' I; a" .1; 5:3- It 521M069 4‘3 Wm 2‘ - n I + 1 z a 7- ; 3’ 3 . . 2r 4' M 5/?)- & l’ 1 e t 7; : ~M5/n36’43 .rM £419 ‘1 .3 :— r) Wm, Problem 2 (35) L -2 Distance 2: of the mass M is measured from a fixed reference. A(i,x) is given as 11(13):): C—' . X (10) a) Find the force of electric origin. (15) b) Write the equations of the system in state space form. I(!) is a specified function of time. (10) c) What is_Wm(i,x)? Problem 3 (35) In the following state space model jl=x2 :— ‘C; (1/ 12.39) 1": =-0.lx:!.ir3—x’+xl ' C 1/ x:- Z’) it,=-2x,xj—x,l-S =9¢3 (X; 29,13) Initial conditions are x.(0) = l. 12(0) = 0.5. 13(0) = 10 at t = 0. (10) a) With a time step of 0.1 sec, find using Euler‘s method xvxrx, at r = 0.1 sec. (10) b) Find all the possible static equilibrium points. (15) c) Find the linearized model at any m of the equilibrium points. 22:, (0.1); x, (0)1 At 4’] (Iggy?) = /+ 0'! (M): MS 12104); 11(0) +11% 1C1(z,/o£ 11(9)} Z’(o)) . 3 = 0’54 wl [‘(odflo'ffll‘) "/ '“J = 0'!" ra—l (-w:)=(0'451 333,04): 1,0) + 0'] C— 2(o.()(/o) -/0 T53 /0-/-0-/ [—15’ = (3'51 1 f ’ _ 53'” ‘9" "z’ " 9"" (0)991) "1) )l x:=5 :tzczo 11(I'ZIL);0 7-1) x]: / fgjbw a I —/ 9 0 o ’W 5 2 I “[r *3 I [—1.1'1wv'5a Midltv/ ” 31 7 7). A —3)t,+r 44,13 4'11; 0 ~213 —I-—1*=~ #/ a 1 0 o / 6 0 a / O I ,,.5- o #1- Q, "‘0‘; o #3 ,2 —-D'{ O o -/o ‘1 o -lo —I o —/o “I ...
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Fall1998_Exam2 - Namcaarim) 50LUT/0N- Section (circle one)...

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