Kristo, What have you tried? I too find this difficult and time consuming. For non linear systems, I use a system of differential equations and Runge Kutta to get close and then modify the parameters to get the actual and estimates to match. This takes too long adjust the parameters by trial and error so it not suitable for implementation in a product. The model is more than good enough for education purposes. It can't be used to verify whether a system will work but it can be used to indicate the system will not work. There are always unmodeled features that keep the real system from performing as well as the model.
I have tried least square estimation for almost linear systems. This is quick and easy using a matrix class in C++. It takes just one line after setting up the arrays. I can get a difference equation that calculates estimated positions that are very close to the actual position even after hundreds of iterations. However, I have had problems getting the model to fit 3 poles plus a pole at 1, for integrating velocity , in the z domain. I can find the one pole at one and another real pole. The two other imaginary poles are very close to 0 and at very high frequency , in the hundreds of hz, even though I know the open loop frequency is only about
24-28 Hz and the closed loop pole is at 13.5Hz. I just seems odd that the difference equation can estimate fairly well, but it doesn't translate in to poles that seem to make sense. The statistic books say that my model is over parameterized, but I know the system has 3 poles. :(Any more ideas anyone?
Peter Nachtwey