hello,
What do we mean by a system with a zero dynamic?
and can you show to me this with an example?
thank you.
Sanjoy Roy
In many papers i saw that before they develop the control law they propose that the system don't have a zero dynamic like in the Feedback linearization.
so, i don't understand the meaning of a system with zero dynamic and what's the influence of that in the develop of that control law.
Dear Yacine,
The name “zero dynamics” is due to its relation to output zeroing and its relation to transmission zeros.
Transmission Zeros can be determined in two ways:
-either By using an embodiment of minimal state that is controllable and observable in its companion form.
-either By using the form of McMillan of G (s), the roots of the numerator polynomial pi (s) in the diagonal Elements of the McMillan of G (s) are called Expired the transmission zeros of the system.
For systems we have finish zeros and infinite zeros , in fact we have several types of zeros: decoupling zeros, tansmissions zeros, invariant zeros and all these types are included in the system zeros.
Concerning the dynamics zeros to their introduction was made mainly for the control of nonlinear systems and nonminimum phase system.
Here is attached a detailed explanation of the concept of dynamics zeros.
If there is still a shadow on the issue does not hesitate to ask again
Best regards
So that explains it.
Thank you, Prof. Lafifi.
Could you please add the cite of the book from which the uploaded file is the Ch. 4 ?
-Sanjay
Dear All,
Here link from which the uploaded file the ch. 4.
Zeros and zero dynamics
https://www.math.kth.se/optsyst/utbildning/kurser/SF2842/ch4.pdf
Best regards
Thanks, Prof. Lafifi.
Unfortunately that helps only to a limited extent, because this seems to be a chapter from some internal monograph of the KTH.
The link, if taken in parts, is not getting me very far. Because it takes me to the Math Department of KTH, and then straight to the chapter itself. All other levels of the path are inaccessible, so I guess we will have to locate the monograph/document in some other way.
Or we may have to locate alternative references.
Let me try !
-Sanjay
It is lecture notes from a course in geometric control theory.
https://www.math.kth.se/optsyst/utbildning/kurser/SF2842/front.pdf
https://www.researchgate.net/profile/Anders_Lindquist
thanks all of you and this is the link of all the parts
https://www.math.kth.se/optsyst/utbildning/kurser/SF2842/
If mathematical model of system is reduced to the systems of algebraic (not differential!) equations, this system can be considered as system with zero dynamics.
Example: dx/dt=-a*x+k*u - system with 1st order dynamics
x= k*u - system with zero dynamics.
Roughly speaking...Do you remember the meaning of zeros in linear systems? Zero dynamics is the analog part to nonlinear systems.
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