Always appreciate control theory articles. But this one needs some editing. Take ice cream example;that is not zero dynamics that's still pretty much convolution. Now zero dynamics examples must have no effect on the system. Thus it is not a zero if you continuously chugging ice cream. It is indeed a step input that you equilibriate at a constant ice cream input and some happiness comes out constantly. The moment you stop happiness goes away. That is not related to zero.
Also a pure zero action is supposed to cancel the input completely. Not at first but completely (restricting the discussion to linear systems).
Zeros effects are not so trivial to untangle as the article suggests unfortunately but fun read anyways and very nice flow.
> Now zero dynamics examples must have no effect on the system. Thus it is not a zero if you continuously chugging ice cream
Thank you for your input! I wonder if you might have misread that example. In this system there's indeed a RHP0 in the transfer function from ice cream consumption happiness. A continuously increasing rate of ice cream intake results in exactly no effect on the output.
Your happiness shouldn't change if ice cream input has a zero. Also it should be independent from the amount of ice cream. In other words if we have an ODE say
ddot y + 2 dot y + y = dot u - 2 u
As long as my input is pure C exp(2t) independent of C I see no happiness and it's not working on my mood. In your example input u effect is cancelled by decay of y cancelling the guilt. Making it not a zero.
In my personal case eating celery is a zero i see absolute no point eating it :) no harm and no benefit just pointless chewing
Also a pure zero action is supposed to cancel the input completely. Not at first but completely (restricting the discussion to linear systems).
Zeros effects are not so trivial to untangle as the article suggests unfortunately but fun read anyways and very nice flow.