How to get process parameters by an arbitrary testrun

Hello,

what I want: I will determine the process parameters of a first order system (maybe also 2nd order).

The problem: I have not the "space" to get the parametes of an long testrun, because there are contraints at the machine of available turns from start to end.

My idea:

- I give a arbitrary signal to the process input. I think its important to have significant high frequencies to get an output to determine the system. It would not be able to get the systemparameters, if I only input a constant to the process.

- I will sample the input and output of the real process for an "adequate" time

- determining the Process parameters: If I know that the process is a first order type (G(s) = K/(1+s*T), I take the formula of the time- domain which describes the relation of the input and output of an first order system. The Parameters are K and T.

- Then I will give the real sampled input and calculate the output by my model, which is a function of K and T.

- Then I will make a benching of the output, e.g. by summation of the square-difference of the real output and the modelled output. As higher the integral summation as more deviation is betwen the real parameters and the model parameters.

- then I will vary K and T and make a new summation of the aquare difference.

- Finally I will take the K and T where the least summation value occurs.

As extension I can also put the input at a second order model. If the square-error-summation has a lower value as the first order type, then I will use the 2nd oder Modell and Parameters for modelling the real process.

How do you think about it?

Wolfgang

Reply to
Wolfgang
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Your system, will be a first order with an integrator that integrates velocity in to position K/(s*(tau*s+1)) unless the RL time constant is large relative to the sample time. See

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500 sample points should be enough. You must sample at the highest sample rate.

This is true. Ramps between 3 or more control signals with ramps that aren't to severe would be nice.

This is for a type 0 or velocity system. Your system has position feedback so it is G(s)=3DK/(s*(1+s*T))

I take the formula of the time-

Sounds good.

That sounds good too.

This is a good plan. Now how are you going to implement it?

I would generate some test cases so you know the answer. You can add random noise if you want. Then you try to do the system identification for the system you already know the answer to. You should spend a lot of time generating data and then making sure you can ID the system.

What algorithm are you going to use to minimize the sum of square error?

Peter Nachtwey

Reply to
pnachtwey

One continuous identification technique that *can* give good results is to inject the process with a pseudorandom binary sequence signal. You then cross correlate the input signal with the process output and the result, if things go OK, is the system impulse response which when integrated becomes the step response. All the elements of the theory behind this technique are googleable.

I've had success doing this, but only when (a) the forcing signal can be made large enough to overcome any low amplitude nonlinearities such as hysteresis and (b) the level of extraneous disturbances can be kept low during the test. Ramping disturbances in particular will wipe you out.

Reply to
Bruce Varley

I don't understand this statement about ramping disturbances will will wipe you out. We use ramps for excitation. They work well. If you mean unmodeled disturbances then I agree.

Wolfgang is trying to develop an auto tuning program for a motion system. You have to look at his previous posts to know this. Random signals are not a good idea as you might hit something. Also, steps are not a good idea either as it is hard on the machinery. Steps are not a good idea as they are hard on machinery.

The way I learned to do auto tuning is to write a simulator to generate data that I could then identify. I could then try different techniques very quickly to see what works and what doesn't. I could add noise to the feed back and/or noise to the excitation and see how the well the system identification works.

Peter Nachtwey

Reply to
pnachtwey

Yes, I'm referring to external disturbances, ramps that persist through the test window and are significantly larger in amplitude than the excitation signal. Ramps are particularly impactive on the PRBS/correlation ID technique.

One advantage of the technique I'm mentioning is that it can function with quite low amplitude test waveforms, the forcing function only has to be slightly above any small signal nonlinearities, can be summed in with the normal control target and can be of the same order as the noise level. However, noted that this approach mightn't suit the OP.

Peter Nachtwey

Reply to
Bruce Varley

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