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Lab 9: Studying State Space FA06_BET_
Lab Task 1
Find transfer function and plot their response:
1. A = B = C = D =
2. A = B = C = D =
3. X = X + r
y = X
syms s _% T = (C((sI-A)^-1))B + D_*
% first: A1 = [-1 1;65 0];
B1 = [1 1 ;1 0];
C1 = [1 0;0 1]; D1 = [0 0;0 0];
I1 = eye(2);
T1 = (C1(inv((sI1)-A1)))*B1 + D [num1 den1] = ss2tf(A1,B1,C1,D1,1)
step(A1,B1,C1,D1)
% second:
A2 = [0 1 0 0;0 0 1 0; 0 0 0 1;-3 -3 -3 -2];
Matlab Code:
Lab 9: Studying State Space FA06_BET_
B2 = [0; 0; 0; 2];
C2 = [1 0 0 0];
D2 = 0;
I2 = eye(4);
T2 = (C2(inv((sI2)-A2)))*B2 + D
[num2 den2] = ss2tf(A2,B2,C2,D2,1)
figure, step(num2, den2) figure, pzmap(num2, den2)
%third: A3 = [-3 1 0 4 2;-3 5 -5 2 -1;0 1 -1 2 8;-7 6 -3 -4 0;-6 0 4 -3 1];
B3 = [2; 7; 6; 5; 4];
C3 = [1 -2 -9 7 6]; D3 = 0;
I3 = eye(5);
T3 = (C3(inv((sI3)-A3)))*B3 + D
[num3 den3] = ss2tf(A3,B3,C3,D3,1)
figure, step(num3, den3)
figure, pzmap(num3, den3)
T1 =
[ s/(s^2+s-65)+1/(s^2+s-65), s/(s^2+s-65)]
[ 65/(s^2+s-65)+(s+1)/(s^2+s-65), 65/(s^2+s-65)]
num1 =
den1 =
Results:
Lab 9: Studying State Space FA06_BET_
Simulink Block Diagram and Results:
Lab 9: Studying State Space FA06_BET_
y =
For Second part:
y =
syms s
% T = (C((sI-A)^-1))*B + D
% first:
A1 = [0 1 0 0 0 0; 0 -3 1 1 0 1; 0 0 0 1 0 0; 1 1 -1 -2 0 1;0 0 0 0 0 1;0 1 0 1 0 -3 ];
B1 = [0; 0; 0; 1; 0; 0];
C1 = [0 0 0 0 1 0];
D1 = 0
I1 = eye(6);
T1 = (C1(inv((sI1)-A1)))*B1 + D
[num1 den1] = ss2tf(A1,B1,C1,D1,1)
figure, step(num1, den1)
Matlab Codes:
Lab 9: Studying State Space FA06_BET_
figure, pzmap(num1, den1)
% second:
A2 = [0 1 0 0 0 0;-1 -2 0 1 1 1;0 0 0 1 0 0; 0 1 -1 -2 1 1; 0 0 0 0 0 1;1/3 1/3 1/3 1/3 -2/3 -2/3];
B2 = [0; 0; 0; 0; 0; 1/3];
C2 = [0 0 0 0 1 0];
D2 = 0;
I2 = eye(6);
T2 = (C2(inv((sI2)-A2)))*B2 + D
[num2 den2] = ss2tf(A2,B2,C2,D2,1)
figure, step(num2, den2)
figure, pzmap(num2, den2)
Results:
