Ph.D. received on: 15/4/1998

E-mail: lovera@elet.polimi.it

Tutor: Prof. S. Bittanti, Politecnico di Milano
 
 

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Subspace model identification: theory and applications   ___________________________________________________________________________________________________________

Advisor:

Prof. S. Bittanti, Politecnico di Milano

Co-Advisor:

Prof. M. Verhaegen, Delft University of Technology

Referees:

Prof. G. Picci, Università di Padova
Prof. R. Guidorzi, Università di Bologna

Summary:

In this thesis, the problem of identification of multivariable state space models by means of subspace methods is considered.
Unlike the classical formulation of the identification problem, which leads naturally to consider the optimisation of some specified cost function with respect to the model parameters, the subspace-based approach does not require a parametric characterisation of the model class and proceeds in two separate stages:
first some geometric properties for the model, like, e.g., a basis for its observability subspace or its state space are estimated from the available input/output data; from the result of the previous stage a state space description of the model is constructed.

This approach avoids the need to parameterise the considered model class; this fact is of particular relevance for the multivariable identification problem.
In addition, the model estimate can be obtained without making use of iterative optimization algorithms, which makes the identification procedure very robust from the numerical viewpoint.

The thesis is divided in two parts. In the first one a general introduction to subspace identification methods is provided and the main theoretical results of the thesis are presented.
In particular, the problem of the estimation of the dynamics of the identified model is considered, some new results on the assessment of the statistical uncertainty associated with the identified models are presented and the problem of recursive implementation of subspace methods is discussed. Finally, the extension of subspace methods to a class of linear time-varying systems, the so-called linear parametrically-varying systems (LPV) is considered.
In the second part the results obtained in some practical case studies involving the application of subspace methods are presented. The examples which are considered are the identification of linear models for a pilot distillation column, of LPV models for the dynamics of a helicopter rotor blade and of linear models for the rainfall-runoff relationship in urban drainage networks.
 

 
MINORS

Statistical quality control techniques for non normal processes with application to the semiconductor industry
 

Advisor: Prof. M. Campi, Università di Brescia

The definition of statistical performance indices for production processes is a problem of great industrial  relevance. However most of the methods which are presently in use in the field of SPC (Statistical Process Control) is referred to the particular case of production processes characterized by normal distributions. In the case of processes with unknown (and in general non normal) distribution the problem of  estimating the distribution itself arises, as a neccessary step before the definition of performance indices.
The aim of this work is the development of new SPC methodologies for non normal processes, with application to the semiconductor industry.

 
On line estimation of damping in electro-mechanical oscillations 

Advisor: Prof. G. Guardabassi, Politecnico di Milano.

The problem of ensuring a satisfactory stability degree (damping) of the electro-mechanical mode in a power system constituted by an asynchronous machine connected to a predominant power network plays an importatnt role in the control of electrical networks.
This problem is usually solved by means of an additional feedback loop from the active generated power to the setpoint of the voltage regulator. However it is possible to show that fixed gain controllers fail to provide an optimal performance of the system in all the possible operating points.
For this reason, adaptive and nonlinear stabilizers are being currently investigated. The design of such systems would be considerably easier if a sufficiently fast (response time not greater than 10 seconds)  estimator of the damping ratio were available, even a fairly rogh one (standard deviation of about 30%).
The proposed technique for damping estimation is based on “model based spectral estimation” of perturbations of the generated active power due to the sole network voltage noise.
 

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