Smooth step function Simulink

Question

I'm trying to implement a smoothed step function in Simulink.

I tried to put a filter after the step function:

The result is not what I wanted. How can I smooth even around 1 the function? My deal is to not have a dramatic change on behavior.

A possibile idea is to have something like:

Thanks in advance

Answer 1

There are a variety of functions that can give you an "S" curve like you want. Check out the Sigmoid function.

I usually use something like this:

$f(x) = \frac{x}{\sqrt{1+x^2}}$

And it can be adjusted for varying amounts of "steepness".

$f(x) = \frac{x}{\left(1 + |x|^{k}\right)^{1/k}}$

Here is one in the range you specified:

$f(x) = \frac{1}{(1.0 + e^{-10x+5)}}$

Answer 2

So you could use the ramp block, but that only has a turn-on time and a slope; there's no limiting it once it's turned on.

What I prefer to use instead is the repeating sequence block, which lets you define an arbitrary output/time pairs.

If your simulation runs for 10 seconds, and you want a ramp that outputs zero at t=0, one at t=1, and holds that value for the full simulation, then you would give time values of:

[0, 1, 10]

and you would give output values of:

[0, 1, 1]

which would build you that ramp. Then, if you want to smooth the corners on that ramp, you can pass the output through the same filter you used for the step input.