Passivity-based control is the kind of nonlinear controller to achieve stability of simple electrical circuit, how can I expand this method to check stability for a complicated electrical circuits?
I will be appreciated your help…
Dear Mustafa,
I suggest to you links and attached files in topics.
- Passivity-Based Control and Estimation in Networked Robotics
https://books.google.dz/books?isbn=3319151711
- Stabilization of closed sets for passive systems, part II: Passivity-based ...
ieeexplore.ieee.org/document/4738824
Best regards
Book L2-Gain and Passivity Techniques in Nonlinear Control
Generally , modelling of the circuits (PBC or otherwise ) is done using RLC model since that allows the flow of (V,I) . So I guess you need to look at the significant contributor of these parameters and model them as equations (for energy transfer )
Commonly used is the Hamiltonian model /equations for energy
Book: Port-Hamiltonian Systems Theory: An Introductory Overview by Arjan van der Schaft and Dimitri Jeltsema
For a multi parallel electrical system, if I insured passivity of each individual subsystem that imply I can get the stability of the whole system? And if that is true is there any systematic manner for that.
Thanks a lot for all.
Yes Mustafa , Each plant's stability contributes to the overall stability . The consideration is no interdependence in terms of feedback .
From the local level, if I insured each subsystem is passive and stable. How can I assured my whole system is stable is there any indications or measurement method for that?
The simplest seem to L1 and L2 norms (numerically) or lyapunov stability .
In the latter case it is generalized for closed loop systems too.
Hi Mustafa,
I will answer your last two questions shortly with "no".
If a system consists of several subsystems, and if you can show that each subsystem is passive (implying strong stability behavior), then you cannot always say that the overall system is passive as well. The connection of these passive systems matter. In fact each system has to be connected to another with a proper feedback interconnection.
Please check the Chapter 6 of the Khalils book for a formal description (I have added an amazon link of the book).
Best,
Burak
https://www.amazon.com/Nonlinear-Systems-3rd-Hassan-Khalil/dp/0130673897
Dear Ilhan Polat
Yes you are right, maybe there are some subsystems is not passive with huge interconnected passive system. In such case how can we deals with this issue? Are there any suggested references or papers for interconnected network system based on passivity method?
Thanks for all
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