Poles and zeros position are determinant in the complexity of the system in order to be identified?
Control system
Identification system
Control System complexity
Not necessarily, Jose.
The complexity (or ease) of identification depends largely on the information available within the signals that are available for measurement. It is not necessarily decided by the different types of controllers.
But one thing is for sure ! The higher the order of a control system, the more difficult it becomes to identify due to many reasons.
Hope that helped.
-Sanjay
The more complex control system to identify is the one which contains more unknown parameters. Of course measurement signals need to be available.
Hope that helped
Hakim
Thanks for the answer.
I have also a question. Normally there are a set of approximation models that we can use to identify the real model:
http://www.control.isy.liu.se/research/reports/2007/2809.pdf
There are a parameter of the system to increase the set of approximate models or to reduce the number of approximate models?
Thanks,
First, I would like to know the system you need to identify is linear or nonlinear ?
If it is linear, the reference pointed above contains all models to use for parameters estimation. If it is nonlinear, adaptive control could be more convenient.
System identification is inherently a nonlinear problem. The more the number of parameters and the more these parameters appear in multiplicative ways ( e.g., unknown parameters p, q, and r, appearing in one of the equations as, say, p^2*q^3*(1+r^2), in another equation as p*r^3 ) the harder the identification gets, in general.
A second, and equally important aspect, is the nature and availability of data. Here there are two main issues to consider: (i) what states (or state surrogates) are measured, and (ii) what is the reliability of these measurements.
i think the order of a dynamic system is a statement of its complexity. That is the higher the order, the more complex it becomes. In addition, the more the number of system's parameters, the more complex it could be when there are uncertainties like unknown parameters and disturbances
Is not easy to say which one is more complex/difficult to identify, but for identification operation, acquired data quality is essential. So, for different time constants, sometime excitation signal is not so easy to be generated.
If a system has Right-Half-Plane poles (unstable system), or Right-Half-Plane zeros (non minimum-phase), it is more difficult to identify.
Thanks for the answer, very useful,
Hi Hakim,
My system can be modeled as discrete linear time-invariant systems.
As has been mentioned, the excitation signals used determine to a large extent how well you can identify the parameters of a given model. Typically, this means that you need to spectrally shape (filter) your input signal before it is applied. This is called 'experiment design'.
The method you use to fit the parameters to the data also affects the results. These days there seem to be some consensus on subspace identification being the method that produces the best results in general. However, depending on the system at hand and the data, other methods can produce much better results. Filtering and weighting of the data also affects the results significantly.
You might want to check out Boyd's book on optimization (Chapter 6) for a more general framework for doing system identification, where you can easily change and experiment with the norm, weighting, and method used.
http://oodgeroo.ucsd.edu/~bob/Bob_zone_site/Literary_diversions_files/P25_Marie_SCL.pdf
http://sites.uclouvain.be/socn/archive/Documents/lec2a.pdf
https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf
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