On Wednesday, July 15, 2015 at 3:15:21 PM UTC-4, John Larkin wrote:
> On Wed, 15 Jul 2015 11:30:15 -0700 (PDT), George Herold
> <gherold@teachspin.com> wrote:
>
> >On Wednesday, July 15, 2015 at 11:56:59 AM UTC-4, John Larkin wrote:
> >> On Wed, 15 Jul 2015 08:33:49 -0700 (PDT), George Herold
> >> <gherold@teachspin.com> wrote:
> >>
> >> >On Tuesday, July 14, 2015 at 4:29:26 PM UTC-4, John Larkin wrote:
> >> >> Imagine a mass that we want to heat with some closed-loop controller.
> >> >> It's C2 below. Voltage represents temperature. Thermal systems are
> >> >> diffusive, which we represent as a bunch of RC lags. Assume the
> >> >> voltage at C4 is the temperature sensor.
> >> >>
> >> >> If I were to design a PID controller, I'd have to really think about
> >> >> it, or fiddle some, to keep it stable. But if I do a dumb on/off
> >> >> thermostat, it seems to always work. I can tweak the hysteresis and
> >> >> vary the p-p temperature excursions and the switching frequency, but
> >> >> it's always stable. Or maybe it's always unstable. But it works.
> >> >>
> >> >> As Vh gets smaller, the oscillation frequency converges to some
> >> >> limiting value, which is I guess the ultimate performance of a
> >> >> thermostat for this physics. To get any less temperature excursion, I
> >> >> guess I'd have to do a real PID loop. Curious.
> >> >>
> >> >> This may have something to do with the fact that there is no thermal
> >> >> equivalent to an inductor.
> >> >>
> >> >> Version 4
> >> >> SHEET 1 880 680
> >> >> WIRE 0 0 -288 0
> >> >> WIRE 528 0 80 0
> >> >> WIRE -288 160 -288 0
> >> >> WIRE -224 160 -288 160
> >> >> WIRE -96 160 -144 160
> >> >> WIRE -16 160 -96 160
> >> >> WIRE 96 160 64 160
> >> >> WIRE 192 160 96 160
> >> >> WIRE 304 160 272 160
> >> >> WIRE 416 160 304 160
> >> >> WIRE 528 160 528 0
> >> >> WIRE 528 160 480 160
> >> >> WIRE -288 224 -288 160
> >> >> WIRE -96 224 -96 160
> >> >> WIRE 96 224 96 160
> >> >> WIRE 304 224 304 160
> >> >> WIRE -288 336 -288 288
> >> >> WIRE -96 336 -96 288
> >> >> WIRE 96 336 96 288
> >> >> WIRE 304 336 304 288
> >> >> FLAG -288 336 0
> >> >> FLAG -96 336 0
> >> >> FLAG 96 336 0
> >> >> FLAG 304 336 0
> >> >> SYMBOL Digital\\schmtinv 416 96 R0
> >> >> WINDOW 0 2 -10 Left 2
> >> >> WINDOW 3 -30 23 Left 2
> >> >> SYMATTR InstName A1
> >> >> SYMATTR Value Vh=0.002
> >> >> SYMBOL cap 80 224 R0
> >> >> WINDOW 0 67 13 Left 2
> >> >> WINDOW 3 64 44 Left 2
> >> >> SYMATTR InstName C1
> >> >> SYMATTR Value 1m
> >> >> SYMBOL cap -112 224 R0
> >> >> WINDOW 0 63 18 Left 2
> >> >> WINDOW 3 64 53 Left 2
> >> >> SYMATTR InstName C2
> >> >> SYMATTR Value 5m
> >> >> SYMBOL cap -304 224 R0
> >> >> WINDOW 0 60 22 Left 2
> >> >> WINDOW 3 66 53 Left 2
> >> >> SYMATTR InstName C3
> >> >> SYMATTR Value 1m
> >> >> SYMBOL res -128 144 R90
> >> >> WINDOW 0 0 56 VBottom 2
> >> >> WINDOW 3 32 56 VTop 2
> >> >> SYMATTR InstName R1
> >> >> SYMATTR Value 1K
> >> >> SYMBOL res 80 144 R90
> >> >> WINDOW 0 0 56 VBottom 2
> >> >> WINDOW 3 32 56 VTop 2
> >> >> SYMATTR InstName R2
> >> >> SYMATTR Value 1K
> >> >> SYMBOL res 96 -16 R90
> >> >> WINDOW 0 0 56 VBottom 2
> >> >> WINDOW 3 32 56 VTop 2
> >> >> SYMATTR InstName R3
> >> >> SYMATTR Value 1K
> >> >> SYMBOL cap 288 224 R0
> >> >> WINDOW 0 67 13 Left 2
> >> >> WINDOW 3 64 44 Left 2
> >> >> SYMATTR InstName C4
> >> >> SYMATTR Value 1m
> >> >> SYMBOL res 288 144 R90
> >> >> WINDOW 0 0 56 VBottom 2
> >> >> WINDOW 3 32 56 VTop 2
> >> >> SYMATTR InstName R4
> >> >> SYMATTR Value 1K
> >> >> TEXT -208 -56 Left 2 !.tran 50 uic
> >> >> TEXT 192 -88 Left 2 ;THERMOSTAT
> >> >> TEXT 192 -48 Left 2 ;JL July 14, 2015
> >> >> TEXT -72 80 Left 2 ;===== thermal lags =====
> >> >>
> >> >>
> >> >>
> >> >>
> >> >> --
> >> >>
> >> >> John Larkin Highland Technology, Inc
> >> >> picosecond timing precision measurement
> >> >>
> >> >> jlarkin att highlandtechnology dott com
> >> >> http://www.highlandtechnology.com
> >> >
> >> >Hmm it seems to me you have a gain knob in there too. Whatever the power is
> >> >coming out when the thermostat is on. (1V in this case... I don't know which spice line changes the amplitude.)
> >>
> >> It's all normalized to 1 volt, which I could arbitrarily call 100
> >> degrees C or something. The gain is 1/Vh (well, 0.5/Vh the way LT
> >> Spice defines hysteresis) so if I set Vh =0 the schmitt becomes an
> >> infinite gain, which actually doesn't change things much.
> >
> >Calling the hysteresis the gain is a bit funny, though I understand what you mean.
> >In theory smaller hysteresis leads to a smaller excursion of the temperature
> >from the set point. At some point I don't think smaller hysteresis will do anything
> >you'll be stuck with what ever time delay is in the loop.
> >(I set you R3 to 1 and C3 to 1p, and lower hysteresis does nothing.)
>
> Yup, low hysteresis corresponds to high gain, ultimately a pure
> comparator with no hysteresis. Thst seems to work, with the p-p temp
> excursions depending on the thermal geometry.
Before I read the other posts, I want to say I was thinking
about this on the ride home. The bang-bang control, comes at
the oscillation of the P-only control.. but from the other side.
(The other side of stability space...)
Which is cool. As long as you don't care about
the time constant, and some oscillation,
then you've got a useful system...
I still say you've got a knob that is the max power of your
bang-bang. (and too much power will give oscillations.)
I've been dreaming about building my own thermal test bed.
I'll now have to include bang-bang.
George H.
>
>
>
> >
> >>
> >>
> >> >
> >> >With 3 RC's and enough gain you should be able to make it oscillate.
> >>
> >> It seems to always oscillate! That's the point of a thermostat. But
> >> the oscillation seems benign.
> >
> >Sure.. It's a bang-bang oscillator vs. one with too much gain and phase shift.
> >I guess I was thinking about the oscillations you get
> >with a P-only controller when you crank the gain up too high.
>
> The bang-bang always oscillates, so you don't worry about it! But
> unlike a PID, the temperature excursion magnitude is limited, whereas
> a PID might bang the process rail-to-rail if it's tuned wrong.
>
> >
> >>
> >> >(I always had to have at least three RC's to simulate thermal loops
> >> >w/ spice...otherwise no oscillations.)
> >>
> >> With hysteresis set nonzero, a single RC oscillates. That's the
> >> classic triangle wave generator.
> >>
> >> I need to build two temperature controllers, on opposite sides of a
> >> round PC board about 1" in diameter, around the electro-optical
> >> gadgets. The thermostat approach is appealing... very simple and the
> >> amplifier won't fry like a linear controller would. Similar to your
> >> recent situation, where PWM would be nice but has side effects, the
> >> side effect in my case being parts count and loop stability. A
> >> bang-bang loop, maybe with zero hysteresis, would sure be easy, but
> >> the temperature excursions would be dominated by the thermal
> >> properties (masses, conductivities) of the "process", which is hard to
> >> model. The controllers on either side of the board will interact too,
> >> more fun.
> >
> >I'm sorry to say that besides the thermostat in my house, I don't know much
> >about them for thermal control. If your set point was higher, so that the
> >heater had to be on for a longer fraction of the time it seems like there
> >might be larger temperature excursions. So picking the power level so
> >that it's on about 1/2 the time might be optimal.
> >(But again I'm totally guessing)
> >
> >>
> >> My customer insists on two controllers, but maybe I can talk him into
> >> one, with lots of thermal vias side to side.
> >
> >Why two? (at only 1" apart?) Are they worried about thermal gradients?
> >It's usually worth while to spend some time thinking about how the heat
> >will flow and putting the heaters and sensors in the "right" places.
>
> No rational reason. I plan to talk him out of it.
>
>
> --
>
> John Larkin Highland Technology, Inc
> picosecond timing precision measurement
>
> jlarkin att highlandtechnology dott com
> http://www.highlandtechnology.com