Catálogo de publicaciones - libros

This chapter gives an overview of the “circle-criterion” design of nonlinear observers, initiated and further developed by the author in a series of papers. It summarizes these results in a concise and unified manner and illustrates them with physically motivated design examples from fuel cell power systems, ship control, and active magnetic bearing systems.

The problems of constructing observers in the presence of unknown inputs and of detecting and recognizing inputs of a special kind are considered for linear time delay systems with commensurable delays. Both problems are studied from an algebraic and geometric point of view, making use of models with coefficients in a ring, of invariant subspaces of the space module and of suitable canonical decomposition into subsystems. Feasible and constructive procedures for the analysis and solution of the problems are presented.

Robustness had become a central issue in system and control theory, focusing the researchers’ attention from the study of a single model to the investigation of a set of models, described by a set of perturbations of a “nominal” model. This set, often indicated as the uncertainty model set, has to be suitably constructed to describe the inherent uncertainty about the system under consideration and to be used for analysis and design purposes. H _∞ identification methods deliver uncertainty model sets in a form suitable to be used by well-established robust design techniques, based on H _∞ or μ optimization methods. The literature on H _∞ identification is now very extensive. Some of the most relevant contributions related to assumption validation, evaluation of bounds on unmodeled dynamics, convergence analysis, and optimality properties of different algorithms are here surveyed from a deterministic point of view.

Algebraic methods are presented for solving nonlinear least-squares type problems that arise in the parameter identification of nonlinear systems. The tracking of the induction motor rotor time constant is solved in detail. Also, an approach to estimating state variables using algebraic relationships (in contrast to dynamic observers) is discussed in the context of speed estimation for induction motors.

The problem of piecewise affine identification is addressed by studying four recently proposed techniques for the identification of PWARX/HHARX models, namely a Bayesian procedure, a bounded-error procedure, a clustering-based procedure and a mixed-integer programming procedure. The four techniques are compared on suitably defined one-dimensional examples, which help to highlight the features of the different approaches with respect to classification, noise and tuning parameters. The procedures are also tested on the experimental identification of the electronic component placement process in pick-and-place machines.

This chapter provides numerical examples to illustrate the recent results by the authors relating asymptotic stability and dissipativity of a linear differential or difference inclusion to these properties for the corresponding dual linear differential or difference inclusion. It is shown how this duality theory broadens the applicability of numerical algorithms for stability and performance analysis that have appeared previously in the literature.

The chapter presents an expository survey of ongoing research by the author on a system theory for oscillators. Oscillators are regarded as open systems that can be interconnected to robustly stabilize ensemble phenomena characterized by a certain level of synchrony. The first part of the chapter provides examples of design (stabilization) problems in which synchrony plays an important role. The second part of the chapter shows that dissipativity theory provides an interconnection theory for oscillators.

In this chapter we discuss a constructive method for anti-windup design for general linear saturated plants with exponentially unstable modes. The constructive solution is independent of the controller dynamics, so the size of the (necessarily bounded) operating region in the exponentially unstable directions of the plant state space is large. We discuss the features of the anti-windup algorithm and illustrate its potential on several examples.

This chapter gives an overview of simple controllers for SISO systems based on the generalization of the linear pole assignment method for constrained systems with dynamics ranging from relay minimum time systems to linear pole assignment systems. The design is based on splitting the n th-order system dynamics into n first-order ones, which can be constrained without any problems with stability and overshooting. It requires a successive decrease of the distance of the representative point from the next invariant set with lower dimension. Since the distance of the representative point to such invariant set can be defined in many ways, the construction of the constrained controllers is not unique. The controllers derived from the second-order integrator are simple, appropriate also for extremely fast application, and easy to tune by a procedure that generalizes the well-known methods by Ziegler and Nichols, or ?Aström and Hägglund, respectively.

Finite-time stability (FTS) is a concept that was first introduced in the 1950s. The FTS concept differs from classical stability in two important ways. First, it deals with systems whose operation is limited to a fixed finite interval of time. Second, FTS requires prescribed bounds on system variables. For systems that are known to operate only over a finite interval of time and whenever, from practical considerations, the systems’ variables must lie within specific bounds, FTS is the only meaningful definition of stability. This overview will first present a short history of the development of the concept of FTS. Then it will present some important analysis and design results for linear, nonlinear, and stochastic systems. Finally some applications of the theory will be presented.