How to properly plot a response of a transfer function in Mathematica?

Question

I'm trying to display the output response of a transfer function in Mathematica with and without a compensator. The problem is very strange: while the transfer function compensate is showing well, the other is not.

The plot seems incomplete and no matter what PlotRange I set, the graph always stays incomplete at the same point.

Here is a screenshot:

Anybody have an idea of what is wrong? I'm pretty sure the math itself is okay, because I get the second transfer function from the first. But when I want to compare the two responses graph, the first always stays incomplete.

Answer 1

o1 isn't always real - it has a small imaginary component. For example o1 /. t -> 4 gives 0.995493 - 5.18448*10^-7 I. What you could do is Chop the output response:

o1 = Chop @ OutputResponse[tfm, UnitStep[t], t];

This gives you a nice smooth graph.

But on the other hand if you look at the unchopped version o1 /. t-> 8 you get 831840. + 332820. I. Not a small imaginary component at all - so maybe chopping it wasn't a good idea.

You could also try an exact equation by replacing 43.35 with 4335/100. This gives real results, but goes haywire when t > 5.

Unfortunately I know nothing about transfer functions to say which might be right.

Answer 2

another solution is to just specify a time interval in OutputResponse .. represented in a "One-liner" below..

Plot[OutputResponse[#, 1, {t, 10}] & 
/@ (TransferFunctionModel[#, s] & 
/@ {43.5/( s^3 + 10 s^2 + 24 s + 43.35), 43.5/( s^3 + 10 s^2 + 71.45 s + 142.35)}),
{t, 0, 10},  Evaluated -> True]

Answer 3

you can add the Abs[o2] Abs[o1] and try it works.

p2 = Plot[Abs[o2], {t, 0, 10}, PlotRange -> {0, 1.25}]
p1 = Plot[Abs[o1], {t, 0, 10}, PlotRange -> {0, 1.25}]