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Trajectory tracking in switched systems: an internal model principle approach: the elliptical billiard system as a benchmark for theory
Get PDFSistemi dinamici caratterizzati dall'interazione tra dinamiche continue e discrete sono detti sistemi ibridi. Un sistema switched è un particolare sistema
ibrido costituito da una famiglia di sottosistemi a tempo continuo e da una
legge che ne regola le transizioni. Questi sistemi hanno numerose applicazioni
nel controllo di sistemi meccanici, nell'industria automobilistica e aeronautica,
nel controllo del traffico aereo, nell'elettronica di potenza, etc.
Questa tesi sarà incentrata sul problema dell'inseguimento asintotico di traiettoria per sistemi switched. Nella prima parte, il problema di inseguimento è stato propriamente definito e risolto prendendo in esame il sistema biliardo
ellittico. Al fine di definire una classe di traiettorie di riferimento ammissibili per il sistema biliardo un problema di pianificazione di traiettoria è stato
approntato e risolto attraverso l'utilizzo di risultati della teoria dei polinomi non negativi e tecniche LMI. Il problema di inseguimento in presenza di incertezze
nei parametri del sistema è stato considerato e risolto sia nel caso di feedback
dallo stato che dalla sola posizione. Nella seconda parte della tesi i risultati
ottenuti per il sistema biliardo sono stati generalizzati per una classe di sistemi
switched con dinamica lineare in ogni modo operazionale, mappe di reset lineari
e dimensione dello spazio di stato possibilmente variabile tra i vari modi. In tutti
i casi la strategia di controllo proposta è basata su una versione discontinua del
principio del modello interno.Dynamical systems that are described by an interaction between continuous
and discrete dynamics are called hybrid systems. Their evolution is generally
given by equations of motion containing mixtures of logic, discrete-valued or digital dynamics, and continuous-variable or analog dynamics. A switched system
is a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. These systems
have numerous applications in control of mechanical systems, automotive industry, aircraft and air traffic control, switching power converters, and many
others.
This thesis will focus on the problem of asymptotic trajectory tracking for
switched systems. First, the tracking control problem is properly stated and
solved for a controlled elliptical billiard system. In order to find an admissible
class of reference trajectories inside the billiards a motion planning problem has
been solved by using results from the theory of non-negative polynomials and
LMIs techniques. The trajectory tracking problem in presence of uncertainties
on the plant parameters has been also considered and solved in both cases of
state-feedback and output-feedback. In the second part, the results obtained for
the billiard system are generalized for a class of switched systems having linear
dynamics in each operating mode, linear reset maps and possible nonuniform
state space among the different modes. In all cases the proposed control strategy
is based on a dynamic compensator, whose state is subject to discontinuities and
whose structure is based on a nonsmooth version of the internal model principle
Robust trajectory tracking for a class of hybrid systems: an internal model principle approach
No full textThis paper deals with the asymptotic tracking of periodic trajectories for hybrid systems having linear dynamics in each operating mode and isolated discrete switching events (switching systems). Parametric uncertainties are considered and the dimension of the state vector is allowed to vary among modes. To deal with the hybrid nature of the system, and the possible discontinuities of its solutions at switching times, a properly amended tracking control problem is defined and a feedback control law based on a discontinuous version of the classical internal model principle is proposed. The innovative design of the discrete-time dynamics of the compensator guarantees the robust existence of a steady-state response giving zero tracking error in the controlled output, and local convergence to it
More appendices for paper “Robust trajectory tracking for a class of hybrid systems: an internal model principle approach” by S. Galeani, L. Menini and A. Potini
Get PDFTrajectory tracking in linear hybrid systems: an internal model principle approach
No full textThis paper deals with the problem of asymptotically tracking periodic trajectories for a class of hybrid systems (switched systems) having linear dynamics in each operating mode, where the reference trajectory and the control action are such that only isolated swithcing events occur. The possible presence of uncertainties in the system description is considered and no assumptions on the uniformity of dimension of the state vectors among modes are made. In order to deal with the hybrid nature of the considered system and the possible presence of discontinuities of its solutions at switching times, a properly amended tracking control problem is defined and a control strategy based on a discontinuous version of the classical internal model principle is proposed
Finite-time control of linear mechanical systems subject to non-smooth impacts
No full textThe goal of this paper is to find a dynamical output feedback compensator that guarantees the Finite-Time Stability for a given mechanical system, with linear continuous-time dynamics, subject to non-smooth impacts. An example is used to show the effectiveness of the proposed controller
Robust asymptotic tracking of periodic trajectories in elliptical billiards
No full textAn infinitely rigid mass subject to friction, with mass and linear damping factor being in general not known exactly, is considered, moving on a planar region delimited by a rigid elliptical barrier (elliptical billiards) under the action of proper control forces. The robust tracking control problem for a class of periodic trajectories, involving nonsmooth impacts between the mass and the barrier at fixed times is stated and solved by means of a controller based on the Internal Model Principle and whose state is subject to discontinuities
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Asymptotic tracking of periodic trajectories for a particle in an elliptical billiards
No full textAn infinitely rigid unitary mass (particle) is considered, moving on a planar region delimited by a rigid elliptical barrier (elliptical billiards) under the action of proper control forces. A class of periodic trajectories, involving an infinite sequence of nonsmooth impacts between the mass and the barrier at fixed times, is found by using an LMIs based procedure and a tracking problem is stated and solved by means of a controller whose state is subject to jumps
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