将下列模型用传递函数,零极点及传递函数,及状态方程形成表示001001100002X=[0101-1]X+[1]U011100001001Y=[00011]Xx=[00100;10000;0101-1;01110;00100]x+[12101]uy=[00011

Question

将下列模型用传递函数,零极点及传递函数,及状态方程形成表示
0 0 1 0 0 1
1 0 0 0 0 2
X=[ 0 1 0 1 -1]X+[1]U
0 1 1 1 0 0
0 0 1 0 0 1
Y=[ 0 0 0 1 1 ]X
x=[0 0 1 0 0 ;1 0 0 0 0 ;0 1 0 1-1; 0 1 1 1 0;0 0 1 0 0 ]x+[1 2 1 0 1 ]u
y=[0 0 0 1 1 ]x

Answer 1

A=[0 0 1 0 0 ;1 0 0 0 0 ;0 1 0 1 -1; 0 1 1 1 0;0 0 1 0 0 ];
B=[1 2 1 0 1 ]';
C=[0 0 0 1 1 ];
sys=ss(A,B',C,0)
a =
x1 x2 x3 x4 x5
x1 0 0 1 0 0
x2 1 0 0 0 0
x3 0 1 0 1 -1
x4 0 1 1 1 0
x5 0 0 1 0 0


b =
u1
x1 1
x2 2
x3 1
x4 0
x5 1


c =
x1 x2 x3 x4 x5
y1 0 0 0 1 1


d =
u1
y1 0

Continuous-time model.

tf(sys)

Transfer function:
s^4 + 3 s^3 + 2 s^2 + 4 s - 7.498e-016
--------------------------------------------------------------
s^5 - s^4 - 2.602e-015 s^3 - 2 s^2 + 1.044e-015 s + 4.757e-016
zpk(sys)

Zero/pole/gain:
s (s+2.796) (s^2 + 0.2037s + 1.43)
---------------------------------------------------------------
(s-1.696) (s-1.542e-008) (s+1.542e-008) (s^2 + 0.6956s + 1.18)