Re: water analogy- a simple calculator

By the time you know enough about the detailed thermal behaviour to specify the RC transmission line parameters, you already know the answer to the problem!

Cheers

Phil Hobbs

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Is a 'crazy' phase shift the same as a long time constant?

I keep wanting to make things small and quick for thermal control, and others want large and slow.

George H.

It's a series of coupled time constants, with the phase shift getting bigger and bigger, faster and faster, as the frequency goes up. Diffusion.

As you increase the gain, things get unstable fast. A typical nasty system will have a heater with some mass, attached to a piece of metal through some thermal resistance, then transport delay (complex diffusive time constants) then a temerature sensor. You wind up with an absurdly slow P+I controller to keep it stable. Large-area, low mass heaters, like the Minco foil things, help some.

John

Regaaarding "I keep wanting to make things small and quick for thermal control, and others want large and slow", i had to tear apart an Omicron thermal controller and alter it due to this penchance for "long and slow". I understand the reason: make it slow enough and there will be a "guarantee" that the "average" temperature (whatever that is supposed to mean) will be "at" the set-point. Never mind the wild swings above and below. Got mine so short it is under a second cycle time. Beats the heck out of me what the tem difference is from lowest to highest on that cycle (controlled volume is a breadnmaker, added small fan to stir that thicker stuff: air). Any guesses?

Hmm, If you give it a step of temperature rise on one end of the system, the temperature rise on the other can't be approximately described by a single RC? I've only limited experinece, but I've always found one piece limiting things.

I think I have that link. I really like heaters in TO-220 pack. I figure you'll always be able to get them. I mount 'em right next to the pass transistor on the heater block. ('cousre that limits the maximum temperature.)

My last project used a pnp 'transdiode' in a TO-220 as a temp sensor.

George H.

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Ahh, I'm not sure I understood. Your temperature is oscillating at 1 Hz? If that is the case, you need to reduce the gain, or perhaps increase the time constant of the control loop (if it has one).

George H.

In most thermal systems, a single RC is not a usable model. The thermal conductors and masses are not lumped, and in most cases are the same things! The model is a string or mesh of cascaded RCs, each acting like a lowpass filter and all loading one another. It's like a lossy transmission with bumps and lumps of varying impedances.

If you take a cold system, with a heater and a sensor, and apply power to the heater, the resulting sensed temperature step is much droolier (that's a technical term) than an RC shape. How much droolier depends on the geometry. A flat plate or a cubic block with a low-mass heater will be fairly RC-like; a long rod or plate with a heater on one end and the sensor on the other will be very drooley.

A TO-220 mosfet is a great heater. Dirt cheap, and if you slap it across a DC supply heat will be linear on drain current. A resistive heater, unless you PWM it, is going to heat according to the square of the applied voltage or current, and that makes the control situation even worse.

National makes the LM35 in TO-220! I kind of like the little platinum RTDs.

This uses a thermistor on the PC board and a Minco foil heater.

ftp://jjlarkin.lmi.net/Brick1.JPG

ftp://jjlarkin.lmi.net/Brick2.JPG

This particular geometry is very 1st-order-RC-ish, so it's easy to close the loop.

John

The other nice thing about doing that is that you can use linear proportional control without guilt (and without PWM crap). Just mount the driver transistor on the same heatsink as the heater. Then next time, leave out the heater and just use the transistor....

Cheers

Phil Hobbs

No...i purposely decreased the time constant in the controller,so now its cycle is under one second instead of 30+ seconds. I cannot measure the temperature change assuming there is one (nano kelvins?). I do know for a fact that the duty cycle changes as one changes the temperature setting. Also the duty cycle is different at differnt settings (once stabilized). I am voting for no temp change; the heater is in the breadmaker wall, which has some (significant in this case, i think) thermal mass to filter the pulse heating, and then the stirred air inside as the final filter. Methinks the thermal TC of the breadmaker wall is much larger than

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Hi Robert I,m still not quite getting it. What's the duty cycle? Is this just a 'bang-bang' heater? No proprotional control...heater either at max or off? If you increase the gain in a proportional control loop the thing will start to oscillate and eventually hit the power rails and turn into a 'bang-bang' heater.

George H.

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The last project I measured was a permenant magnetic. On the ouside is TEC and heatsink. A copper rod conducted the heat into the pole piece (`3/4" diam. and maybe 3" long.) The RC time was dang close to the models I made. (Almost all of it due to the copper rod.)

The wooden box in the magnet. (It looks like a wooden toaster!)

I used both the resistor and npn as heater. I was a bit worried at stressing the transistor at the highest temperatures and this way the transistor's share of the heat input reduces at high temperatures. I've got this in our Rb discharge lamp. Typical operating temperature is 120C, but I've run it up at 135- 140 C for several days without anything failing. You get about double the light intensity at the higher temperautres.

Do mosfets or bipolar's work better at high temperature?

Interesting, (I need to buy myself a good camera)

George H.

Yup. If you heat a large thermal mass through a low-mass rod, that's close to a single-pole RC. The electrical model would be a series of short time constant RCs (the rod), or a lossy transmission line, dumping into a big capacitor. In that case, the small Cs don't matter much and the rod looks mostly resistive.

If you didn't have much mass at the end of the rod, the Cs in the rod would dominate, and the response would be like a very lossy transmission line, very messy.

John

The unmodified controller is a bang-bang, and that did not change (naturally) when i changed the time constant. Cycle time, ie time between each turn-on, is about 0.5 sec; duty cycle changes according to temp setting. Settings approaching room temp result in a duty cycle near zero (ie: off most or all the time), and settings in the 200C region result in a duty cycle where it is on a fair amount longer than not (and "fair amount" is a scientifically precise value); maybe 3/4.

In the 170-185C region, leakages get dicey for both - so for linear operation, one must use rather low power dissipation in the device so as not to aggravate that. Above 185C you are in trouble in River City..

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Hmm, Most of the heat capacity was in the copper rod. (at least that was how I modeled it.) There was a donut disk of magnetic meterial at the end and this was only loosely coupled to the iron yoke with a bit of stainless steel 'air gap'.

If there are heat losses along the rod this doesn't change the time constant. (does it?) Well as long as those losses are small.

George H.

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Well that can be understood from energy conservation. There is a heat leak rate to the outside. The amount of heat that leaks out is proportional to the temperature difference. To keep the temperature constant you have to add the same amount of heat into the system. Heat =3D voltage x current x time

George H.

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Simulate it! In Spice, you can use a chain of may RCs, or the lossy transmission line model. Compare the step response to an RC.

It's like equalizing the step response of a lossy transmission line, like the vertical delay line in an oscilloscope. Such equalization networks tend to be complex. I have a similar situation with eddy currents in NMR gradients. The effects are diffusive, so need many RCs to de-drool them.

Of course, if the step response looks, eyeball-wise, sort of like an RC, which a thermal response may well, it's not hard to compensate a slow control loop around it. The higher-order phase shifts will getcha when to try to crank up the gain to get faster response.

You can use the "g" (shunt loss) part of the transmission-line model to simulate heat loss along the rod.

John

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Yup, I'll have to try simulating it.

By cranking up the gain do you mean adding some derivative term in the feedback loop? It's only recently that I got a 'handle' on the D of PID's. I built a PD thing to try and improve response time.

George H.

Where is the inductance analogy? An inquisitive mind wants to know.

Cheers, John