Question

3-22. An electromechanical system has the following system equations. L. + R1 + Kjw = e(t) - dw J + Bw – K2i = 0 dt T For a unit-step applied voltage e(t) and zero initial conditions, find responses i(t) and wat). Assume the following parameter values: L=1HmJ = kg m², B= 2N ms, R=11, K1 =1V s, K2 = 1 N m/ A.

Answer 1

Given cdi + R 1 tkw - ett) . de I dw +Bw - K2 i 2o. at L=1H; Ja legm i B2 Sums & Rain KISW kr 1 elt) = ult) From Idi +1 (1) + 1) = ult) Applying capace transform on both sides sics) +its) twis) = 2 -) ils) 15+1) - - wis) ) wls) = + 1 - irs) (5+1) From 2) (1dw & 21w) – 1(1): 0 Applying taplane transform on both sides & swls) + 2 w 1s = its) 3) wis) (5+2) = ics) From Bollyw(s) = _ - Wis) (5+2)(s+1) wes) + wis) (5+1)(5+2) = ls & wis) (1+ 8 +35+2) = ls + wis) = S(&' +95 +2) - 3 316 paggages

Subject :..... Exam. : Page No. : ..........Date MARKS * Butas pasa) Applying inverse (aplave transform wilt) = 1 l ult) - 3t cost Wit) (ult) -ehk (60463t) - 28 3in101) from @ 7) wis). (5+2) = its) V3 pcs) st2 - T +35+3) - 25th 5+3 5+3 Applying inverse taplace toansform is) E 232 230) et Fie geste) - chocolate the ele ains.) fuet) - ale ta (atoeat} + sing t)