PID autotuning - not working for heating application
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From: Oliver Betz on 10 Nov 2009 03:49 "Frank W." wrote: >"Tim Wescott" <tim(a)seemywebsite.com> wrote: > >> To hazard a guess, I'd say that one way or another when you command a 6% >> drive to your heater you're getting 1/4 as much heat as when you command a >> 12% drive >95C steady state with 7% heat and 80C steady state with 3.5% heat. Heating Did you consider possible long time constants for "steady state"? Slow warming of enclosures can ruin your model extraction. And what is "heat", IOW how do you control the heater - phase angle, full wave? As Tim wrote, there might be a nonlinear function. And if you control a SCR without mains synchronisation, you might get huge uncertainties for low power values. >from room temperature to 95C takes ~1min, cooling takes hours (cooling from >95C to 80C takes 15min). 1k/min : 70k/min = 1.4%, that's not so far off from 3.5% to assume nonlinear behaviour. And your cooling experiment might be influenced by a hot environment. Oliver -- Oliver Betz, Munich despammed.com might be broken, use Reply-To:
From: Frank W. on 10 Nov 2009 04:40 "Oliver Betz" <obetz(a)despammed.com> wrote: > And what is "heat", IOW how do you control the heater - phase angle, > full wave? Full wave. Phase angle is not permitted here with so much wattage. > you control a SCR without mains synchronisation, you might get huge > uncertainties for low power values. The relay has a ZC circuit. 50hz power and 1s cycle time means 100 zero crossings/cycle, ie. 1% granularity, equals 0.5% average error.
From: Datesfat Chicks on 10 Nov 2009 11:54 "Frank W." <frankw_usenet(a)mailinator.com> wrote in message news:7lggquF3dt584U1(a)mid.dfncis.de... > > Since all PID temperature controllers have Autotune, there must be a > solution for this problem. Any ideas? As you probably know from control theory, the basic theory of a PID controller is that you have a system described by a set of linear differential equations that is inherently unstable or has some performance problems. As a result you strap a PID controller onto it (with said controller also described by its own linear differential equations), and the resulting system (now described by linear differential equations which are a mathematical mix of the underlying system and the PID controller) has better characteristics. Did you notice that there is a word that appears many times in my description above? Want to guess what the word is? That word is "linear". A system with a time delay is not described by linear differential equations. Strapping a PID controller onto it is bad math. One of the more classic examples is a shower or an industrial process that mixes fluids of varying temperature and the sensor is located substantially downstream from the mixing value. This is a pure time delay. My shower at home is like that. I turn the water a little hotter. Nothing happens. I turn it a little more hotter. Nothing happens. Then I turn it a little more hotter. Then the wave of hot liquid hits me and I scream in agony. Over time, I've adapted to my shower. I don't burn myself anymore. I think the control algorithms you want to use for a system like yours fall outside the range of PID. I'm sure there is a body of theory that covers it, but I don't know what that is. I would heat the system full bore for a fixed period of time, then stop and wait to see how the temperature catches up. And work from there. The best control strategy for that system isn't going to be PID. That is a non-linear system. Datesfat
From: Datesfat Chicks on 10 Nov 2009 12:00 "Datesfat Chicks" <datesfat.chicks(a)gmail.com> wrote in message news:qZSdncz-fbqoB2TXnZ2dnUVZ_uGdnZ2d(a)giganews.com... > "Frank W." <frankw_usenet(a)mailinator.com> wrote in message > news:7lggquF3dt584U1(a)mid.dfncis.de... >> >> Since all PID temperature controllers have Autotune, there must be a >> solution for this problem. Any ideas? > > As you probably know from control theory, the basic theory of a PID > controller is that you have a system described by a set of linear > differential equations that is inherently unstable or has some performance > problems. As a result you strap a PID controller onto it (with said > controller also described by its own linear differential equations), and > the resulting system (now described by linear differential equations which > are a mathematical mix of the underlying system and the PID controller) > has better characteristics. > > Did you notice that there is a word that appears many times in my > description above? > > Want to guess what the word is? > > That word is "linear". > > A system with a time delay is not described by linear differential > equations. Strapping a PID controller onto it is bad math. > > One of the more classic examples is a shower or an industrial process that > mixes fluids of varying temperature and the sensor is located > substantially downstream from the mixing value. This is a pure time > delay. My shower at home is like that. I turn the water a little hotter. > Nothing happens. I turn it a little more hotter. Nothing happens. Then > I turn it a little more hotter. Then the wave of hot liquid hits me and I > scream in agony. > > Over time, I've adapted to my shower. I don't burn myself anymore. > > I think the control algorithms you want to use for a system like yours > fall outside the range of PID. I'm sure there is a body of theory that > covers it, but I don't know what that is. > > I would heat the system full bore for a fixed period of time, then stop > and wait to see how the temperature catches up. And work from there. > > The best control strategy for that system isn't going to be PID. That is > a non-linear system. From Wikipedia's entry on PID controllers: http://en.wikipedia.org/wiki/PID_controller <QUOTE> Another problem faced with PID controllers is that they are linear. Thus, performance of PID controllers in non-linear systems (such as HVAC systems) is variable. Often PID controllers are enhanced through methods such as PID gain scheduling or fuzzy logic. Further practical application issues can arise from instrumentation connected to the controller. A high enough sampling rate, measurement precision, and measurement accuracy are required to achieve adequate control performance. </QUOTE> I don't know what the best control strategy is, but it ain't PID. Datesfat
From: Tim Wescott on 10 Nov 2009 12:54
On Tue, 10 Nov 2009 11:54:36 -0500, Datesfat Chicks wrote: > "Frank W." <frankw_usenet(a)mailinator.com> wrote in message > news:7lggquF3dt584U1(a)mid.dfncis.de... >> >> Since all PID temperature controllers have Autotune, there must be a >> solution for this problem. Any ideas? > > As you probably know from control theory, the basic theory of a PID > controller is that you have a system described by a set of linear > differential equations that is inherently unstable or has some > performance problems. As a result you strap a PID controller onto it > (with said controller also described by its own linear differential > equations), and the resulting system (now described by linear > differential equations which are a mathematical mix of the underlying > system and the PID controller) has better characteristics. > > Did you notice that there is a word that appears many times in my > description above? > > Want to guess what the word is? > > That word is "linear". > > A system with a time delay is not described by linear differential > equations. Strapping a PID controller onto it is bad math. > > One of the more classic examples is a shower or an industrial process > that mixes fluids of varying temperature and the sensor is located > substantially downstream from the mixing value. This is a pure time > delay. My shower at home is like that. I turn the water a little > hotter. Nothing happens. I turn it a little more hotter. Nothing > happens. Then I turn it a little more hotter. Then the wave of hot > liquid hits me and I scream in agony. > > Over time, I've adapted to my shower. I don't burn myself anymore. > > I think the control algorithms you want to use for a system like yours > fall outside the range of PID. I'm sure there is a body of theory that > covers it, but I don't know what that is. > > I would heat the system full bore for a fixed period of time, then stop > and wait to see how the temperature catches up. And work from there. > > The best control strategy for that system isn't going to be PID. That > is a non-linear system. I've been resisting forking this over into the control newsgroup: now it's compelling. Systems with delay can be perfectly linear, as well as time invariant -- they just can't be described by ordinary differential equations with a finite number of states. To be linear, a system only needs to satisfy the superposition property. A delay element satisfies superposition just fine. And while a PID controller may not be the theoretically best controller for a system with delay, in many cases it's not a bad choice at all. PID controllers can and will give perfectly satisfactory service with plants that have significant delay. The thousands, if not millions, of PID controllers in mills and factories around the world that are controlling plants whose responses are dominated by delay certainly belie any declaration that the PID controller isn't a good choice to control a plant with delay. None of the above is intended to minimize the difficulty in analyzing and designing a truly optimal controller for a plant with pure delay -- that's an exercise that can make your brain hurt, and fast. And nothing of the above is intended to chase you away from taking plant delays more directly into account if a discrete-state controller such as a PID won't let you eke the performance that you need out of your plant. But in the absence of significant nonlinearities or time varying behavior you can use all the analysis tools that are suitable for linear time invariant systems on a system with delays just fine. You can do good design work, without ever having to explicitly write out the differential equations, much less solving them. So if you don't want to get lost in Mathemagic Land searching for performance that isn't necessary for your product's success, a good ol' PID controller may be exactly the optimal controller -- in terms of adequate performance and reasonable engineering time -- even if it doesn't satisfy any egghead academic measure of "optimal" for the particular plant you're trying to control. -- www.wescottdesign.com |