Interpolation

What is the process? At (approximately) what rate does the controlled parameter change with a change of SP?

Hi John,

My low & high limit of OP is -5 and 105.

I asked about the rate of change of response.

Hi,

That depends on the process and environment. I am considering real time processes like flow, level, temperature and level. Rate of change is not constant practically and not possible also. i have PV, SP and OP data for 5 sec interval, but my algorithm needs data for every sec. Please help .

Is this a theoretical exercise, or a practical application?

Practical application

If you are designing a system operates in interpolation, it is a cheat. This is like You get a 1 second screen reading everytime but actually your sensor updates only every 5 second. How are you sure AR interpolation is applicable to a process. Processes are not all linear. Ideally interpolation is most suitable to a quasi-equlibrium process only plus a 5 second gap is not infinitisimal enough.

What you are implying is precisely an aspect of the Nyquist sampling rate theorem. This is why I am trying to get a clarification on this 5 second history obfuscation.

I'm trying to get this very topic across to several of the software weenies I deal with at work. In my work case there is a large array of thermocouples (TC) measuring many points on a complicated machine. The PLC that is measuring these TC has a 60Hz notch filter and reads all of these points at 10 Hz to protect this machine from ripping itself apart. The PLC chosen for us does not have the ability to archive any large amount of data. To archive this data this array of measurements are sent to a server (IOC) once every ten seconds. The weenies think that their IOC data sample rate is 10 Hz when it actually is 0.1 Hz. When the power demands on this machine eventually increases to peak operating conditions I expect mystery TC trips to become a problem.

All analog inputs to your plc module in one cpu, you mean? I guess there are better ways to deal with such condition but needs a little twist, redesign and up grade, of course additional investment to owner. It's always true not only to mechanical design, that the strongest link of a system is the weakest link. Holds true to automation also, a careful selection or integration of elements should be match, otherwise one or more elements do not make sense at all-such a waste of resource.

I know exactly what you are talking about!

The Nyquist sampling rate is so critical! And it is "optimistic" in my experience, since so many want to roll off the frequency "noise" and don't appreciate they introduce phase shift into the measured data.

I deal a lot with variable speed drives, and although they often want steady state precision and slow accels and decels to keep the process under control, the drive can have response times at 100 rad/sec. When backlash creeps into the drive train I need the bandwidth and fast sample rates to control what is happening - you just can't filter the feedback to get rid of the problem. Slow sample rates just give aliased data, and I have seen the process people with their PI system with 5 second sample periods insist we have a low frequency speed oscillation, when in fact the system is tearing itself apart with high frequency oscillation. Nyquist rules! You can't beat it!.

Now if they want some curve fitting algorithm and actually know their bandwidth - that can be a different story, but should not be used to "predict" future points without some elegant modelling, and always keep in mind the data has been tinkered with.

(That data tinkering reminds me of someone selling penny stock - OK, even my RSP funds.)

Good points - but servo motor drive systems and smelting furnaces have very different response times. The OP, despite repeated requests, refuses to give any indication of the time constant of his system - the whole 5 second/1 second thing may be a load of bunk (way too slow or too fast). He also refuses to clarify the actual sampling rate (despite Redfred's best efforts).

I'm out

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Servo motor drives?

These are several hundred HP drives on Paper Machine sections. J of connected load is often 1 minute!

Disconnect the load (backlash) and "all hell" breaks loose. They want precision speed and respond quickly to load, and give me sloppy elastic gear trains - "It worked OK with the line shaft, what do you mean it isn't good enough for sectional motor drives?"

OK, I am ranting.

If you do not try to violate Nyquist's sampling theory then applying a Kalman filter to your data set can produce more accurate data analysis. It can also lead you completely astray. A Kalman filter analysis can identify seemingly random effects in your data set and remove them. But what if the randomizing process was actually altering what you want measured and not a measurement error.

Getting back to Nyquist sampling, I'm puzzled why you identify that your sampling time is 1 second but your data is archived in Historian every 5 seconds. If all five discrete 1 second data points are placed in an archive every 5 seconds then you do have a 1 second samples. If you instead do any mathematical combining of this data to put this into archive in 5 second intervals then you have a filtered 5 second sample time.

Hi ,

My algorithm needs every one sec data and my sampling frequency should satisfy the nyquist sampling theorem. Will kalman filter fit for my application and noise is not a problem for me. But i want a more robust data at every sec (where the data is interpolated previously) and Kalman filter estimate will be better? if its, can you tell me how its works?? ( kalman filter needs true value of the output, how will it works with the missing(interpolated) points??

You did not explain your 5 second attribute at all, so I do not know how or if I can help you.

I also do not grasp at all your comment that noise is not a problem for you. Estimating the standard deviation of the process and measurement noise components is the point of doing a Kalman filter. If you do not care about noise then consider your measurements are your actual values.