Watch Mr. Wizard -- Carefully

[From Rick Marken (960125.1900)]

Remi cote (250196.1926)

I made the simulation you suggested (Bill P.) and there is something wrong.

Are you sure? In order to learn from Mr. Wizard -- er..Powers -- you
have to do the lab exercises carefully, thinking all the time about
the _meaning_ of what you are doing. You say:

If I increase the cooling at 0.9 per dt, the asymptote is heading to 11.

Compare to 20, it is 55%. Not 85%!

But you got this result by changing the size of the _disturbance_, NOT
the output gain. That is, in your equation for the heat input:

0.1*(20-0) - cooling

you changed the value of "cooling" from 0.3 to 0.9. But the control system
still has the same ability to deal with the disturbance by adding heat.
This ability is reflected in the _output gain_ of the system, which in
this case is the multiplier 0.1 (units of output per units of error). With
a 0.9 disturbance and the same output gain (0.1), when the temperature
input to the thermostat reaches 11 degrees, the heat output is 0.1* (20 - 11)
= 0.9 units which, as Bill noted in his post, is exactly enough to balance
out the disturbance (now -.9).

So you really just repeated your previous simulation in a much more
severe environment (you moved the thermostat from St. Louis to

The exercise Bill suggested was the following:

For now, just try increasing the output gain. Raise it to 0.2, 0.3, and
so on, and see what happens to the asymptotic temperature.

In your equation above, leave cooling at 0.3 and change the
multiplier (0.1) to 0.2, 0.5, 1.0, 1.5, etc. and see what happens
to the input variable (temperature).

As Bill said:

As you continue increasing the output gain G from 0.1, you will
eventually run into a problem. After you have seen it, tell me about it
and I will tell you what we do next to prevent the problem.

I would also suggest that you leave the output gain constant at, say,
0.8 and see what happens as you change the reference temperature (which
is set to 20 in your simulation).

Happy experimenting.