Electronic and thermal feedback loops

Say you have for simplicity two TEC modules, something like:

each mounted on one side to a large aluminum plane of heatsink, large enough to be considered more-or-less infinite in extent from the perspective of the module. On the other you have a block cooler with cooling fluid piped through the two coolers in series, and a temperature sensor to sense the cooling block's temperature, and the cooling blocks are connected in series for fluid flow.

You want to feedback-control the two TEC modules via the temp sensors on the heatsink blocks to maximize the "exhaust" block temperature wrt the "input" block temperature for a given flow rate (I'm assuming that's the proper situation for maximal cooling of the working fluid input to output but please correct if not.)

Question I have is whether it's possible for the thermal coupling between them via the heatsink they're connected to to destabilize the individual feedback-control loops. my guess is yes it's possible it all depends on the particulars of the mounting geometry, the thermal resistances involved, and the speed of the individual electronic loops.

Is there a canonical method to analyze closed-loop systems that have both electrical and thermal feedback paths?

Reply to
bitrex
Loading thread data ...

You'd presumably be controlling the two Pelter junctions separately.

The effectiveness of a Peltier junction - in terms of watts of heat transfe rred in or out of the object whose temperature is being controlled per amp through the Peltier junction - depends on the temperature difference across the Peltier junction - my 1996 paper describes a set-up where we could hav e a seven to one difference in watts per amp.

This means that you ought to monitor the temperature of the heat-sink block as well as the temperatures of the objects whose temperature was being con trolled.

Thermal gradients across the heat-sink could mess that up a bit, but the id ea is to make the aluminium plate thick enough that such gradients would be negligibly small.

--
Bill Sloman, Sydney
Reply to
bill.sloman

Ya, in this situation (cooling high-power processor which needs to be in very compact enclosure to fit in a tight space) I'm going to try to use the aluminum enclosure itself to sink the blocks to, so the surface area is large but there isn't much thickness going on.

It may be possible to get away with passive liquid cooling only I hope so but I'd like to learn more about active heat sinking in the meantime. I thought using a string of water blocks where each block's temperature is individually regulated in inner loops to maintain the total loop input to exhaust temperature as close to optimal as possible for a given flow rate was a cool idea though probably not a novel one.

Reply to
bitrex

re

s

on

e

he

l
.

nsferred in or out of the object whose temperature is being controlled per amp through the Peltier junction - depends on the temperature difference ac ross the Peltier junction - my 1996 paper describes a set-up where we could have a seven to one difference in watts per amp.

lock as well as the temperatures of the objects whose temperature was being controlled.

e idea is to make the aluminium plate thick enough that such gradients woul d be negligibly small.

TEC modules might not help. They do shift heat, but the current through the m generates resistive heating - which you also have to get rid of, so you a re spending money on the TEC modules for a decidedly marginal improvement i n temperature at the processor, at the cost of having to dissipate even mor e heat to the outside world.

It might be worth looking at heat pipes - they aren't as messy as pumped li quid cooling, and they do shift heat from the warm end (at the processor) t o the heat-sink end with remarkable effectiveness.

The thermostat set-up described in my 1996 paper started off water-cooled, but the water circulation kept on getting blocked by air-bubbles (after abo ut six months of operation) and the production guy went over to a heat-pipe assembly.

He had to set up a test-rig to make sure that the guys who put the assembly together had pumped out all the air in the system before they sealed it of f - it they haven't the heat transfer at low temperature differences is rot ten - and started off sending back a quarter of the assemblies he got, but that improved rapidly.

--
Bill Sloman, Sydney
Reply to
bill.sloman

Define maximal cooling - do you want the lowest possible output temperature but with very limited capacity to move heat from it or the greatest possible flux of heat taken out of the medium being cooled.

The former arises in cooled CCD cameras and the latter in heat pumps.

Although it might be theoretically possible the time constants for the thermal feedbacks are sufficiently slow that it probably won't be an issue in practice. If you are stacking the TECs then it might make sense to have a thin sheet of aluminium to even out the temperature.

Last time I was doing something like this I had a small one capable of working very hot and another chunkier one doing the grunt work.

Routh feedback stability criterion if you can draw the network.

formatting link

It may well be overkill in this case.

--
Regards, 
Martin Brown
Reply to
Martin Brown

Is that the TEC and 'infinite' heatsink? Does it have forced air cooling? (that will help)

Your first TEC thing? I think the biggest mistake with first TEC's is to make the TEC too big, or the hot side heat sink too small... (same problem.)

You need to put in some numbers, heat in, heat out, some guess on temperatures. Your TEC forms the biggest thermal short between the hot side and cold side.

Sounds complicated, once you've got the right size TEC and heat sink, the thermal loop is not that hard. You are mostly dealing with the time delay between TEC and temp sensor.

First order is too just do an RC type thing. JL had a one page 'cheat sheet' with various numbers, I'll see if I can dig it up when I get to work. (or JL may share the link again.)

Reading your other post it sounds like you want a forced air heat exchanger for your liquid loop. Putting a TEC in the thermal loop means more heat to get rid of at the hot side.

TEC's are fun though

George H.

Reply to
George Herold

e

My 1996 paper has a formula for plugging TEC parameters (from the manufactu rers data sheet) and thermal resistance numbers. It's not wildly precise bu t it's good enough for design work

n

e

The catch is that you are controlling the current through the TEC and the a mount of heat transferred - in watts per amp - can vary quite a bit as you go from heating to cooling. You really wna to measure the temperatures on b oth sides of the TEC - not only the object whose temperature you are trying to control, but also the temperature of the heatsink on the xhaust side of the TEC.

But not cheap.

--
Bill Sloman, Sydney
Reply to
bill.sloman

On Wednesday, September 26, 2018 at 11:02:02 AM UTC-4, snipped-for-privacy@ieee.org wr ote:

te:

ure

ks

turers data sheet) and thermal resistance numbers. It's not wildly precise but it's good enough for design work

on

he

the

e

amount of heat transferred - in watts per amp - can vary quite a bit as yo u go from heating to cooling. You really wna to measure the temperatures on both sides of the TEC - not only the object whose temperature you are tryi ng to control, but also the temperature of the heatsink on the xhaust side of the TEC. I never had to do that... except maybe when I'm first building/ tuning it. Feedback hides a lot of sins.

You do need to have a big enough heat sink... or it can fry itself. I guess I'm pretty conservative in design... and check the edges.

I was testing this ~50 watt heater, and using an Al bread board. (1/2" x 2' x 4') to dump the heat into... After a while the whole thing was up at 40C (or something) and I had to add a zip lock bag filled with ice to keep it cool.

Anyway I couldn't find JL's thermal cheat sheet.

George H.

ll

s.

Reply to
George Herold

The idea of using several small blocks is to make design more tractable for situations where you have a "difficult" form-factor where a conservatively-designed large single sink + cooler might have to be hard-to-acquire custom size. That would be the best if you have space to do it, surely.

A series of small blocks gives some flexibility in doing trial-and-error design where one doesn't have access to some fancy thermal-modeling software. Okay I have three in series is the cooling not enough? add another. Too much? Remove one. etc.

Active cooling the individual modules might be a win or it might cause more problems than it solves. The TECs wouldn't have to run full-blast all the time, the idea is that say you realize you need four heatsink blocks to cool effectively but you can only fit three, some extra active-cooling on the individual blocks might be enough that you can reduce the space requirement just enough without having to run them so hard that you're losing on i^2r losses in the coolers themselves.

My intuition is that if you just used one small block with a TEC running full-power, you would lose, but maybe not if the cooling load were distributed among several. Would have to do the math and see if you can "win" that way.

Reply to
bitrex

Or the cold plate too large. Thermal diffusion is what sets the maximum loop bandwidth, so if you make the cold plate smaller, it helps a great deal. PID is no use once diffusion delays start to be important, because the phase shift increases without bound with frequency, so adding a derivative contribution makes things worse rather than better.

Yup. And the slew rate depends on the Q-dot - DeltaT * (thermal conductance). It gets super slow near the temperature limits.

Yup. For smallish heatsinks used with diode lasers and IR photodiodes and that sort of stuff, you can fit a model by eyeball with good success. The model I nearly always use is a time delay followed by an integrator.

  1. Put a known current step into the TEC and watch the temperature output on a scope. The resulting step response will do nothing for awhile, then curve up a little, then rise linearly for a bit, and finally curve over like an RC lowpass.
  2. Extract the delay and integrator slope: draw the horizontal baseline and the tangent to the inflection point of the rising edge. The inflection point is often about 1/8 of the way between the baseline and the final temperature.
  3. Measure the time delay tau between the current step and the intersection of the tangent and baseline.
  4. Measure the slope K of the tangent in volts per second per amp.
  5. The plant model is then

Hplant(f) = exp(-j 2 pi f tau) * K mu /(j 2 pi f),

where mu is the transconductance of your current driver. Use a proportional + integral loop, and apply the usual frequency compensation procedure to achieve a phase margin of 60 degrees or so. Quicker things such as PLLs can often manage with a 45 degree margin, but the resulting ringing makes the settling time slower.

Yes. If the heatsink gets too hot, the TEC current can easily get high enough that the I2R losses make Qdot negative, so that the sign of the loop gain changes and the TEC melts (or at least sits at some gross high temperature where the current driver runs out of stooch).

You always have to have an over-temperature cutout on a TEC system to prevent this.

Multi-stage TECs are worse--it's not unknown to have one melt if you apply power too abruptly. This is because the only thermal spreader between stages is the thin alumina end plates, and it takes time for the lateral temperature gradient to develop sufficiently to cool the middle of the lower stages. (The optimal design needs about a 3x area increase from one stage to the next lower.)

Yup.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
 Click to see the full signature
Reply to
Phil Hobbs

e

ture

cks

s

facturers data sheet) and thermal resistance numbers. It's not wildly preci se but it's good enough for design work

s on

the

the

ime

the amount of heat transferred - in watts per amp - can vary quite a bit as you go from heating to cooling. You really wna to measure the temperatures on both sides of the TEC - not only the object whose temperature you are t rying to control, but also the temperature of the heatsink on the xhaust si de of the TEC.

it.

h

Hmm, yeah do some math. Certainly if you design too small of a heat sink such that it can't get rid of the maximum power without over heating, then it will operate better at some reduced current. But I would call that a bad design and not a TEC failing. (TEC's are crappy coolers, like only 10% of the theoretical efficiency... ideal heat engines.)

Send me an email gherold-atsign-teachspin.com and I can send you a copy of Phil H's thermal chapter from his book. It might be on his website too. It's got a few pages on TEC's that you might find useful. (I'll also forward the II-IV Marlow newsletter that just arrived in my inbox.)

Here, ftp://ftp.wiley.com/public/sci_tech_med/electro-optical/thermal.pdf

George H.

e

all

ps.

Reply to
George Herold

Or you design a passively cooled system with a small TEC and huge heat sink, test it by letting it run maxed out... and then dial back the maximum current if it's needed... Well that's my student proof approach.

I may have already shared this, but when looking for a small TEC, I realized why the smallest ones you could buy with a vapour seal around the edges are about 1/2" square. For smaller sizes the vapour seal becomes a significant part of the shorting thermal resistance. Really small TEC's need to live in vacuum, or at least dry environs.

George H.

Reply to
George Herold

Good info here, thank you! I think it's definitely best to start with a simple system to think of how to analyze a more complicated system like the one I've proposed before even thinking about TEC cooling and feedback control loops, etc.

If analyzing the most simple system I can think of that's reminiscent of the basis of the problem as I've stated it, isn't tractable, or doesn't give results that jive with reality then there's little point in continuing the exercise. I'm not intellectually curious enough to invest in supercomputer time to figure this one out, either. ;)

I think just seeing if it's possible to analyze a fluid-cooling consisting of one heat source and two heat sinks both coupled to the same flat plate subject to Newtonian cooling to ambient, quantitatively, might be a good first start. I'm not an expert in thermal transport or nothing so this is my best-effort at a electrical/resistance model of the loop:

The temperature increase of the chip to be cooled above ambient is modeled by a voltage source at bottom (there should be a Vambinet source in series with it, probably.) The working fluid has a thermal admittance, Y_l.

There's a thermal resistance at the interface of the IC to the block, and a thermal resistance from the cooling block to the liquid. There are thermal resistances from the liquid to the heatsink plate-mounted blocks, and a thermal resistance from those two blocks to the plate itself. Then there's a thermal resistance through the plate between the two heatsinks, and thermal resistance to ambient with the ambient temperature represented by a voltage source V_amb.

The internal thermal resistances from the working fluid to the various blocks are drawn as variable resistances to represent fluid flow velocity, as the flow rate increases those resistances go down and vice versa.

The difficult ???? numbers are the spreading resistances from the cooling blocks to the Newtonian plate and the mutual resistance between which will depend heavily on geometry and stuff. But I'm pretty sure there are papers in the literature that mathy-analyze thermals of volumetric heat sources mounted to one side of Newtonian plates.

So that's my first stab at it, any corrections would be appreciated.

Reply to
bitrex

For Newtonian "plates" which are not actually just large plates but are say one side of a metal box with some LxWxH dimension, if it's a relatively large box compared to the size of the cooling blocks the fringe effects may be able to be compensated for by the infamous "fudge factor"-method.

Reply to
bitrex

ure

ks

's is

aximum

on

he

the

he time

odes

y an

r

n

things

g

ll

s.

high

h

er

e

crease

So you can make a very simple thermal model. In terms of electrical things.

Temperature (K) => Voltage (V) Heat flux (J/s, Watt) => Current (coul./sec, Amp) Heat capacity (J/K) => Capacitance (Coul./V) Thermal resistance (K*W) => resistance (V/amp.)

Heat sources become current sources, fixed temperatures become voltage sources.

You can then make an RC model of your gizmo, which sometimes helps.

George H. I'm not sure what newtonian plates are, nor the fudge factor method.

Reply to
George Herold

ge

h

ature

ocks

EC's is

maximum

at

,

r.

rs on

the

s the

,

the time

diodes

by an

for

ne

nd

ion

r things

ing

he

all

ops.

et high

e

igh

ader

the

le

increase

e

f

t
,

e

e

s.

oops................^(K/W)

Reply to
George Herold

Real-world PIDs usually don't use the derivative term at all. And if they do, it's just a soft phase bump, not a real derivative. In addition to the diffusion issue, there's noise to worry about.

The first PID that I designed, sophomore year at Tulane, was the throttle control for a 32,000 horsepower steam turbine. It did use a bit of D.

I never did take a controls system course. Oops.

You can use Spice to model thermal systems, either with simple RCs, or maybe a few to approximate diffusion.

The following equivalences are accurate to about 10%...

ELECTRICAL THERMAL

1 amp 1 watt 1 farad 1 gram aluminum 1 volt 1 degree C 1 second 1 second 1 ohm 1 K/watt

I suspect the Spice lossy transmission line model would be pretty good to model thermal diffusion.

--
John Larkin         Highland Technology, Inc 
picosecond timing   precision measurement  
 Click to see the full signature
Reply to
John Larkin

A "Newtonian" heat sink in this context is one where heat diffusion to ambient air from the plate surface is modeled by Newton's law of cooling, i.e. transfer to the external medium is primarily conductive i.e. conductive >> convective >> radiative transport.

Reply to
bitrex

I think it's more often used in things like servo drivers and valve actuators to compensate for backlash/stiction of the mechanism.

I'm unsure whether my "model" such as it is models the fluid transport to the cold plates correctly. It's kind of like a heat-wire, yeah? With a thermal admittance?

Reply to
bitrex

That is to say as liquid flow rate increases does the thermal admittance of the fluid itself increase, or does the thermal resistance of the fluid -> water block interface decrease?

Reply to
bitrex

ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.