Transfer function vs. gains, differentiator, integrator = different, but I don't know why?

Hi,

I'm really confused why the two systems shown in the picture below give different outputs. I thought they were mathematically equivalent but give different outputs.

http://www.newelldesign.co.uk/systems.png

Please could someone show me where I have gone wrong!

Many thanks,

Peter

Answer 1

[Fangjun Jiang]

It must be due to the limitation of calculating du/dt. If you are using all the default setting, you'll notice some warning message in the Command Window regarding step size.

There is no perfect way of calculating the theoretical du/dt in numerical simulation. Doing the du/dt first and then the integration is the problem. If you move the two integrators ahead of the du/dt block (right after the negative feedback summation block), you'll find that the results match perfectly.

[Peter]

Thanks for your answer.

Would there be any way that I could determine a mathematical equation of the first system then?

(I'm trying to match that system to a desired curve, i.e. a desired Y(s) where Y(s)=T(s)R(s) ).

Thanks!

[Fangjun Jiang]

For canonical realizations, see http://en.wikipedia.org/wiki/Realization_(systems)

[Fangjun Jiang]

Or a better reference at http://arri.uta.edu/acs/Lectures/realization.pdf