E-mail: balduzzi@polito.it

Tutor: Prof.  G. Menga, Politecnico di Torino

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Modeling, analysis and control of hybrid manufacturing systems   ___________________________________________________________________________________________________________

Advisor:

Prof.  G. Menga, Politecnico di Torino

Summary of the thesis

Many physical systems today are modeled by interacting continuous and discrete-event systems, such as air traffic management systems, automated highway, communication networks and manufacturing systems, exhibiting both continuous-time and discrete-event dynamics. There has been an increasing interest in these types of hybrid systems during the last decade, mostly due to the growing use of computers in the control of physical plants.
Hybrid system models, suitable for describing with a single formalism the hybrid dynamics of a fairly large class of manufacturing systems, are proposed in this thesis. The continuous dynamics is described by differential equations whose evolution in time depends on continuous states and inputs as well as discrete states. The discrete dynamics is modeled either by finite state automata and Petri nets.
The first part of the thesis focuses on an efficient state space formulation for describing the dynamics of manufacturing systems, which embeds all information required to evaluate performance measures, gradients and their uncertainties. This hybrid model distinguishes two levels of aggregation. On one hand, discrete dynamics are described by finite state automata, representing the transitions of the system through a sequence of admissible macro-states at the occurrence of a limited number of events, the macro-events. On the other hand, continuous dynamics are represented in terms of first and second order fluid approximations.
We envisage the continuous-flow model of the system as part of the higher level control that responds to random events --- or to large deviations from the expected behavior --- by resolving this model under the new circumstances, and using its solution until the occurrence of the next event. Of course, since this model is non-anticipating with respect to future random events, the overall control will be generally suboptimal. In particular, we investigate the performances of two different two-levels dynamic production control policies for part routing and machine scheduling in manufacturing systems. At the higher level (macro-level) a piecewise stationary control policy is formulated and solved via a sequence of linear programming problems. At the lower level (micro-level) a real-time dispatcher will be used to track the solution of the upper level controller (the average flow rates sequence) as closely as possible.
Stability is one of the most important properties of dynamical systems. This problem is addressed in terms of the stability of discrete linear inclusions, whose evolution in time can be efficiently described by language theory and finite automata methods. Particularly, we will show that steady regimes are defined by sets of idempotent matrices all infinite products of which do converge, hence the state of a hybrid manufacturing system is always bounded. This original approach makes evidence of an intriguing relationship existing between idempotent matrices (the closed-loop system matrices) and the proposed approximation of the discrete event processes driving the evolution in time of the system.
The second part of this thesis is concerned with hybrid Petri nets. Precisely, we define First-Order Hybrid Petri Nets, a class of hybrid nets consisting of continuous places holding fluid, discrete places containing a non-negative integer number of tokens, and transitions, either discrete or continuous. We set up a linear algebraic formalism to study the first-order continuous behavior of this model and we show how its control can be framed as a conflict resolution policy that aims to optimize a given objective function. Furthermore, we discuss the relationship between hybrid Petri nets and hybrid automata.
Complex manufacturing systems, consisting of unreliable machines, finite buffers and subject to configuration-based specifications, can be described in a modular fashion through the composition of elementary hybrid Petri net modules. Moreover, we address the problem of how evaluating performance measures and making gradient estimation in order to find optimal control policies for manufacturing systems of practical significance. Since, the dynamics of hybrid Petri nets are formulated in terms of linear algebraic models, we can apply sensitivity analysis techniques that pertain to such models to the proposed hybrid framework. Therefore, we will be able to study of how changes in the structure of the model influence the nominal behavior.
 

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