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Mental
Modeling
Experiencing the Flow
One way to understand a dynamic system is to
get into it and to experience it fully, like the scientist above is
demonstrating. Another way is to think about it and to model it as a structure
of levels, rates and policies - and to simulate its behavior.
Later, we can go to program the system structure in a simulation language (Excel
works fine.) and simulate the system behavior, one moment of
now at a time. For now, we take the first step and build a
mental model.
The model building process
is an excellent way to define and refine assumptions and theories
about how a system operates.
The Flow Rate Changes the Level
One way to understand a dynamic system is to model it as a structure
of levels, rates and policies.
A System Structure Diagram
shows how the elements interact.
In this model, your milk glass filling policy
determines the milk flow rate. The level informs this policy.
One policy (the proportional method) is to keep
the flow rate proportional to the distance remaining to the target.
Another policy (slam-shut method) is to
start the flow "at the max" and then to "slam the
valve shut" when
the level approaches the target.
This policy may easily over-shoot,
particularly if you have some reaction time in the policy.
Another policy (small pulses method) is
to stop the flow when the level nears the target and then to zero-in
on the target by adding small pulses of milk, allowing time to think
between pulses.
Your "optimal" policy, depends upon your
objective function (bliss function). For example, your view of
optimal may depend on your relative valuation of (1) the speed of
filling the glass and (2) the accuracy of filling.
In general, a policy that fills the
glass quickly with high accuracy is optimal.
The model building process
is an excellent way to define and refine assumptions and theories
about how a system operates.
In the next section,
we build an excel model of the proportional method.
the excel model
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Clips:
http://lh3.ggpht.com/_9_Am7NXTPzc/SgbxyC54NGI/
AAAAAAAADnw/jUZnayAPJwM/milk1%5B6%5D.jpg
http://heureuxpourtoujours.files.wordpress.com/
2008/08/milk_pouring1.jpg |
