pade-laplace: stuck with pade approximation!

hi..im try to use pade-laplace method in matlab to model multi exponential,however im stuck at part with pade approximation. here my code,

for t=1:100
syms A1 A2 L1 L2

y(t)=A1*exp(-L1*t)+A2*exp(-L2*t);

end

lap=laplace(y)

i dont know how to use pade approximation with this function for the next process. can someone guide me? thanks.

[Walter Roberson]

What are "L1" and "L2", and do they relate to "l1" and "l2" ?

[Amir Hamzah UTeM]

sorry,they related..i am forgot that change it into capital when i re-type here.

[Amir Hamzah UTeM]

my problem is right now,i dont know how to use pade approximation for the next procedure. when i do it manually like pade=L(s-1)/L(s) matlab take too long to produce the last equation.

for t=1:100

syms A1 A2 L1 L2

y(t)=A1*exp(-L1*(t-1))+A2*exp(-L2*(t-1)); %y(t-1)

y1(t)=A1*exp(-L1*t)+A2*exp(-L2*t); %y(t)

end

lap=laplace(y); % get L(s-1)

lap1=laplace(y1); % get L(s)

pad=lap/lap1; % take too long to process L(s-1)/L(s

Answer 1

[Paulo Silva]

Why do you define the symbolic variables in every loop? there's no need for it, just define the symbolic variables once before the for loop.

Now for the time it takes you probably know the reason, the symbolic operations and mostly the laplace is causing the slowness.

Try the pade function from the Control System Toolbox

This version of your code should be faster

syms A1 A2 L1 L2
t=1:100;
y(t)=A1*exp(-L1*(t-1))+A2*exp(-L2*(t-1)); %y(t-1) 
y1(t)=A1*exp(-L1*t)+A2*exp(-L2*t); %y(t) 
lap=laplace(y); % get L(s-1) 
lap1=laplace(y1); % get L(s) 
pad=lap./lap1; % take too long to process L(s-1)/L(s)

[Amir Hamzah UTeM]

thank for replied,

how can i use pade function from the control system toolbox?

when i try type,

test=pade(lap,2)

it gives following error: ??? Error using ==> pade at 46

Function 'lt' is not implemented for MuPAD symbolic objects.

for the last result,i want an equation from rational expression obtained by the division of two polynomials of lap and lap1

[Amir Hamzah UTeM]

it is possible to get?

[Paulo Silva]

Looking at your code more carefully I think that you are making some errors, first the pade approximation is for time delays on the frequency domain in the form exp(-s*T), your expression is in the time domain and when converted to the frequency domain gives exponential values but they are constant not in the form exp(-s*T) so they are not delays.

[Amir Hamzah UTeM]

so how can i get in form exp(-s*T)? what should i do? i really don't have any idea.

[Paulo Silva]

here's a clue

s=sym('s')

il=ilaplace(exp(-s*0.1))

laplace(il)

[Paulo Silva]

http://www.mathworks.com/help/toolbox/control/ug/bstzkhr.html