Trouble with inverse laplace operation

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Deepayan Bhadra
Deepayan Bhadra 2017-12-18
评论： Star Strider 2017-12-18
I'm trying to run a code like this:
s = tf('s')
sys = exp(-0.1*s);
sysx = pade(sys,3);
x0 = randn(10,1);
L = D-A (A,D,L are constant matrices)
H = 1/(s+L*sysx);
K = H*x0;
ilaplace(K)
Essentially, I want to get a vector x(t) in the end as per the equation xdot = -Lx(t-0.1).
But this returns the error: Undefined function 'ilaplace' for input arguments of type 'tf'.
How do I go about this? Thanks a lot.

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Star Strider
Star Strider 2017-12-18
You go about it with difficulty, because the Control System Toolbox and Symbolic Math Toolbox do not have any way of communicating with each other without your intervention.
Try this:
s = tf('s');
sys = exp(-0.1*s)
sysx = pade(sys,3)
sysxn = sysx.Numerator;
sysxd = sysx.Denominator;
x0 = randn(10,1);
syms A D L s t
L = D-A; % (A,D,L are constant matrices)
Nsysx = poly2sym(sysxn{:}, s);
Dsysx = poly2sym(sysxd{:}, s);
TFsysx = Nsysx / Dsysx;
H = 1/(s+L*TFsysx);
K = H*x0;
kh(t) = ilaplace(K, s, t);
kh(t) = vpa(kh(t), 5)
The result are a (10x1) symbolic function vector in ‘t’, ‘z’, and ‘s4’ that I will leave it to you to untangle.
Personally, I would not involve the Symbolic Math Toolbox at all, and instead evaluate the system with step, impulse, or lsim, and be happy with the result.
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Deepayan Bhadra
Deepayan Bhadra 2017-12-18
I understand. I stuck to the Control System Toolbox and used this instead:
s = tf('s')
sys = exp(-0.1*s);
sysx = pade(sys,3);
x0 = randn(10,1);
D = diag([2 3 4 4 4 4 4 4 3 2]);
A = [0 1 1 0 0 0 0 0 0 0;1 0 1 1 0 0 0 0 0 0;1 1 0 1 1 0 0 0 0 0;0 1 1 0 1 1 0 0 0 0;0 0 1 1 0 1 1 0 0 0;0 0 0 1 1 0 1 1 0 0;0 0 0 0 1 1 0 1 1 0;0 0 0 0 0 1 1 0 1 1;0 0 0 0 0 0 1 1 0 1;0 0 0 0 0 0 0 1 1 0];
L = D-A;
H = 1/(s+L*sysx);
K = H*x0;
[y,t] = impulse(K)
The output y is null (K seems to have blown up) Somehow, this doesn't add up. I'm wondering what went wrong now.
Star Strider
Star Strider 2017-12-18
If you do:
K = H*x0;
Num = K.Numerator
Den = K.Denominator
you will see the problem. I have no suggestions as to how to solve it.

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