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Robust output tracking control of a linear brushless DC motor with time-varying disturbances

IEE PROCEEDINGS-ELECTRIC POWER applications 2002年第1期149卷 39-45页

作者： Shieh, NC Tung, PC Lin, CL Natl Cent Univ Dept Mech Engn Chungli 32054 Taiwan Feng Chia Univ Dept Automat Control Engn Taichung 40724 Taiwan

Robust output tracking control of a linear brushless DC motor for transportation within a manufacturing system is presented. System identification for a linear motor with a driver is performed by a dynamic signal analyser, thus providing a linearised model for the motor. External disturbances corrupting the driver and modelling uncertainties due to payload variations and identification errors are considered. A tracking control scheme with a guaranteed H, tracking performance is proposed. It is shown that a state feedback control law achieving the desired objective can be obtained by solving a Riccati matrix equation. Computer simulation and experimental implementation are completed and compared. These results demonstrate the effectiveness of the proposed scheme for output tracking control of the linear brushless DC motor, and also confirm the feasibility of its implementation in industrial applications.

关键词： electric machine analysis computing linear motors dynamic signal analyser payload variations system identification Power engineering computing machine theory Riccati equations linear algebra (numerical analysis) H∞ control manufacturing system Optimal control control performance control simulation control design linear brushless DC motor time-varying disturbances transportation industrial applications control system synthesis Riccati matrix equation machine control H∞ tracking performance Control system design and analysis linear machines tracking Control system analysis and synthesis methods computer simulation numerical analysis robust output tracking control Control of electric power systems brushless DC motors d.c. machines robust control identification errors Stability in control theory control system analysis computing modelling uncertainties

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Computing a robust D-stability bound using a parameter-dependent Lyapunov approach

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IEE PROCEEDINGS-CONTROL theory AND applications 2002年第6期149卷 505-510页

作者： Bachelier, O Peaucelle, D Arzelier, D ESIP LAII F-86022 Poitiers France CNRS LAAS F-31077 Toulouse 4 France

The problem of robust matrix root-clustering against additive structured uncertainty is addressed. A bound on the size of the uncertainty domain preserving matrix D-stability is derived from an LMI approach. A recently proposed sufficient condition for robust matrix D-stability with respect to convex polytopic uncertainty is used. It is relevant to the framework dealing with parameter-dependent Lyapunov functions. Using this condition, the problem of computing the robustness bound is formulated as a generalised eigenvalue problem, that enables the bound value to be maximised.

关键词： robustness bound LMI approach feedback linear matrix inequalities control system analysis linear algebra (numerical analysis) robust D-stability bound sufficient condition stability convex polytopic uncertainty eigenvalues and eigenfunctions matrix D-stability additive structured uncertainty robust matrix root-clustering parameter-dependent Lyapunov approach Control system analysis and synthesis methods generalised eigenvalue problem robust control Stability in control theory

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Array algebra expansion of matrix and tensor calculus: Part 1

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SIAM JOURNAL ON MATRIX ANALYSIS AND applications 2002年第2期24卷 490-508页

作者： Rauhala, UA BAE SYST San Diego CA 92150 USA

Array algebra expands the foundations of linear and nonlinear estimation theories, differential and integral calculus, numerical analysis, and fast transform techniques. It originates from an extension of the two-dimensional Kronecker or tensor products and related operators of the traditional vector, matrix, and tensor calculus using the general theory of matrix inverses called "loop inverses." A summary of the foundations of multilinear array algebra and loop inverse estimation is presented in part 1 of this paper. It is then expanded to include the latest developments in nonlinear estimation and applied mathematics using some unified matrix and tensor operators. The new operators are used in part 2 to derive the general theory of direct solution (one "hyper" iteration) techniques of rank-deficient nonlinear systems as an expansion of the loop inverse estimators and Q-surface tensor solution.

关键词： multilinear array algebra tensor product loop inverse estimation fast transforms nonlinear array polynomials Q-surface nonlinear tensor methods decentered normals multigrid normals array relaxation

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Delay-dependent stability and output feedback stabilisation of Markov jump system with time-delay

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IEE PROCEEDINGS-CONTROL theory AND applications 2002年第5期149卷 379-386页

作者： Boukas, EK Liu, ZK Shi, P Ecole Polytech Dept Mech Engn Montreal PQ H3C 3A7 Canada Def Sci & Technol Org Land Operat Div Salisbury SA 5108 Australia

The stochastic stability and stabilisation problems of the Markov jump system (MJS) with time-delay under dynamical output feedback control law is considered. LMI-based sufficient conditions are established for the system to be stochastic stable and exponentially stable. A sufficient and necessary condition for the MJS to be stabilisable in the mean square quadratic stable sense, which implies the stochastic stability of the system, is established. An LMI-based control design method is proposed and a numerical example is included to show the usefulness of the theoretic results.

关键词： asymptotic stability stochastic systems numerical example feedback Time-varying control systems output feedback stabilisation stochastic stability linear matrix inequalities Markov jump system stability criteria sufficient necessary condition mean square quadratic stability Markov processes algebra dynamical output feedback control law control system synthesis exponential stability LMI-based control design method time-delay Control system analysis and synthesis methods delay-dependent stability delay systems LMI-based sufficient conditions Stability in control theory stochastic dynamic systems

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A unified theory for Krylov algorithms 5

A unified theory for Krylov algorithms

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5th International conference on Algorithms and Architectures for Parallel Processing

作者： Xie, G Inst. of Comput. Applications CAEP China

ISBN: (纸本)0769515126

Large systems of linear equations arise in many different scientific applications. For example, partial differential equations discretized with finite difference or finite element method yield system of equations Large systems can be solved with either sparse factorization techniques or with iterative methods These two approaches can be combined into a method that uses approximate factorization preconditioning for an iterative method Krylov algorithms are iterative numerical methods for large unsymmetric systems of linear equations In this paper, we set up a general theoretical framework for Krylov algorithms and so highlight their common essentials. As a Preparation work, we at first introduce the conception of orthogonality between linear subspaces We then formulate a unified definition for Krylov algorithms. On this basis, we study some of their common properties This work may give useful hints on formulating new better iterative methods for unsymmetric problems.

关键词： Iterative methods

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On the application of numerical continuation methods to the calculation of magnetostatic equilibria

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JOURNAL OF ATMOSPHERIC AND SOLAR-TERRESTRIAL PHYSICS 2002年第5-6期64卷 639-644页

作者： Romeou, Z Neukirch, T Univ St Andrews Sch Math & Stat St Andrews KY16 9SS Fife Scotland

Sequences of magnetostatic equilibria can often be used to model the quasi-static pre-eruptive energy storage phase of eruptive phenomena in e.g. Earth's magnetosphere or the solar corona. During these phases the systems evolve only due to slow changes in their environment, being practically in equilibrium on large scales. The eruption onset would then be identified with a bifurcation or catastrophe point in the solution diagram. Different energy storage mechanisms can be studied by different parameterizations of e.g. the boundary conditions. Also from the more fundamental point-of-view of the theory of dynamical systems, studying the possible stationary states and the bifurcation properties of plasma systems should be the first step towards a more thorough understanding of their full dynamical behaviour. In any case one will have to solve highly non-linear partial differential equations with the possibility of the existence of multiple solutions (or of none at all) for a given set of boundary conditions. Such problems can, in general, only be solved numerically. The most appropriate class of numerical algorithms for this type of problem are continuation methods which can calculate complete solution branches and detect bifurcation points. In this work a numerical bifurcation code based on a continuation method is presented. In addition to solving the non-linear magnetohydrostatic equations, the code can check a sufficient linear stability criterion for each solution. Some preliminary results for simple magnetohydrostatic equilibria are presented and potential future applications are discussed. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： magnetostatic equilibria numerical bifurcation continuation methods

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An algebraic preconditioning method for M-matrices:: linear versus non-linear multilevel iteration

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numerical linear algebra WITH applications 2002年第8期9卷 599-618页

作者： Kraus, JK Univ Leoben Dept Math Appl A-8700 Leoben Austria

In a recent work, the author introduced a robust multilevel incomplete factorization algorithm using spanning trees of matrix graphs (Proceedings of the 1999 International conference on Preconditioning Techniques for Large Sparse Matrix Problems in Industrial applications, Hubert H. Humphrey Center, University of Minnesota, 1999, 251-257). Based on this idea linear and non-linear algebraic multilevel iteration (AMLI) methods are investigated in the present paper. In both cases, the preconditioner is constructed recursively from the coarsest to finer and finer levels. The considered W-cycles only need diagonal solvers on all levels and additionally evaluate a second-degree matrix polynomial (linear case), or, perform nu inner GCG-type iterations (non-linear case) on every other level. This involves the same type of preconditioner for the corresponding Schur complement. The non-linear variant has the additional benefit of being free from any method parameters to be estimated. Based on the same type of approximation property similar convergence rates are obtained for linear and non-linear AMLI, even for a very small number nu of inner iterations, e.g. nu = 2.3. The presented methods are robust with respect to anisotropy and discontinuities in the coefficients of the PDEs and can also be applied to unstructured-grid problems. Copyright (C) 2002 John Wiley Sons, Ltd.

关键词： multilevel iteration hierarchical orderings preconditioning

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Computability of linear equations

IFIP Advances in Information and Communication Technology

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IFIP Advances in Information and Communication Technology 2002年 96卷 95-106页

作者： Brattka, Vasco Ziegler, Martin Theoretische Informatik 1 FernUniversität Hagen 58084 Hagen Germany Heinz Nixdorf Institute University of Paderborn 33095 Paderborn Germany

ISBN: (纸本)9781475752755

Do the solutions of linear equations depend computably on their coefficients? Implicitly, this has been one of the central questions in linear algebra since the very beginning of the subject and the famous Gauß algorithm is one of its numerical answers. Today there exists a tremendous number of algorithms which solve this problem for different types of linear equations. However, actual implementations in floating point arithmetic keep exhibiting numerical instabilities for ill-conditioned inputs. This situation raises the question which of these instabilities are intrinsic, thus caused by the very nature of the problem, and which are just side effects of specific algorithms. To approach this principle question we revisit linear equations from the rigorous point of view of computability. Therefore we apply methods of computable analysis, which is the Turing machine based theory of computable real number functions. It turns out that, given the coefficients of a system of linear equations, we can compute the space of solutions, if and only if the dimension of the solution space is known in advance. Especially, this explains why there cannot exist any stable algorithms under weaker assumptions.

关键词： linear equations

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A unified theory for Krylov algorithms

A unified theory for Krylov algorithms

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IEEE International conference on Algorithms and Architectures for Parallel Processing (ICAP)

作者： Gang Xie Institute of Computer Applications CAEP China

ISBN: (纸本)0769515126

Large systems of linear equations arise in many different scientific applications. For example, partial differential equations discretized with the finite difference or finite element method yield a system of equations. Large systems can be solved with either sparse factorization techniques or iterative methods. These two approaches can be combined into a method that uses approximate factorization preconditioning for an iterative method. Krylov algorithms are iterative numerical methods for large unsymmetric systems of linear equations. In this paper, we set up a general theoretical framework for Krylov algorithms and so highlight their common features. We first introduce the conception of orthogonality between linear subspaces. We then formulate a unified definition for Krylov algorithms. On this basis, we study some of their common properties. This work may give useful hints on formulating new better iterative methods for unsymmetric problems.

关键词： Iterative methods Iterative algorithms Differential equations Partial differential equations Finite difference methods Finite element methods Difference equations Gradient methods Computer applications Application software

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Right coprime factorisations using system upper Hessenberg forms - the multi-input system case

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IEE PROCEEDINGS-CONTROL theory AND applications 2001年第6期148卷 433-441页

作者： Duan, GR Queens Univ Belfast Sch Mech & Mfg Engn Belfast BT9 5AH Antrim North Ireland Harbin Inst Technol Dept Control Engn Ctr Control Theory & Guidance Technol Harbin 150006 Peoples R China

Based on a method for right coprime factorisations of linear systems using matrix elementary transformations, it is shown that a very simple iteration formula exists for right coprime factorisations of multi-input linear systems in system upper Hessenberg forms. This formula gives directly the coefficient matrices of the pair of solutions to the right coprime factorisation of the system Hessenberg form, and involves only inverses of a few triangular matrices and some matrix products and summations. Based on this formula, a simple, efficient procedure for determining a right coprime factorisation of a multi-input linear system is proposed., which first converts a given linear system into its system Hessenberg form using some orthogonal similarity transformations and then applies the iteration formula to the converted system Hessenberg form. An example demonstrates the use of the approach.

关键词： algebra iterative methods iterative method Interpolation and function approximation (numerical analysis) controllability coprime factorisations triangular matrix Hessenberg forms matrix algebra Control system analysis and synthesis methods linear systems

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