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Trouble with inverse laplace operation

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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.

Accepted Answer

Star Strider
Star Strider on 18 Dec 2017
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.
  4 Comments
Deepayan Bhadra
Deepayan Bhadra on 18 Dec 2017
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 on 18 Dec 2017
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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