We all know that if an LTI system is completely controllable, it can be transformed into a controllability canonical form. But what's the use of such a canonical form? We know that it may be of some help in pole assignment problems. Are there any other uses besides the aforementioned?
Please list as many as you know.
Thank you very much.
The controllability canonical form can be used to determine whether the system is controllable. Other than that, it may not be as useful as the controller canonical form, where one can actually compute the controller gain using pole placement.
In system identification, observability and controllability canonical forms could be useful if he parameters have physical meaning, while the system would be parsimonious (small number of parameters, i.e., could be useful for adaptive parameter estimation). There are applications where characteristic features of the system are important. For instance, in electronic nose technology, the transient signal is used to extract important features from the data. Having a model in a canonical form could provide a reduced set of parameters as a feature vector, thus a summary of the information the system carries. I believe also the impulse response and Markov parameters are easy to compute.
1) It is much easier to design a gain vector K to arbitrarily place the poles in a closed loop system when the plant is in CCF.
2) It is easy to derive the equivalent classical representation of a state-space system when it is in CCF.
3) It is easier to realize the system using (one of the standard forms) when the system is in CCF.
I guess the main downside is that your modelling/analysis might not result in a system in CCF; however, you can transform it into CCF, by changing the internal coordinates of the model, using a linear combination of the original non CCF coordinates.
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