Convert state-space representation (MIMO) to transfer function matrix

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EMAD ALHANI
EMAD ALHANI on 26 Nov 2020
Answered: EMAD ALHANI on 26 Nov 2020
how to convert state-space model (mimo) to transfer function matrix

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Accepted Answer

Walter Roberson
Walter Roberson on 26 Nov 2020
Ran in:
https://www.mathworks.com/help/matlab/ref/ss2tf.html
But if you have an existing ss system created with https://www.mathworks.com/help/control/ref/ss.html then use tf()
A = [-1.5,-2;1,0];
B = [0.5;0];
C = [0,1];
D = 0;
sys = ss(A,B,C,D)
sys = A = x1 x2 x1 -1.5 -2 x2 1 0 B = u1 x1 0.5 x2 0 C = x1 x2 y1 0 1 D = u1 y1 0 Continuous-time state-space model.
sys_as_tf = tf(sys)
sys_as_tf = 0.5 --------------- s^2 + 1.5 s + 2 Continuous-time transfer function.

More Answers (2)

EMAD ALHANI
EMAD ALHANI on 26 Nov 2020
it is giving me wrong result I would like to have only four transfer function .
>> A = [ 0 0 -0.1 0.1;
0 0 -4.6 -4.5;-0.0008 0.0008 0 0;0 -4.0 0 5.6];
B = [ 14.8 32.2;
35 -24;-0.75 -0.41;0 0];
C = [ 1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1];
D = 0;
>> sys = ss(A,B,C,D )
sys =
A =
x1 x2 x3 x4
x1 0 0 -0.1 0.1
x2 0 0 -4.6 -4.5
x3 -0.0008 0.0008 0 0
x4 0 -4 0 5.6
B =
u1 u2
x1 14.8 32.2
x2 35 -24
x3 -0.75 -0.41
x4 0 0
C =
x1 x2 x3 x4
y1 1 0 0 0
y2 0 1 0 0
y3 0 0 1 0
y4 0 0 0 1
D =
u1 u2
y1 0 0
y2 0 0
y3 0 0
y4 0 0
Continuous-time state-space model.
>> sys_as_tf = tf(sys)
sys_as_tf =
From input 1 to output...
14.8 s^3 - 82.81 s^2 - 280.8 s - 3.019
1: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
35 s^3 - 192.6 s^2 - 19.27 s - 0.2893
2: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
-0.75 s^3 + 4.216 s^2 + 13.41 s + 0.2243
3: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
-140 s^2 - 13.8 s - 0.2067
4: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
From input 2 to output...
32.2 s^3 - 180.3 s^2 - 570.1 s - 2.167
1: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
-24 s^3 + 136.3 s^2 - 10.44 s - 0.6743
2: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
-0.41 s^3 + 2.251 s^2 + 7.632 s + 0.456
3: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
96 s^2 - 7.544 s - 0.4817
4: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
Continuous-time transfer function.
EMAD ALHANI
EMAD ALHANI on 26 Nov 2020
thank you.
>> A = [ 0 0 -0.1 0.1;
0 0 -4.6 -4.5;-0.0008 0.0008 0 0;0 -4.0 0 5.6];
B = [ 14.8 32.2;
35 -24;-0.75 -0.41;0 0];
C = [ 1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1];
D = 0;
>> sys = ss(A,B,C,D )
sys =
A =
x1 x2 x3 x4
x1 0 0 -0.1 0.1
x2 0 0 -4.6 -4.5
x3 -0.0008 0.0008 0 0
x4 0 -4 0 5.6
B =
u1 u2
x1 14.8 32.2
x2 35 -24
x3 -0.75 -0.41
x4 0 0
C =
x1 x2 x3 x4
y1 1 0 0 0
y2 0 1 0 0
y3 0 0 1 0
y4 0 0 0 1
D =
u1 u2
y1 0 0
y2 0 0
y3 0 0
y4 0 0
Continuous-time state-space model.
>> sys_as_tf = tf(sys)
sys_as_tf =
From input 1 to output...
14.8 s^3 - 82.81 s^2 - 280.8 s - 3.019
1: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
35 s^3 - 192.6 s^2 - 19.27 s - 0.2893
2: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
-0.75 s^3 + 4.216 s^2 + 13.41 s + 0.2243
3: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
-140 s^2 - 13.8 s - 0.2067
4: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
From input 2 to output...
32.2 s^3 - 180.3 s^2 - 570.1 s - 2.167
1: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
-24 s^3 + 136.3 s^2 - 10.44 s - 0.6743
2: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
-0.41 s^3 + 2.251 s^2 + 7.632 s + 0.456
3: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
96 s^2 - 7.544 s - 0.4817
4: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
Continuous-time transfer function.
>> C = [ 0 0 0 0;0 0 0 0;0 0 0 0;0 0 0 1];
>> sys = ss(A,B,C,D)
sys =
A =
x1 x2 x3 x4
x1 0 0 -0.1 0.1
x2 0 0 -4.6 -4.5
x3 -0.0008 0.0008 0 0
x4 0 -4 0 5.6
B =
u1 u2
x1 14.8 32.2
x2 35 -24
x3 -0.75 -0.41
x4 0 0
C =
x1 x2 x3 x4
y1 0 0 0 0
y2 0 0 0 0
y3 0 0 0 0
y4 0 0 0 1
D =
u1 u2
y1 0 0
y2 0 0
y3 0 0
y4 0 0
Continuous-time state-space model.
>> sys_as_tf = tf(sys)
sys_as_tf =
From input 1 to output...
1: 0
2: 0
3: 0
-140 s^2 - 13.8 s - 0.2067
4: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
From input 2 to output...
1: 0
2: 0
3: 0
96 s^2 - 7.544 s - 0.4817
4: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
Continuous-time transfer function.
>> C = [ 0 0 0 0;0 1 0 0;0 0 0 0;0 0 0 1];
>> sys = ss(A,B,C,D)
sys =
A =
x1 x2 x3 x4
x1 0 0 -0.1 0.1
x2 0 0 -4.6 -4.5
x3 -0.0008 0.0008 0 0
x4 0 -4 0 5.6
B =
u1 u2
x1 14.8 32.2
x2 35 -24
x3 -0.75 -0.41
x4 0 0
C =
x1 x2 x3 x4
y1 0 0 0 0
y2 0 1 0 0
y3 0 0 0 0
y4 0 0 0 1
D =
u1 u2
y1 0 0
y2 0 0
y3 0 0
y4 0 0
Continuous-time state-space model.
>> sys_as_tf = tf(sys)
sys_as_tf =
From input 1 to output...
1: 0
35 s^3 - 192.5 s^2 - 19.27 s - 0.2893
2: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
3: 0
-140 s^2 - 13.8 s - 0.2067
4: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
From input 2 to output...
1: 0
-24 s^3 + 136.3 s^2 - 10.44 s - 0.6743
2: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912
3: 0
96 s^2 - 7.544 s - 0.4817
4: ---------------------------------------------
s^4 - 5.6 s^3 - 18 s^2 - 0.02016 s + 0.002912

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