Question

i) Obtain the state model for the reduced-form model 2x + 68 + 12x = 10y(t). Use x, and xz as the state variables. Put the equations in standard form and find [A] and [B] matrices. Given the state-variable model = x; – 5x, + f(t) , where fi(t) and f (t) are the inputs, *, = -30x, +10/20 and the output equations y = x; – x2 + f,0 y2 = x2 Y; = -x + f20 obtain the expressions for the matrices [A], [B], [C], and [D].

Answer 1

Q © Giens Pä+68+122= 10yet) As vele know that state space equations sepresented by x = AX + BU Y = CX + DU Where; XI State variables ; U = Input Variables. let X = X1 da = dt x = = xq X = X2 dze dh put the values in egn @

ܟܟ 2X2 +6X1 + 12x4 = toy(t) 2X2 + 6Xg+ 12 x1 = 10 ylt) 2X2 = 10 y(t) = 6X2-12 X 1 X2 5 5707) - 3X2-6 XL. X = X2 ho Put the eqn 0 and eq o in Matrix form X 0 1 -XL a t 1 from 0 -6 X2 -3 X2 Сл 다. llence's Aa -6 -3 Ans B La

Given % = H1 - 5H2 + filt) = -3030 + 10 frit) Also YA X1 - Hq + filt) y2-22 y = -x 1 + falt) The Sports State space sepresent w A], [B], [C]' and [D] matsin 'foam X = AXT BU Y =cy tou 4 re -5 24 filt) こ t HE H2 -30 o 12 10 f26)

In the system there are thoxe autputs; 1 Y 2 = [1 - 114 12 + o falt) Y = [0 14 to H2 Y =[-10 4 12 filt) falt) 2 Hence, 01-63-1 1 o [C] E [1 - 1 1-11, 012 IGJE(1), DJECO) [3] = [-10 L [Ds] = Ti 1
please upvote, if it helps