Dividing by dt
Posted: Wed Oct 27, 1999 10:42 pm
While I too abhor the general idea of dividing by dt in a rate equation, I
have found it hard to avoid when modeling such systems as a simple home
heating system. One needs a way to model whether the furnace is off or on.
I use a stock that was either 0 (off) or 1 (on). To turn the furnace on
when it is off and the room temp goes below the setpoint minus the deadzone,
the inflow becomes 1/dt. To turn off the furnace when it is on and the room
temp goes above the setpoint plus deadzone, the outflow becomes 1/dt.
One can get the same effect using pulses of weight one, but this is really
the same thing (1/dt).
Is there a better way to do this that does not involve dividing by dt to
assure that model behavior is not impacted by changes in dt? Ive pondered
this a number of times, but to no avail. I still have not figured out how
to eliminate the use of 1/dt to fill or dump the "furnace on" stock.
Wayne Wakeland
Adjunct Professor of Systems Science
Portland State University
From: "Wayne Wakeland" <wwakeland@uswest.net>
have found it hard to avoid when modeling such systems as a simple home
heating system. One needs a way to model whether the furnace is off or on.
I use a stock that was either 0 (off) or 1 (on). To turn the furnace on
when it is off and the room temp goes below the setpoint minus the deadzone,
the inflow becomes 1/dt. To turn off the furnace when it is on and the room
temp goes above the setpoint plus deadzone, the outflow becomes 1/dt.
One can get the same effect using pulses of weight one, but this is really
the same thing (1/dt).
Is there a better way to do this that does not involve dividing by dt to
assure that model behavior is not impacted by changes in dt? Ive pondered
this a number of times, but to no avail. I still have not figured out how
to eliminate the use of 1/dt to fill or dump the "furnace on" stock.
Wayne Wakeland
Adjunct Professor of Systems Science
Portland State University
From: "Wayne Wakeland" <wwakeland@uswest.net>