E. Milonidis

Response function for solar-energy collectors

Abstract The thermal behavior of a generalized solar-energy collector under transient operating conditions has been analyzed. The mathematical model employed is based on the collectors response function, which is an inherent characteristic. Due to the distribution of the fluid flow through a real collector. an analytical expression for this response function cannot easily be predicted. However, its magnitude can be readily obtained experimentally: with this, the analysis of experimental data—acquired during transient operating conditions—can then be facilitated. The method developed is applicable particularly when a step-by-step prediction of a collectors thermal behavior is required at small time intervals. This facilitates the accurate testing of solar-energy collectors under transient operating conditions. For longterm performance predictions, however, simplified models also provide satisfactory predictions. The presented analysis is not restricted to solar-energy collectors; it is also applicable to the transient thermal behavior of a wide range of open and distributed heat-processing systems. such as heat exchangers.

Structured transfer function matrices and integer matrices : the computation of the generic McMillan degree and infinite zero structure

The computation of the McMillan degree and structure at infinity of a transfer function model is considered for the family of early design models, referred to as Structured Transfer Function (STF) matrices. Such transfer functions have certain elements fixed to zero, some elements being constant and other elements expressing some identified dominant dynamics of the system. For the family of large dimension STF matrices the computation of the generic McMillan degree and structure at infinity are considered using genericity arguments which lead to optimization problems of integer matrices. A novel approach is introduced here that uses the notion of “irreducibility” of integer matrices, which is developed as the equivalent of irreducibility (properness) of polynomial matrices. This new notion provides the means for exploiting the structure of integer matrices and enables the termination of searching processes in a reduced number of steps, thus leading to an efficient new algorithm for the computation of the generic value of the McMillan degree and the structure at infinity of STFs. Links are made to standard optimization problems and to graph theory. The formulation of the optimization algorithm in terms of bipartite graphs offers better results and reduces the computational effort.

Structural Identification: The Computation of the Generic McMillan Degree

The McMillan degree of a transfer function model is one of the most important structural characteristics of a system. In this paper the problem of identifying the generic McMillan degree of a rational matrix is considered. The transfer function matrices of interest are those referred to as Structured Transfer Function (STF) matrices and have certain elements fixed to zero, some elements being constant and other elements expressing some identified dominant dynamics of the system. For the family of STF matrices the problem of determining the generic McMillan degree is considered using genericity arguments and an optimisation procedure based on path properties of nonnegative integer matrices. A novel approach is introduced that exploits the structure of integer matrices and this leads to an efficient new algorithm for computation of the generic value of the McMillan degree. Links are made to standard problems of optimisation and in particular to the optimal assignment problem. The problem examined here belongs to the general area of Structural Identification where the evaluation of structural characteristics of STF models is under investigation with robust computational methods. Such problems are of interest to large scale system studies.

Finite settling time stabilisation for multivariable discrete-time systems: a polynomial equation approach

The multivariable case of Finite Settling Time Stabilisation (FSTS) of linear discrete-time systems is considered in this paper. An algebraic approach is adopted which leads to the solution of a polynomial matrix Diophantine equation. This gives rise to the parametrisation of all FSTS controllers in a Kučera–Youla–Bonjiorno sense and the FSTS problem is further reduced to a linear algebra problem over the real numbers. Subsequently, the family of all causal FSTS controllers is parametrised, and necessary and sufficient conditions for strong FSTS (stable controllers) are derived. The minimal McMillan degree solution and minimal complexity controllers are examined and new bounds are given. The analysis provides the means for the parametrisation of families of FSTS controllers with certain complexity. Finally the problems of tracking, disturbance rejection and partially assigned dynamics in FST sense are considered and conditions for their solvability are given.

Simultaneous Finite Settling Time Stabilization: Some New Results

Abstract A special case of the simultaneous stabilization problem, namely the stabilization in Finite Settling Time (FST) sense of a family of discrete-time plants by a single compensator is examined in this paper. Necessary and/or sufficient solvability conditions for the general MIMO case are given and testable conditions for the case of vector plants are derived. Finally, the problem of simultaneous FST stabilization and tracking is considered for the case of vector plants.

A flexible visual inspection system based on neural networks

In this work, we propose a neural networks-based machine vision system, which is intended to act as a reconfigurable inspection tool, for use in manufacturing environments. The processing engine of the system is a second-order neural network, which extracts geometric features invariant to translation and rotation. A major issue with the use of higher-order neural networks is the combinatorial explosion of the higher-order terms, which is addressed here with the use of the alternative image representation strategy of coarse coding. We developed a genetic algorithms tool, which allows the automated determination of the optimal number of hidden units in the neural networks architecture. The inspection system is tested in two application areas, namely inspection of axisymmetric components and classification of rivets. Numerous tests are carried out to evaluate the robustness of the proposed system to complex noise sources.

LQR distributed cooperative control of a formation of low-speed experimental UAVs

The paper presents a cooperative scheme for controlling arbitrary formations of low speed experimental UAVs based on a distributed LQR design methodology. Each UAV acts as an independent agent in the formation and its dynamics are described by a 6-DOF (degrees of freedom) nonlinear model. This is linearized for control design purposes around an operating point corresponding to straight flight conditions and simulated only for longitudinal motion. It is shown that the proposed controller stabilizes the overall formation and can control effectively the nonlinear multi-agent system. Also, it is shown via numerous simulations that the system provides reference tracking and that is robust to environmental disturbances such as nonuniform wind gusts acting on a formation of four UAVs and to the loss of communication between two neighbouring UAVs.

Reduced sensitivity solutions to global linearisation of the pole assignment map

The problem of pole assignment, by static output feedback controllers has been tackled as far as solvability conditions and the computation of solutions when they exist by a powerful method referred to as global linearisation. This is based on asymptotic linearisation (around a degenerate point) of the pole placement map. The essence of the present approach is to reduce the multilinear nature of the problem to the solution of a linear set of equations. The solution is given in closed form in terms of a one-parameter family of static feedback compensators, for which the closed-loop poles approach the required ones as e → 0. The use of degenerate compensators makes the method numerically sensitive. This paper develops further the global linearisation framework by developing numerical techniques which make the method less sensitive to the use of degenerate solutions as the basis of the methodology. The proposed new computational framework for finding output feedback controllers improves considerably the sensitivity properties by using a predictor-corrector numerical method based on homotopy continuation. The modified method guarantees the maximum distance from the degenerate point. The current numerical method developed for the constant output feedback extends also to the case of dynamic output feedback.

Nearest common root of polynomials, approximate greatest common divisor and the structured singular value

In this paper the following problem is considered: given two coprime polynomials, find the smallest perturbation in the magnitude of their coefficients such that the perturbed polynomials have a common root. It is shown that the problem is equivalent to the calculation of the structured singular value of a matrix arising in robust control and a numerical solution to the problem is developed. A simple numerical example illustrates the effectiveness of the method for two polynomials of low degree. Finally, problems involving the calculation of the approximate greatest common divisor of univariate polynomials are considered, by proposing a generalization of the definition of the structured singular value involving additional rank constraints.

Structural Methods for Linear Systems: An Introduction

This paper assumes familiarity with the basic Control and Dynamics, as covered in undergraduate courses. It introduces the different alternative system representations for linear systems and provides a quick review of the fundamental mathematical tools, which are essential for the treatment of the more advanced notions in Linear Systems. The paper focuses on some fundamental concepts underpinning the study of linear systems and dynamics and which play a crucial role in the analysis and design of control systems; thus, the paper deals with notions such as those of Controllability, Observability, Stability, poles and zeros and re lated dynamics and their properties under different compensation schemes. There is a concrete flavour in the current approach which runs through this presentation and this is that of the underlying algebraic structure. The term “structure” refers to aspects of the state space/transfer function description, which remain invariant under a variety of transformations. The set of transformations considered here are of the compensation type and include state feedback and output injection, dynamic compensation, as well as of the representation type transformations that include state, input, and output co-ordinate transformations. This structure stems from the system description and defines the nature of the dynamics and the related geometric proper ties and these in turn define what it is possible to achieve under feedback; such an approach is known as a structural approach. Central to our analysis are the notions of poles and zeros. The poles of a system are crucial characteristics of the internal system dynamics, characterise system free response, stability and general aspects of the performance of a system. The poles of a system are affected by the different compensation schemes and their assignment is the subject of many design methodologies aiming at shaping the internal system dynamics under different compensation schemes. The notion of zeros is more complex, since they express the interaction between internal dynamics and the effort to control and observe the system and they are thus products of overall system design, that apart from process synthesis involves selection of actuation and measurement schemes for the system. The significance of zeros is mainly due to that they remain invariant under a large set of compensation schemes, as well as that they define limits of what can be achieved under compensation. This makes zeros crucial for design, since they are part of those factors characterising the potential of a given system to achieve certain design objectives under compensation. The invariance of zeros implies that their design is an issue that has to be addressed outside the traditional control design; this requires understanding of the zero formation process and involves early design stages mechanisms such as process instrumentation. Poles and zeros are conceptually inverse concepts (resonances, antiresonances) and such mechanisms are highlighted throughout the paper. The role of system structure in characterising different system properties is central to this paper and it is defined by a set of discrete and continuous invariants; these invariants characterise a variety of key system properties and their type/values define the structure of canonical forms and determine somehow the potential of a given system for compensation. Invariants and canonical forms under the general transformation group are linked to compensation theory, whereas those associated with representation transformations play a key role in system identification. The emphasis in this article is to provide an overview of the fundamentals concepts, the back ground mathematical tools, explain their dynamic significance and link them to problems of control and systems design.