This is a student question and will soon be deleted.
What is the non-parametric frequency domain method? It must be a new fad so supply a link. I am more old school but I have IDed non-linear systems before. I just like to use differential equations.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com
http://forum.deltamotion.com/

Instructor or not, the simple explanation is that linearity is often defined interms of amplitude dependencies.

All most systems become non-linear at some point, but the linearity assumption helps quantify the system response and its stability. Even the solution of differential equations is done on a piecewise linear basis and discrete element modeling.

Quote:

Even the solution of differential equations is done on a piecewise linear basis and discrete element modeling

If you look at my Tank Level Control I used non differential equations. I substituted functions for the coefficients. I did not assume the gains or the time "constants" were constant.
It is easy to define non-linear systems using differential equations. Once you define the differential equations, use an optimizer to find the coefficients or parameters for the non-linear functions that replace the coefficients.

In the case of the tank level control it is necessary to know the general shape of the tank so the correct formula can be used but the system identification can find the parameters like diameter, length, height, etc.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com
http://forum.deltamotion.com/

No disagreement there, but all numerical solutions are a step by step integration of some sort and all digital controls are based on sampled data. In both cases one is dealing with systems of discrete time solutions. It is a matter of whether one is implementing practical controls in an operating environment versus having to quantify a given model or evaluate the accuracy of solution method off-line.