For calculating/simulating a control loop one needs a control transfer function. This can be generally found by evaluating mathematically a step response as SIEMENS does, too:
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SIEMENS uses a semi-analytical method (obviously patent pending) whereas I use a 100% approximation method that is much more accurate.
The basis is just using 2 'representative' points for finding the differential equation. These 2 points can be found best via least-square polynomial approximation with appropriate number of measured points.
Are there other methods known as far as more accuracy is concerned?
I assume you mean _plant_ transfer function. To simulate a control loop you need a differential equation describing the dynamics of the plant -- not a transfer function. In the case of plants with significant nonlinearities you don't want to even think about linearizing the plant model, which means that you have to throw the concept of a "transfer function" out the window.
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Take a system with torquer motors, some cabling, high-frequency rolloff in the amplifiers and sensors, and at least one mechanical resonance that's high enough to be dealt with but low enough to interfere with getting adequate loop closure.
How in heck are you going to make an adequate approximation of a dozen unknowns by taking just two points out of a step response?
Swept-sine frequency response measurements will get a highly accurate plant model. They have the (significant) drawback that any attempt to fit a transfer function to the measurements will lose accuracy, but they have the (significant) advantage that if you can state your control system requirements in frequency domain terms you can design the whole thing using frequency domain design techniques.
As far as methods that takes the response to a step or other n-th order input and extracts the differential (or difference) equation coefficients directly, pursuant to getting a transfer function, they are going to be doomed to inaccuracies at higher frequencies. With such measurements there is so much energy at the low frequencies that the high frequency data (corresponding to fast responses) gets swamped out.
Note: I'm not _against_ step response testing -- if you need something better than a manual, heuristic tuning method but your needs are too modest to require frequency sweeps or there is some reason that frequency sweeps are too expensive or dangerous then it works fine.
I don't know how you get a transfer function or coefficients for differential equations with just two point either. Usually I use 500 to 2000 points. The link below shows the results of system identification of my hydralic system back in the shop
More easy way fo TF calculation should be a software that could do by itself without too many problems
PiControl Solutions
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offer such solutions for TF identification PITOPS-TFI . Just connect the OPC with the existing data historian or the Database where the PID tags are stored. and the software will do the rest. It will give you the TF as well as full graphics. Data can be alos taken in Excel format as Plant data input file
PITOPS TFI offfer special new release that can calculate the very precise TF by new methods, The Geometric method is the old method provided in the old Pitops TFI. Use this first and if this does not give good results, then try the Gradient method for first and second order transfer functions or the Gravity method for zero-order (ramp) transfer functions.
Click on the 3G Plots to see the new screens.
When using Gradient method, Pitops TFI calculates first order differencing on the data to eliminate drift and disturbances. The identifier tries to fit the gradient CV with the gradient model shown on the 3G plot screen.
When using Gravity method, Pitops TFI calculates second order differencing on the data to further eliminate drift and disturbances. The identifier tries to fit the gravity CV with the gravity model shown on the 3G plot screen.
For ramps, Gravity method should be used, not Gradient. For first and second order, Gravity method could also be used in addition to Gradient method. When drift and disturbance level is high, Gravity method will work better since it rejects disturbances more that Gradient or Geometric methods.
The new Pitops TFI automatically adds filtering on the raw CV (plant data). You can see the Filter value options - None, Weak... etc. Pitops TFI automatically sets filtering but you can manually adjust the filtering also by looking at the Gradient and Gravity trends.
If using Gradient method, and if Gradient CV still looks noisy, then increase filtering more manually to get better results.
If using Gravity method, and if Gravity CV still looks noisy, then increase filtering more manually to get better results.
Regards
Manmeet snipped-for-privacy@amritconsulting.com
calculating/simulating acontrolloop one needs acontroltransfer
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