Configurable MU for CommonMath

Summary

The $\mu$ parameter, which represents the sharpness of the piecewise approximants, needs to be configurable per-component/caller instead of a static value.

Rationale

There is an edge case I had not considered before:

A smoothed band pass window in state space, $f(x; w, \mu)=\sigma(x;\mu)-\sigma(x-w;\mu)$ , has a width $w$. When the width shrinks to scales below $w<\dfrac{5}{\mu}$, the smooth approximation begin to fail as a piecewise indicator.

While validating individual governor models I observed the effects of this when the limits $[V^{\min}, V^{\max}]$ become very tight $w=V^{\max}-V^{\min}$.

Description

In the motivating example above, I need to be able to set $\mu$ and pass it as an argument to functions such as antiwindup or inside in CommonMath. A global $\mu$ is not preferred because one model could have subsystems with varying constraints on $\mu$!

Additional information

I temporary solution could be to raise $\mu$ to a larger value, but since that impacts the whole system it hurts performance especially on large cases.