xi= y-βux, =j-βu-βux=j-βi-βu-βun-1 = y(n-2) - β,u (n-) -.- β,-,t -β,-_ [xn = y(o-1) - βou(r-1) ....-βn-2i-βn-1useveral phase variables y, j, ., ,(r-1)can be developedy=x + βuj=x +βu+βuj=x, +βi+βu+β,un(n-2)1+ β,uor-2) + ..+ βμsu + βe,-2-uEx.1(n-1)) = , + β,ur-1) +..+ β,--u+ β,-u(n) +ay(n-1)+..+an-1j+any=bum) +b,u(n-1) +...+bn-ju+b,u
() =-{ax, +axn- +.+an--+ +a,x)+ βBu) + βu(n-1) ++ β.-u+β,uy=x +βuj=x, +βu+ βuj=x, +βu+Bu+βuyon-2) = X- + Bou-2) +.+ βu+ β2u,(r-1) = , + β,u-1) +.-+ βn-i + β,uxi= y-βouxz =j-βu-βux=j-βi-βu-β,uDifferentiating x- = (-2) -βB,u-2) -.-- β,ju- β-u[, = ,(-1) - eou (-1) .. - β,- i - β,-
x=j-βu=(x+u+Bu)-βi=x +Bux=j-βi-βu=x+βux =x+βu:美xn-1 = xn +βn-iux, = J() - βpu() _..- β,2 - β,-ri=-(ax, +a2Xm-1 + .-+an-ix + a,++βou( + βu(r-)+..+ βu + β,u - βoun ...- β-ii - βui=(-a, -ar-r, -..-a,xn-1 -axn)+β,uy= xi + βuwe can obtain the state space model of the system in vectornotation
(n) +a1y(on-1)+...+an-1ij+any= b,u() +bu(n-1) +.+bn-u+ b,ucompanion matrix010β,00x×200β,001In-)00000βsX3u+-.-100001βr-1XmXn-1专B.an小→ar-lan-2aastateequationXiX2X30+[β. ] u００...0output equationXn-lXn
In-1
The state spacemodel and can be illustrated asoA71...十了妆a1