Siemens PID FB41 block

Hello,
I need to set up the following PID controller:
K(1+1/(Tis)+Tds)=0.6(1+1/(8s)+2s) (s-domain)
in Step 7 project using PID FB41.
I set up FB41 just like you can see in attachment.
This PID block in OB35 works (scaling and unscaling is done in OB1), but response is
somewhat different from what can be expected.
I'm not sure if this K(1+1/(Tis)+Tds) is PID algorithm that is used in Siemens FB41.
Also that time lag TM_AG is not clear to me. Does this what is in attachment really PID
controller: 0.6(1+1/8s+2s) or maybe FB41 calculate parameters in some another way.
I know that simulation is ideal but difference in responses is really noticed (10-30%)

Thanks for help.

I found this:

http://bestune.50megs.com/PLC.htm

Apparently the S7 uses the parallel form of PID. K(1+1/(Tis)+Tds) is really interpreted as:
K+1/(Tis)+Tds
This means the PID gains need to be recalculated.

Your instructor calculated the gains assuming the wrong form of PID.

Thank you for reply Peter, I'll check it on Monday.
I really don't know how to thak you, if you're closer I would buy you a beer.
Cheers

I hate it when this happens

The attached PDF is from the online help in Step7.

Siemens seems to be talking out of both sides of it's mouth in this PDF. First they say that the PID is a 'position form' PID. But then they show a diagram that leads one to believe it is a dependent gain implementation.

Peter, you seem to lean toward Bestune showing the correct implementation. Based on Siemens track record with documentation I would be inclined to agree, I guess. But that'sa pretty big miss on Siemens' part.

Keith

The .pdf shows it is a parallel position ( I hate that term position form because it has nothing to do with position ) form PID. The time constants are in seconds too! I think Bestune is right in this case.

Note, I am not a Bestune fan. Not because of the product but because one of their engineers tried to tell the world, in sci.engr.control, that the I-PD form of PID was the best. Hog wash. It depends on the application but if all you know is process control then it may appear I-PD is the best. However for following a motion profile the PID FORM is still the best

Keith, did you figure out the s?

I am bad. I didn't work out a new solution given the fact FB41 is a parallel position form of PID. Actually Pandiani's doesn't require a derivative gain for critically damped control since Pandiani's 'plant' is only a first order lag system like a RC circuit. Therefore Pandiani should be able to calculate a critically damped response with two real poles in the characteristic equation. One from the PI controller and one from the 'plant' itself. Hint.

The earlier PID values were contrived which is why I asked Pandiani where he got the solution. Now I bet he and the instructor are wondering what to do next since the FB41 does not follow the standard ISA form.

Does anyone want to give tuning this system a crack? I will calculate a solution if there are any takers. Pandiani?

OK, just to make sure I have my terms right:

By position form we are talking about the absulute form (as opposed to the incremental form) and by parallel we are talking about the independent form (as opposed to the ISA dependent form). Something tells me that I am getting messed up in the terms somewhere.

The diagram in the PDF looks to me like an absolute dependent OID implementation as the overall gain is a passthrough for proportional and a scaler for integral and derivative.

No, I haven't gotten a handle on the s-domain versus time domain constants. But I didn't really dig into it either. Temporarily disregarding the equation form the originally listed PID transfer function is:


I also recognise that 1/s is the Laplace integral. And that the s-domain transfer function matches up in form with the real-time PID equation:


So we are saying that the s-domain coefficients Pandiani listed can enter directly into the FB41 PID function as times in seconds and be valid. So the 1/s Laplace integral is directly equivalent to the realtime integral (e)dt and seconds is the common unit.

Ho far off am I?

Keith

I found another problem

Your time constants are in seconds in the FB41. Your update time should be much faster than your time constants. .1 seconds is marginal. .01 seconds works very well.

Below is the simulation I promised. Note that you can modify the response by changing lambda. Lambda is the time constant for the desired closed loop poles for your plant and controller. Note that K and tau_i are calculated as a function of the desired response. The simulation likes lambdas ( time constants ) that are about 2 seconds or higher. Try it in Matlab too. You can change lambda and still have a critically damped system.

ftp://ftp.deltacompsys.com/public/PDF/Mathcad - Pandiani Simulation.pdf

Quiz. Why doesn't this system need a derivative gain?

I'll take a rip

Pandiani's plant only has real poles, making it a Type 0 system. It doesn't require damping as there are no complex poles to make it oscillate.

Keith

Peter Nachtwey said:

Quiz. Why doesn't this system need a derivative gain?

Click to expand...

Because it is a Type 0 system, when the output is shut off, the process value returns to normal state, i.e. room temperature.

Close but note quite right

Pandiani's plant has only one real pole so it takes only one gain which is the proportional gain. One can't count the the integrator gain because it comes with its own pole. A plant with two poles like my example:
ftp://ftp.deltacompsys.com/public/PDF/Mathcad%20-%20TempPID.pdf
requires two gains, one for the plant time constant and one for the sensor time constant.

One should never use more gais than are necessary. It is possible to use fewer gains but then there will be closed loop poles that are not placed so the system will be underdamped and there will be overshoot.

The mechanical/hydraulic engineers must learn to design their systems to be as tight as possible so they have a minimum number of poles. If the system has a lot of poles then it will be impossible to tune the system so it has a critically or over damped response.

A type 0 system with 4 real poles will be difficult to tune proplerly with a just the P I and D gains. Checkout this file Excel spreadsheet file that I created for a series of PID threads.

ftp://ftp.deltacompsys.com/public/PID/T0P4%20I-PD2D3D.zip

Note the PID form used in this spread sheet is I-PD 2D and 3d.
This system requires four gains not counting the integrator gain because the system has four poles.

Did you notice how the integrator winds up in the previous .pdf I posted? Notice also that initially most of the control signal is due to the proportional gain and over time most all of the control signal comes from the integrator term alone. As the error between the SP and PV is reduced the P term shrinks toward zero. Therefore the I term must contribute more and more of the steady state control signal until the control output due to the I term contributes all of the control signal.

I have noticed that FB41 supports feed forward. When Pandiani catches up I will move forward to cover feedforwards.