Question

2. i) Obtain the state model for the reduced-form model 28 + 61 + 12x = 10y(t). Use x, and xz as the state variables. Put the equations in standard form and find [A] and [B] matrices. ii) where f (t) and f (t) are the inputs, Given the state-variable model i; = x; – 5x, +f,(t) * = -30x, +10f20) and the output equations Y; = x; – x2 + f (0) Y2 = x2 Yz = -x + f2(t) obtain the expressions for the matrices [A], [B], [C], and [D].

Answer 1

Soin- 2.) ;) 23 +65 +122= 10 o yet) Given state variables = x1, % Let x= x x = x = x * ä = i Substituting these in differentialega: 2 + 6% +1284, = 10 yat) or, is = -6X, -3 32 +5 y(t) U Also, x, z Egons ci) and ui) form state space egois- 14 1 ille -- ( 0); yet) 5 - 6 a -3 x + B u - x

Thus, A=50 MI: ) and tale jj) state variable model 24 = x,- 5th+ filt) by = -30%,+ 10 facts Output eqns: Y =2,-X2+ ficts Y₂ = 4 Y3z-xit folt) Z state space representation:- -57 11 fiti 10 be + 0 10 6 x fact) Ut) 2, -30 B А X + x so 1 x, 1 O + fict) facts न 0 % -1 Yz Яз Y u c X a + -

Thus, -5 A- BE 10 -30 Lo 2X2 2X2 COL. :). 1 ܥܙ 3X2