Date of final exam: 13/01/2000

E-mail: cuzzola@elet.polimit.it

Tutor: Prof.  S. Bittanti, Politecnico di Milano

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Filtering and control via LMI optimisation   ___________________________________________________________________________________________________________

Advisor:

Prof.  S. Bittanti, Politecnico di Milano

Summary of the thesis

Several well-known problems of system and control theory can be reformulated as convex optimisation problems. This possibility appears advantageous when an analytical solution is not available. Indeed, the algorithms as the Interior Point Methods, which have asymptotic polynomial complexity, can be applied. These techniques are known in literature with the acronym LMI (Linear Matrix Inequality). This thesis is subdivided in two parts: in the first some theoretical results concerning unbiased filtering of Linear Time Invariant, Parametrically Varying, Periodically Varying and Uncertain systems are presented. The second part provides some practical results obtained applying the theory of the previous part: in particular the problem of rejecting periodic disturbances in helicopters is faced in a very general framework.

Filtering

Filtering a dynamic system consists in estimating the state vector or a set of linear combinations of the state vector exploiting the measurements available until the current time. This is a classical problem going back to the early papers by Kalman.
Mainly, we consider the H¥ filtering criterion that is customarily used when either no a priori information on the disturbance statistical properties is available or the designer aims to cope with the worst noise perturbation.
In this thesis we provide some useful techniques in order to face the filtering problem of linear systems both in continuous-time and discrete-time. In particular we focus on LMI filtering techniques based on the so-called unbiasedness condition. The unbiasedness condition provides a twofold advantage in an LMI context. Indeed, unbiasedness reduces the number of the unknowns and hence leads to a lower computational effort. Moreover, it allows to face in an LMI framework the filtering problem of unstable systems without the necessity of resorting to any frequency shifting methods.
An interesting characteristic of the filtering techniques proposed herein is given by the possibility of obtaining a significant parameterisation of the filters meeting some design requirements. It is believed that this approach can be extended to other types of reconstruction problems as the so-called deconvolution problem.
The robust unbiased LMI filtering problem can be faced as well by resorting to a simple trick based on the extension of both the input noise and of the measured signal.

Applications

The LMI-periodic techniques previously described have been successfully applied to some practical problems such as the problem of rejecting periodic disturbances in helicopters. In such application the computational advantage offered by LMI Periodic filtering technique turns out to be very sensible since offers the opportunity of tackling, for the first time, the generic flight condition in a very simple and computationally advantageous way.
Other sophisticated LPV (Linear Parametrically Varying) have been applied to the control of trajectory in mobile robots and in the problem of compensating nonlinearities in industrial current transformers.
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OTHER THEMES DEVELOPED

Modelling and control of a plant for the gasification of biomass

Supervisor: Prof. A. De Marco, Politecnico di Milano

In view of the possible changes to the world's climate, commonly referred to as the Greenhouse Effect, and the associated consequences, the industrialised world has made a strong commitment to reduce the emissions of the Greenhouse gases into the atmosphere.
Power-generation constitutes an important contribution to the emission of one of the most important Greenhouse gases, i.e. carbon dioxide (CO2), which is avoided when using biomass as a fuel.
The Integrated Gasification Combined-Cycle (IGCC) technology has been identified as an efficient technique to convert biomass to power for medium to large-scale applications. A plant of such a type is now under construction near Pisa in the framework of the Energy Farm project under the THERMIE programme of the European Commission. It features an atmospheric, air-blown, circulating fluidised bed (CFB) gasifier, integrated with a 10.9 MWe, gas-turbine and a heat-recovery steam-generator (HRSG) providing steam to a 5 MWe condensing steam-turbine. The plant's net efficiency amounts to 33 per cent.
The close integration of the different plant components requires careful design of the plant's control system. This work is aimed at the study of the dynamic behaviour of the overall plant, which makes it possible to verify the operating procedures under normal conditions and to identify a good design of the plant's control system.

Some considerations on the IEC 1499 draft for the design of software automation systems

Supervisor: Prof. L. Mezzalira, Politecnico di Milano

The automation tasks, i.e. acquiring data and controlling devices, machines and plants, consist of activities performed along time. Some of these operations cause significant changes in a rather short time interval, and for many purposes can be considered instantaneous. They actually take a certain, usually relatively small, amount of time, but the simplification is acceptable as long as the time is short compared with other related timings and, most important, as long as we are not interested in a detailed evolution but only in the overall changes produced. These operations can be called actions.
Usually Function Block formalisms, a kind of data flow diagrams, mainly support activities as their basic behaviour, while computers operate executing sequences of actions. Possibly because of this fact, the IEC 1499 formalism privileges events and actions inside its Function Blocks. The purpose of this paper is to provide a more defined semantics for the Function Block behaviour. Starting from these considerations it seems worthwhile carrying on a critical analysis on how actions and activities can be implemented with those Function Blocks and what features can be desirable to improve clarity, correctness and portability of designs described in terms of Function Blocks.

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