Cost of precise comfort - who knows ?

An incredibly important and simple question came up the other day and I have absolutely no idea of the answer.

http://en.wikipedia.org/wiki/Some_Like_It_Hot

I would really welcome any insight or references in the comments, and will happily link and give credit for any interesting articles in a follow up. So please do contribute if you can - sharing ideas we all win.

Here were the given facts :

Determining if a room is too hot or too cold for comfort is subjective - it follows that any target will be disputed.

To achieve a "comfortable building", an optimum is assumed when fewest people express discomfort. 
We know it is impossible to please all the people any of the time. So this is pragmatic - and democratic.

Around 7% of people are uncomfortably hot or cold as an optimum.

It gets worse if conditions affect people of different age, sex, build, current activity level or health !

• Any warmer and more people complain they are now too hot than stop complaining they were too cold.
• Similarly any cooler and more people complain they are now too cold than cease from complaining they were too warm.

In short - "Some like it hot" - when others want to chill.


The question:

"What is the cost of over-shooting target in pursuing temperature goals?"

My first thoughts are that we can assume some parameters for our problem.

If we know the volume of air that must be heated or cooled to achieve "target", we know how much energy is needed (lets ignore pressure and humidity to keep this simple).

We can assume an ideal situation where air is perfectly mixed and no significant stratification arises.

We can assume a minimum fresh air make up rate requirement, and a percentage enthalpy recovery by heat exchange.

We can calculate perfect response costs (assuming 100% efficient plant).

BUT when we factor in an exact target (as is very commonly and absurdly done), and if we allow both chilling and heating primary plant to operate (though not simultaneously in an air handler), we see that theoretical cost tends to infinity (and is only limited by plant capacity), if we have anything less than perfect control.

Note this infinity arises from the implicit assumption of zero error tolerance.  To correct instantly requires infinite power, and is thus not attainable.  It must therefore pay to tolerate inaccuracy, because humans cannot perceive infinitesimal discomfort.

But how much does it pay back - and what is the shape of the sweet spot.

I accept this depends on thermal lag and all sorts of assumptions about plant configuration and control loops - but is there NO research o the subject.

I would imagine that at least a rule of thumb could be developed and promoted as global policy (e.g. a minimum legal target dead-band of say 2.5 Celsius or 4.5 Fahrenheit.)

- Any thoughts, comments, questions or reference material, ideas or pragmatic approaches happily received.