PID tuning

[Roy Matson]

In response to Peter Nachtwey

Once you understand the math you will never see PID tuning the same.

Some of us are blessed with mathmatical minds, I doubt I will ever understand PID that way (I don't even want to), but I can visualize the different terms and what effect they have on loop tuning. I still maintain ZN is a good place to start.
Roy

 

[parky]

I once worked with an expert on PID control he taught me the following for in-line steam injectors.
This has worked well for me in the past.
Put I&D to 0, Start with P 50% (this will depend on how the "P" is scaled), reduce P until it becomes unstable (I find 10% seems ok), increase until stable then introduce I to remove overshoot. D is rarely used but depends on the process.
I have found that a lot of PLC's that have PID don't work quite the same.

 

[kamenges]

Originally posted by parky[/b[:

I have found that a lot of PLC's that have PID don't work quite the same.

There are several reasons for this. But in parky's example it has to do with definition. parky's example uses proportional bnd instead of proportional gain. In a system where the PV and CV are scaled to 0-100% proportional band defines the range of PV over which the CV changes from 0-100%. So if you have a proportional band of 10% the CV will change from 0-100% as the PV changes from 0-10%. So lower numbers for proportional band make the system more responsive. Also, as you may already notice, proportional band = 1/K_p if everything is scaled to percent.

But more to Peter's point, there is a mathematical reason that parky's method works in his case. understanding that reason will allow you to work with a greater variety of systems. At the very least it will tend to make you appreciate what then limits of a system are.

Modern digital controls have made us pretty lazy. When James Watt came up with the steam engine governor he couldn't just tweek a couple of numbers if he was wrong or 'turn up the gain until it oscillates'. If he was off by an order of magnitude he was cutting new metal. That was a serious undertaking back then. So he had to calculate what the system would do before he even drew up his first part. Just becaue we can easily change our way out of mistakes these days doesn't mean we shouldn't try to understand what a system is doing.

Keith

 

[parky]

True & I must admit my first setup was flying blind.
& yes modern electronics does make us lazy, take a eurotherm, put it in auto tune & hey presto.
The guy I worked with started his life tuning the old electro mechanical PID controllers That must have been an art, a tweak with a screwdiver a few mechanical knobs & maybe even a piece of cigarette packet jammed in here & there.

 

[Roy Matson]

The guy I worked with started his life tuning the old electro mechanical PID controllers That must have been an art, a tweak with a screwdiver a few mechanical knobs & maybe even a piece of cigarette packet jammed in here & there.

Yes, thats the way I learned also. Apparently nowdays you have to be a mathmatical genius to tune a loop. I'd like to see one of the math wizards try an old Foxboro 43AP on for size.
Roy

 

[Mickey]

Yes, thats the way I learned also. Apparently nowdays you have to be a mathmatical genius to tune a loop. I'd like to see one of the math wizards try an old Foxboro 43AP on for size.
Roy

WOW Roy , that brings back memory's. Those were very good controllers. Used a lot of those in the oil and gas fields.
As long as they had a good clean air/gas supply.
Of course I still prefer Fisher "Wizard 1"

 

[TurpoUrpo]

http://en.wikibooks.org/wiki/Control_Systems/Poles_and_Zeros
http://virtual.cvut.cz/dynlabmodules/ihtml/dynlabmodules/syscontrol/node18.html

If not then I will try tomorrow.

Wow, thank you, have to use more than one day for those links

 

[Peter Nachtwey]

You must have done some searching to find that

Wow, thank you, have to use more than one day for those links

If you like those then you should look at this
http://www.engin.umich.edu/group/ctm/PID/PID.html
This link shows how the PID gains are used to place the poles of the characteristic equation and therefore achieve the desired response.
This thread goes into how to apply the PID gains
http://www.plctalk.net/qanda/showthread.php?t=36407&highlight=Advanced+Control

 

[Roy Matson]

WOW Roy , that brings back memory's.
Of course I still prefer Fisher "Wizard 1"

Yes they were very good for high vibration applications like mining float cells where a 43AP would rattle to pieces.
Roy

 

[Ryan Feeley]

Good discussion. Unfortunately, I find that once you know the math, it is easy to be frustrated by the inflexibility of a PID. Three knobs to turn isn't much reward for the mathematical sophistication needed to plow through the theory.

The greatness of the PID lies in its intuitiveness and tuneability. The P, the I, and the D each consider the process error in a different way and combine to generate the output of the controller.

Proportional gain: controller correction effort is proportional to the present value of the process error. Large temperature error, turn the heater on high.

Integral gain allows the controller to remember: correction effort is proportional to the integral of the error from the past until the present (although simplistic to the point of inaccuracy, you can think of the integral as the average value of the past error over a certain time window times the length of the time window). I-gain reduces damping and can increase oscillation, since the contribution from the I term depends on a window of the past instead of just the here and the now. However, it can remove steady-state error precisely because it remembers the past.

Derivative gain helps the controller anticipate: correction effort is proportional to the present rate of change of the error, so if the error increasing, the corrective effort is raised accordingly to bring the process back where it belongs. The D-term adds damping, and can allow you to use higher P-gain without excessive oscillation. However the derivative is very sensitive to (amplifies) noise in the measurements, latencies, and update rate, which is one reason it is not always used. It is a valuable tuning knob, but can be hampered by inadequate instrumentation.

That's the essence of PID. If you want to know why bigger isn't always better for the three gain terms, or why certain adjustments can cause oscillation or instability, then you need to start diving into the math.

 

[Roy Matson]

Good Explanation Ryan.
I still don't agree that you need to understand maths though, i understand that I don't need to use a sledgehammer to drive a 2" nail without having to do the calculation.
LOL
Roy

 

[Peter Nachtwey]

Good Explanation Ryan.
I still don't agree that you need to understand maths though, i understand that I don't need to use a sledgehammer to drive a 2" nail without having to do the calculation.
LOL
Roy

You may not. I do. That is my job. I write auto tuning programs.

No i do not know what a pole is (google does not give anything i recognice to explain what pole is). But i believe you'll explain it to me.

A transfer function that looks like K/(s+a) has a pole at -a. If you are a mathematician you can see that if s=-a the the gain is infinite. I find the mathematical explanation meaningless in when applied to the real world. In the real world a pole represents something that stores energy and therefore keeps it from going where you want it. A few examples are required. A motor and load has inertia. Energy applied to the motor can not instantly spin it up to the desired speed because the rotating mass absorbs energy and the energy transfer rate is not infinite. Another example is a mass on a spring. One can push on the spring. Not all the energy goes to moving the mass. Some is absorbed by the spring. The mass absorbs energy too. One cannot instantly accelerate to the desired speed. It accelerates to the desired speed. A mass on a spring has two energy storage elements. The mass stores kinetic energy and the spring store potential energy. In the case of the mass and spring the two energy storage elements transfer energy back and forth. This is why a mass on the spring oscillates until some amount of resistance dissipates the energy.

So what items absorb and store energy in your system?
Think about it and you will understand your system better.

 

[Roy Matson]

My hat's off to you Peter. I understand your explanation but the formula does nothing for me.
Time you changed your quote.
Roy

 

[Peter Nachtwey]

I understand your explanation but the formula does nothing for me.

That is OK, the explanation is only a partial one. I must have made a connection between the physical world and the word pole. To go further we need to make a connection or translate between the word pole and how it is expressed mathematically. Then the math would makes more sense.