Date of final exam: 25/01/2002

E-mail: lorenza.magnani@unipv.it

Tutor: Prof.  R. Scattolini, Università di Pavia

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VARIABLE STRUCTURE CONTROL FOR A CLASS OF HYBRID SYSTEMS   ___________________________________________________________________________________________________________

Advisor:

Prof.  R. Scattolini, Università di Pavia

Summary of the thesis

Technological innovation pushes towards the consideration of dynamical systems of a mixed continuous and discrete nature, which are called "hybrid systems". Indeed many consumer products (cars, micro-wave units, washing machines and so on) are controlled by digital embedded software, rendering the overall process a system with mixed dynamics.

From these examples it is obvious that a too general study of hybrid systems will lack decisive power: it will not result in detailed informations on individual elements in the studied class. Therefore, one has to consider a subclass of hybrid systems carrying a clear additional structure allowing analysis of its behavior (e.g. stability, well-posedness, simulation...) and facilitating systematic controller synthesis. However, the chosen subclass must also contain many interesting examples form an application point of view.

The class of nonlinear continuous-time dynamic systems in controllable canonical form is the subject of the thesis and satisfies both requirements. The study of this class is motivated by a broad range of physically interesting systems. Examples include mechanical systems, flexible structures, variable structure systems...

The aim of this thesis is to design and analyze a hybrid control strategy for these systems. To do this, it is important to define a physically relevant mathematical model of hybrid systems, general enough to encompass most of the hybrid phenomena of interest in engineering and suitable to describe the chosen subclass of nonlinear continuous-time dynamic systems in controllable canonical form controlled by the hybrid control strategy here introduced.

The new hybrid control strategy proposed in the thesis is a hybrid variable structure control strategy (HVSC). This strategy can be named "hybrid" since its design is based on a system state decomposition into regions with which different control laws can be associated, so that the selection among the various laws is event-driven. Contemporarily, it is inherently of VSC nature because the individual control laws are designed according to the theory of variable structure control. It is characterized by the fact that only a control component is used at any time. The theoretical properties (stability, absence of limit cycles, improved control performance) of the proposed HVSC control strategy are examined and simulation results are reported to point out the advantages gained by applying this hybrid approach.

Finally, a practical control problem is dealt with: the vibration suppression of a large space structure. This goal is achieved introducing another hybrid variable structure control strategy suitable for linear stable systems under control with an arbitrary number of control variables. The advantages gained with the adoption of this hybrid variable structure control strategy are improved control performance and reduction of energy consumption. To establish this, some experimental results, compared with whose achieved with other control strategies, are given.
 

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