How do I plot a system with gain, first-order lag and time delay?

Question

I want to plot the output response of a system with gain, first-order lag and time delay, where the transfer function is

tf = 2 Exp[-0.1 s]/(.1 + s)

To plot a time delay, we need to use an approximation, as Mathematica's TransferFunctionModel is restricted to rational transfer functions. We can use a Padé approximation

pa = PadeApproximant[tf, {s, 0, 5}]

and then determine the output response and plot it using

model = TransferFunctionModel[pa, s]
output = OutputResponse[model, UnitStep[t], t];
Plot[output, {t, 0, 10}, PlotRange -> All]

My output response looks very weird:

Can somebody please explain to me what I'm doing wrong?

Answer 1

If you add Chop to your output:

output = OutputResponse[model, UnitStep[t], t] // Chop
Plot[output, {t, 0, 10}, PlotRange -> All]

you will get

which is quite different. Chop removes small (in your case imaginary) roundoff errors. At this stage though I would try and make sure the result actually makes sense. These roundoff errors are slightly suspicious. One test you can do is ask for higher precision in the computation, via say

pa = PadeApproximant[tf, {s, 0, 5}]//N[#,20]&

which in this context seems to produce the same solution.