Bill,
My interest in a two level system derives from the argument which I'm
constructing in economics that control theory provides the only method of
analysis that has anything like comprehensive applicablity. Orthodox econmists
begin with assumptions about the theory of valuation, stablity considerations
and what not that allow, or perhaps require that they make mistakes of the type
that generate the Giffen and many other paradoxes and anomolies. If one starts
with the assumption that economics is a kind of biological/ecological process
then one is going to reach very different conclusions that those who begin with
the orthodox assumptions. However, when one begins with a context in which
econmic behavior is treated as a biological process then it seems to me one
ought to continue with it and show how using componates of very modest gain it
is possible to construct the sort behaviors ( zero steady state errors ) which
are commonly observed. And this is what a two level loop does.
For me the fact that when two loops, each with a gain of ten are combined the
result is a gain not of 100 but an infinite gain is a marvel. For you to say
it is not interesting I find puzzling. Sure, you can geneate a zero steady
state error with a single level integral controller. ( Did you know that the
space shuttle's control stick is an integral controller ? ) But, for me this
in no way diminishes the lement of wonder invovled in what combinations of such
simple componates can do. While writting this it occured to me that I can vary
the gain in the upper level control loop and the effective over all gain of the
two level controller will continue to be infinite. Most people I think would
find this surprizing.
Bill
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