Find steady state of constant heat application

[MTEXX]

Hey all. I sure hope somebody can assist with this!

I am a hobby beer brewer and am writing my own heat control algorithms. Part of the process involves heating water to a desired temperature setpoint. I'm using an electric water heater element (5500W) inside the water vessel (~5-10 gal). I can pulse the heater element for a desired duty cycle (0 to 100%). The vessel is not well insulated as to allow quicker recovery from a temperature overshoot. Precise temperature control within about 1F is my goal.

Let's say that I apply 20% duty cycle. Over a VERY LONG time (hours) , the temperature stabilizes at say 127F. The curve is similar to a cooling curve but it rises toward an "asymptote" which is the steady state. I believe it is logarithmic.

My question is this- how can I predict the steady state with a few minutes of data instead of waiting hours upon hours?

Thanks in advance !
-Micah

 

[LCKurtz]

Hey all. I sure hope somebody can assist with this!

I am a hobby beer brewer and am writing my own heat control algorithms. Part of the process involves heating water to a desired temperature setpoint. I'm using an electric water heater element (5500W) inside the water vessel (~5-10 gal). I can pulse the heater element for a desired duty cycle (0 to 100%). The vessel is not well insulated as to allow quicker recovery from a temperature overshoot. Precise temperature control within about 1F is my goal.

Let's say that I apply 20% duty cycle. Over a VERY LONG time (hours) , the temperature stabilizes at say 127F. The curve is similar to a cooling curve but it rises toward an "asymptote" which is the steady state. I believe it is logarithmic.

My question is this- how can I predict the steady state with a few minutes of data instead of waiting hours upon hours?

Thanks in advance !
-Micah

A logarithmic curve will not approach an asymptote. It just grows so slowly it might give that appearance. Perhaps you could model it with a logistic curve with appropriate scaling, the right side of which seems to fit your description. You might take a look at:
http://en.wikipedia.org/wiki/Logistic_function