The thermostat feedback system modeled by the Excel
workspace FEEDLAB.XLS (see page ![[Ref]](i/cross_ref.gif){kind=small}
) isn't
really practical to work by hand. The amount of calculation required
to simulate one day is such that you'll almost certainly give up
before gaining the intuitive understanding of feedback that comes
from changing parameters and seeing the computer immediately simulate
the consequences.
Nonetheless, here is the mathematical basis of the model. From these equations you can implement the simulation in another spreadsheet or as a standalone program. The parameters that control the model are identified by their labels on the FEEDLAB control panel.
Given:
| A | = | Range |
| D | = | Delay |
| G | = | Goal |
| L | = | Insulation |
| N | = | Noise |
| P | = | Power |
| R | = | Random |
Calculate the following variables for each time step i:
| Oi | = | Outside temperature |
| Ei | = | Error (deviation from goal) |
| Ci | = | Correction applied by feedback |
| Ti | = | Inside temperature |
with the following initial conditions:
| O0 | = | 70 |
| T0 | = | 70 |
For each 10 minute time interval 
calculate the inside
temperature Ti as follows. 
is a pseudorandom number ranging
from -1 to 1, with a new value generated at each occurrence of
.
