Ph.D. received on:  8/7/1997

E-mail: calafiore@polito.it

Tutor: Prof. Basilio Bona, Dip. Automatica e Informatica, Politecnico di Torino.

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Structural properties of the zeros for matrix second order systems: theory and applications   ___________________________________________________________________________________________________________

Advisor:

Prof.  Basilio Bona, Dip. Automatica e Informatica, Politecnico di Torino.

Referee:

Prof. Giovanni Celentano, University of Neaples.

Summary:

The subject of the Thesis is the study of structural and algebraic characteristics of the zeros of multivariable linear dynamic systems described by second order matrix differential equations. This class of models is widely used to describe the behaviour of lumped-parameters mechanical and electro-mechanical systems and in Finite Element analysis of distributed parameter systems. The interest towards zero modes of such systems stems from the fact that the zero locations determine fundamental limitations on the closed-loop performance of the system and are intimately related to the coupling of the system internal dynamics with the inputs and outputs, i.e. to the selection of suitable positions for sensors and actuator placement. In the Thesis a structural interpretation of the zero modes is provided, which relates the zero frequencies to natural frequencies of a subsystem of the original system determined by the selected input and output sets. This interpretation also leads to efficient numerical algorithms for zero computation. An alternative method based on bond-graph analysis to identify the zero-providing subsystems is also discussed in the Thesis, and various examples of applications are reported. In the last chapter of the Thesis the problem of optimal transducers positioning based on controllability/observability measures is discussed and a solution scheme based on genetic optimization algorithms is proposed.
 

 
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