How does state space form include input delay in MATLAB?

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Sol Elec
Sol Elec 2022-4-9
编辑： Sam Chak 2022-4-10
I got this code from 'Time Delays in Linear System' MATLAB help.
A=-2; B=3; C=[1;-1];D=0;
G = ss(A,B,C,D,'InputDelay',1.5)
Now I want to implement this in another model where matrix are-
A=[1 2 3;4 3 2;1 2 3]; C=[0 3 0];
D=[0 -1];
B=[3;5;7];
H = ss(A,B,C,D,'InputDelay',[1.5;2.1;3.2])
But after running the above code, we got an error. "The values of the "a" and "b" properties must be matrices with the same number of rows.".
Please help me in this regard. Thank you.
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Sol Elec
Sol Elec 2022-4-9
@Star Strider After correcting D=[-1]; again get this error-Error using ss (line 345)
The value of the "InputDelay" property must be a vector with as many entries as input channels.
Star Strider
Star Strider 2022-4-10
Exactly.
And ‘B’ and ‘D’ are not the same sizes, an additional error.

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Sam Chak
Sam Chak 2022-4-9
编辑：Sam Chak 2022-4-9
@Sol Elec
If you look at the matrices for the desired state-space system
A =
1 2 3
4 3 2
1 2 3
B =
3
5
7
C =
0 3 0
D =
0 -1
you'll see that the system matrices C(1x3), B(3x1) and D(1x2) are definitely incompatible.
The dimension of D should be (1x1) because the dimension of is .
Another possibility is that if the dimension of D is (1x2), then it implies there are two inputs and the dimension of B must be (3x2).
In general, it should satisfy this:
when you type this out:
[A B; C D]
  2 个评论
Sol Elec
Sol Elec 2022-4-9
编辑：Sol Elec 2022-4-9
@Sam Chak After modifying D=[-1];
I got this error- Error using ss (line 345)
The value of the "InputDelay" property must be a vector with as many entries as input channels.
Sam Chak
Sam Chak 2022-4-10
编辑：Sam Chak 2022-4-10
Hi @Sol Elec
The error stemmed from a set of 3 tau's for a single input, u1:
'InputDelay', [1.5; 2.1; 3.2]
If there is only 1 tau in the input u1, then your state-space model looks like this:
A = [1 2 3; 4 3 2; 1 2 3];
B = [3; 5; 7];
C = [0 3 0];
D = [-1];
sys = ss(A, B, C, D, 'InputDelay', 1.5)
sys =
A =
x1 x2 x3
x1 1 2 3
x2 4 3 2
x3 1 2 3
B =
u1
x1 3
x2 5
x3 7
C =
x1 x2 x3
y1 0 3 0
D =
u1
y1 -1
Input delays (seconds): 1.5
Continuous-time state-space model.
Please mathematically show how your time-delay LTI system looks like.
In transfer function form of the time-delayed SISO system looks like this:
[num, den] = ss2tf(A, B, C, D);
G = tf(num, den, 'InputDelay', 1.5)
G =
-s^3 + 22 s^2 + 18 s + 120
exp(-1.5*s) * ------------------------------------
s^3 - 7 s^2 - 7.47e-15 s + 4.174e-15
Continuous-time transfer function.
If you confirm that there are 3 inputs with time delays, then the sample code is given by:
A = [1 2 3; 4 3 2; 1 2 3];
B = eye(3);
C = [0 3 0];
D = [0 0 0];
sys = ss(A, B, C, D, 'InputDelay', [1.5; 2.1; 3.2])
sys =
A =
x1 x2 x3
x1 1 2 3
x2 4 3 2
x3 1 2 3
B =
u1 u2 u3
x1 1 0 0
x2 0 1 0
x3 0 0 1
C =
x1 x2 x3
y1 0 3 0
D =
u1 u2 u3
y1 0 0 0
Input delays (seconds): 1.5 2.1 3.2
Continuous-time state-space model.
Hope this clears up your confusion.

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