Re: PID control

Varun Aggarwal wrote:


I'm posting this to the sci.engr.control newsgroup. Please direct any further comments there -- not only will your interesting question be posted for the benefit of all, but you'll get a richer variety of opinions than just mine.
I don't have any information on Z-N tuning on my site.
If your plant were truly 2nd order with no delay then yes, you could increase P to infinite values and you'd never see oscillation. In the real world you don't have to worry about this, because when you push it fast enough anything will show higher order behaviors.
Ignoring that issue for the moment, you can extract plant information using the plant's step response, then doing some curve fitting to get the various parameters you need for Z-N tuning. It's called "open loop" Z-N tuning.
If you're serious about this, check out Astrom-Haggerlund tuning -- Karl Astrom is one of the giants of control theory (at least practical control theory). He was unsatisfied with the tunings he got using Z-N because it often results in an under damped system. He and Haggerlund came up with a similar method that they claim works better than Z-N, and at least gives more conservative results. If I had to use one or the other I'd use Astrom-Haggerlund. Before I used either I'd want to use a system identification/structured design approach.
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Tim Wescott
Wescott Design Services
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I don't have near the training you guys have, but I thought that anything over a first order process showed some "inherent deadtime", and therefore would oscillate. I thought that only the first order process with no deadtime would not oscillate...
curtis
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Curtis wrote:

Even a first-order system has some delay. In a linear system the delay shows up as a certain phase shift vs. frequency relation. A 2nd-order non-minimum phase system approaches the requisite 180 degrees of phase shift asymptotically at the same time that it's gain approaches zero.
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Tim Wescott
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Assuming that a control system is digital (a good assumption these days) with a finite scan rate (usually 4 times/sec or slower) there is an inherent time delay of 1/2 the scan time.
A first order process will have sustained oscillations if the gain is high enough. If the single lag time constant is not much different from the scan time, the gain does not have to be very large.
A second order system with two equal lags and the small scan time will often have sustained oscillations at a moderate gain.
There are certainly loops that will not oscillate at even a high gain. Then the ZN closed loop is not useful. The ZN open loop method may be used if the "pseudo dead time" (the small lag before the point of inflection in the response curve) can be measured. If that cannot be measured, ZN (and other tuning methods) cannot be of much help. A high gain may be used, with the limitation on the gain being the effect of any noise or sepoint adjustments on the valve (not wanting the valve to be always moving back and forth).
John Shaw www.jashaw.com/pid
Tim Wescott wrote:

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John Shaw wrote:

That's a good measure of the average delay is processing time is small (and at 4 scans/sec it will be). The peak delay can be as much as a full scan time, and sometimes that matters.
Jerry
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You should make it clear that it is the dead times and long sample times that are the cause of the sustained oscillations, not the fact the system is a first or second order system.

There are other forms of tuning that work very well without dead time.
Peter Nachtwey
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Peter:

True. It is often the dead time, sample time, and other small lags in the measurement and control system, and final control element (such as variable speed drive) that has the greatest affect on the tuning.

Sometimes the ZN open loop (and related methods) will work even when sustained oscillations cannot be produced for the ZN closed loop. For a simple two lag process with some oscillation that is not sustained at a high gain, the gain can be reduced until 1/4 wave damping is achieved, reset added based on the period of the decaying oscillations, and the gain then further reduced.
Also, for simple one or two lag processes the tuning may be based on criteria other than best control of the controlled variable. For example, not long ago I reduced the gain of a well controlled pressure loop (N2 header supplying gas to the top of a vessel) because the high gain on the controller was causing upsets on the header, affecting other parts of the process.
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Define delay. The last time I look at first order response it was something like 1-exp(-a*t). Even at time t=0+ there is some response. I suppose that even an ideal RC circuit has some dead time if you consider the dead time due to the speed of electric current.
Peter Nachtwey
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Peter Nachtwey wrote:

Classic phase delay. I'm surprised at your example, because it's not restricted to 1st-order systems: any continuous-time, linear system with a finite number of states has some response at time t = 0+; in a strict sense "dead time" only has meaning in sampled-time systems and systems with an infinite number of states (thermal, fluid flow and long strings of coax all come to mind).
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Tim Wescott
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In some times of control this may make dead time unusual. However, in process control there is almost always some amount of dead time, although, fortunately, it is usually small. It comes from the transport delay between where the action happens (mixing, heating, etc.) and the measurement is made (analyzer, temperature, etc. in a pipe). Frequently the dead time is too small to have any serious consequence other than limiting the gain that can be used on an otherwise almost 1st or 2nd order system.
Since control systems are usually digital, the scan time is also a factor if the scan rate is slow. Scan rates should be as fast as possible. It is rare for a scan rate faster than 1 sec. to produce a dead time that has any serious effect, except on some fast loops such as flow loops. Scan rates of 4 seconds or longer (I have seen people use 10 seconds) will often limit the allowable gain.
My suggestion on configuration of a DCS is to buy many controllers, putting only a few loops on each, and run all the loops fast. But I used to work for a company that made DCSs ;-}
Tim Wescott wrote: <snip>

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John Shaw wrote:

I do high-performance motion control stuff, generally with full custom hardware. There are enough other contributors to phase delay that "dead time" per se is just not an issue.

I think the slowest loop I've ever closed was at 10Hz, and that was a "park" mode for a controller that used a few too many processor cycles during an active move for the communications queue to get serviced correctly. Aside from that the lowest one is a 60Hz loop on a temperature controller (with deep integrators -- it closes at around 1 or 1/2 Hz).

That may not be bad advice -- in low production environments (like the one-off mill that you have to keep running) it's often better to solve problems by throwing equipment at them rather than by spending lots of time.
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Tim Wescott
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Tim Wescott wrote:

That is one of the big differences between process control and other types of control, and why it helps to know which world a question is coming from.
John Shaw www.jashaw.com/pid
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says...

I've kept quiet on conversations that involve mathematical calculation of control response. I must admit that I have been somewhat lost. Some of this has to do with the way I came up in the field and some has to do with the changes that have occurred while I have been absent so I am trying to catch up to the point where I at least follow what is being discussed. Most of the discussions to me have little practical usage in my business anyway. So excuse me if my intrusions seem lost, they are.
Tim, you seem to think in electronic and/or digital terms. Part of my problems may be definitions here. Can a definition of "dead time" be given here thinking in physics terms and differentiate that from hysteresis.
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Paul Montgomery
Progressive Gauging Inc.
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A. Paul Montgomery wrote:

If _I'm_ not lost folks are using "dead time" to mean pure delay. Take as an example an art installation that has a machine that's dropping synthetic human excrement onto a conveyor*. A measurement of the weight of the 'product' one foot away from where it is dumped (as it were) will be wholly** independent of the weight of the product 1/2 foot away, so there will be a pure delay in the measurement.
Contrast this with a one-state low-pass filter where (in theory) the output starts to rise _immediately_ as the input is increased.
Hysteresis complicates things because the dead zone gives rise to dead time, but it's a variable dead time that depends on the system state. In process control (I believe) one is usually concerned with a constant 'real' dead time that arises from real honest-to-gosh mass transfer issues like conveyors or flow in pipes***, or one is concerned with effectively real dead times like heat transfer in a material****, or one is trying to model something like hysteresis where the dead time varies and generally messes everything up.
* No sh--! Um, I mean: No kidding! I saw a documentary on this on PBS. They went to some lengths to achieve veracity with just the right mixing and fermentation so they could put ham sandwiches in one end and get 'art' out the other. I was profoundly thankful that it was a European endeavor for two reasons: there would be no way that _I_ would be expected to go to the opening and eat Brie and crackers next to the thing while making witty comments, and I wouldn't have to fess up to my tax dollars funding it.
** Belt stiffness, nothing's perfect, yadda yadda -- you know what I mean.
*** Which, come to think of it, would cause a varying dead time if the flow is varied.
**** Depending on who's theory you use there will be some pure delay, or there will be a minuscule 'immediate' response that only a theoretician would quibble about.
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Tim Wescott
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Tim,
I love your example. I will have to remember it. I am just glad that the "stuff" is synthetic.
Paul,
In the process industries (refining, power, pulp and paper, etc.) dynamics can usually be broken into two types.
Dead Time is just like Tim described it. Our stuff is usually carried in pipes. The stuff is heated, reacted, mixed, etc. at one point and a measurement is made at another point, hopefully, but not always, very close. It takes time for the stuff to move through the pipe from where something happened to where it is measured. For example, in a paper mill, stock (fiber and water) may be diluted by injecting a stream of water into the suction of a pump. At some convenient point on the pipe leaving the pump (perhaps many feet away) a device will measure the consistency (ratio of fiber to total flow) in order to control the flow of water back at the pump suction. The delay of movement from the mixing point to the measurement is dead time. It is hard to control. If the only dynamics (or the major dynamics) is dead time, the control loop will oscillate if the controller gain is too high.
The other kind of dynamics is a single order lag. This is similar to a capacitor and resitor type of delay if you studied electrical engineering, or the temperature of a rock thrown into a pot of boiling water. Processes involving mixing, heating, reacting, etc. in a tank of liquid respond with the lag. It is easy to control.
Both lags and dead time are often referred to as "delay", resulting in frequent confusion when that term is used.
Tim: I know of a waste treatment plant where the "sludge" (dried "stuff") was carried to an incinerator on a conveyor belt using a load cell a few feed away to control the amount of sludge dropped on the belt. I never knew it was art.
John
Tim Wescott wrote:

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John Shaw wrote:
...

Sludge in a sewage plant is a mass of bacteria, alive when first extracted. Some of it is pumped back to the head of the process to serve as a starter culture. At "my" plant, there are two such loops; one to remove mostly carbon from the process stream, the other, mostly nitrogen. Sludge has a mild but distinctive odor when still alive. I've learned to distinguish the two cultures by nose. Like most animals (in this case, animalcules), it stinks when dead.
http://sbrsa.org /
Jerry
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Jerry,
I have had a little experience with waste treatment, but not much. I did learn about what sludge is (dried "stuff" is rather simplistic, but we know where it comes from). When the concept of return activated sludge was explained, it was compared to taking a spoonful of yogurt to start the next batch.
On the wall of the maintenance shop of the plant was a sign directed to us from the outside: "It may be s*** to you, but it's bread and butter to us".
John Shaw www.jashaw.com/pid
Jerry Avins wrote:

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John Shaw wrote:

The oddest part of the experience for me was that I came in on the middle of it, the sound was turned down and I wasn't really paying attention. First it took me a while to realize that a team of people were working on making a machine that produces crap. Then I was thinking "well this is gross, but I suppose there's good science in understanding just what our guts do from one end to the other".
Imagine my surprise when they showed the room filling with the arty crowd, and people were waxing enthusiastic over this new art form. Then I was thinking "what a waste* of time".
* This whole subject is just filled with opportunities for double entendres.
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Tim Wescott
Wescott Design Services
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When I was first involved in the control systems industry many years ago I attended a large water/waste treatment trade show (commonly known as the "S**** Show"). This was before computers and CRTs were common in vendor's booths. Many equipment and process design firms had working models of their processes and equipment, complete with plastic vessels and pipes with water, some of which contained solid material that was removed in the demo. I talked to a model maker who worked on the exhibits and who told me that what I saw was "synthetic crap". At least it was white, I guess to avoid grossing anyone out.
One thing I learned was that people in that industry had a sense of humer in their work. We had an early eight color CRT on our system. Many customers asked if brown was one of the colors! It wasn't.
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John Shaw wrote:
...

Not just people in the industry, but people associated with it. My kids occasionally introduced me as the S*** Commissioner.
Jerry
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