Re: Approximating Differential Equation on the Basis of Measured Values

JCH wrote:
So:
1 what equation did you use to generate the test data?


1/(0.123*s+1)^5 (+/-1% error for making real)


2. What were the initial conditions for you generated test data?


Initial values zero.


3 Doesn't your optimize algorithm return a parameter the indicates how
good the fit is like a norm, sum of squared errors or mean squared
error?


Sum(|errors|) => MIN, automatically, but still manually adjustible if
necessary

I think you should try squaring each error and summing it and minimizing the sum of square error ( SSE ). I like to divide by the number of points do normalize the error ( MSE ). This doesn't affect the optimizing at all. Obviously if there are more points the error will be bigger. Dividing the sum of square error by the number of points gives me a better idea of how close the fit is.

As far as making things easy. I won't be. Even your 3 poles solution is too complicated to be used on a PLC because they only have PIDs, not PID2D closed loop control. A PID can only be used to place two poles because the I gain comes with its own pole. In total there will be 6 poles but only two can be placed.

I will see if I can find a suitable control method for your 5 repeated poles. Obviously the plant is already stable so the goal would be to be able to get the control the PV from 0 to 1 faster than what can be done in open loop. I will use the my model to calculate the pole positions but run the simulation using your transfer function used to generate the test data because that is the actual system. At this time the sun is out and must be enjoyed so maybe tomorrow.

Peter Nachtwey

.

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