MaplePrimes - answers and comments on Question, DEQ from Transfer Function

not possible

Joe Riel — Sat, 21 Jan 2012 22:37:04 Z

This isn't generally possible; the zeros of the numerator are the problem. You can use two equations, d(x) = u, y = p(x,u), where d(x) is a differential expression in x(t) and p is an algebraic equation in x(t) and u(t). Consider, for example, the simpler G = Y/U = s/(s+1). You can represent that as

diff(x(t),t) + x(t) = u(t)
y(t) = -x(t) + u(t)

I thought I had an easy solution for that.

ThU — Sun, 22 Jan 2012 01:18:42 Z

I thought I had an easy solution for that. For instance, I typed

Y(s)/X(s)=1/(s+1)

Then context menu->cross multiply->context menu->inverse laplace transform. Unfortunately, terms like

invlaplace(s*Y(s),s,t) are not transformed to d/dt invlaplace(Y(s),s,t)

For the latter, one could define an alias and the deq would look fine.

addtable

ThU — Sun, 22 Jan 2012 02:53:52 Z

thanks, this looks good to me, addtable is useful.

addtable

Joe Riel — Sun, 22 Jan 2012 01:50:54 Z

1/(s+1) is expressible as a single diff-equation because there are no zeros (in the numerator). That isn't the case for s/(s+1).

You can use ?addtable to define a laplace transform:

with(inttrans):

addtable(invlaplace, Y(s), y(t), s, t):
addtable(invlaplace, U(s), u(t), s, t):

eq := (s^2+s+1)*Y(s) = U(s):
y(0) := 0:
D(y)(0) := 0:

invlaplace(eq,s,t);
                     / 2      \
                     |d       |   /d      \
                     |--- y(t)| + |-- y(t)| + y(t) = u(t)
                     |  2     |   \dt     /
                     \dt      /