Linear Lumped Parameter Research Articles

Optimal control for a class of distributed parameter systems where the cost functions are norms

Some problem in optimal control, for a class of linear distributed parameter systems, are posed. By using a theorem of approximation theory, a maximum principle, which is applicable to these optimal control problems, is given. It is shown, that for the problems posed in this paper, this maximum principle is an extension of Butkovskii's maximum principle and of Demyanov and Rubinov's theorem. In addition, two optimal control problems, in linear lumped parameter systems areposed. For these problems it is shown that the maximum principle given in this paper, is an extension of Pontryagin's maximum principle.

Direct interpretation methods in applied geophysics

In contrast to the use of master curves and other trial-and-error processes, the direct methods of interpreting geophysical data are based on computational procedures which yield the unknowns in a more direct way. The present paper emphasizes the usefulness of these methods, and it is shown that they are closely related to the methods of electrical network synthesis. The driving point exploration and synthesis of linear lumped parameter ladders on the basis of continued fraction expansions is shown in some detail. An analogous procedure is applied to systems with distributed parameters. It is shown that the interpretation of D.C. conduction data obtained in the case of a horizontally stratified earth is equivalent to the driving point synthesis of an elastic bar composed of homogeneous sections and capable of longitudinal displacements. Similarly, the interpretation of magneto-telluric data is equivalent to the driving point synthesis of an electric line composed of sections with constant specific inductance and specific resistance. Formal solutions of the synthesis problems involved are given, and further geophysical cases are discussed.

The synthesis of nearly optimal on-off controllers with application to chemical processes

A new technique is presented for designing a set of on-off controllers for processes which can be approximated by linear-lumped parameter models of any order. The design is based on the minimization of a quadratic function of the process outputs. Each higher member of the set of systems approaches optimal control ever more closely. Our major concern, however, is with the lowest member of the set which is implemented by using only a relay and a simple summing device. Several analog computer examples are presented using this control scheme. In all cases, the system response is excellent from both quantitative and qualitative viewpoints. One of the examples presented is the control of a simulated six stage liquid—liquid extraction unit. Here, the lowest level control is shown to outperform an experimentally tuned standard three-mode type of control as well as a control strategy based on dynamic programming which was developed for the same process by a previous investigator.

On the Stability of Solutions of Linear Differential Equations with Periodic Coefficients

Previous article Next article On the Stability of Solutions of Linear Differential Equations with Periodic CoefficientsI. W. SandbergI. W. Sandberghttps://doi.org/10.1137/0112041PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Jack K. Hale, Oscillations in nonlinear systems, McGraw-Hill Book Co., Inc., New York, 1963, 21– MR0150402 (27:401) 0115.07401 Google Scholar[2] I. W. Sandberg, On the properties of some systems that distort signals-II, BSTJ, (1964), 91–, January Google Scholar[3] J. J. Bongiorno, Jr., An extension of the Nyquist-Barkhausen stability criterion to linear lumped-parameter systems, IEEE-PGAC, (1963), 170–, April Google Scholar[4] R. E. Kalman, Lyapunov functions for the problem of Lur' e in automatic control, Proc. Nat. Acad. Sci. U.S.A., 49 (1963), 201–205 MR0151696 (27:1680) 0113.07701 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Instability of Periodically Time-Varying Linear Control SystemsSIAM Journal on Control, Vol. 6, No. 1 | 18 July 2006AbstractPDF (789 KB) Volume 12, Issue 2| 1964Journal of the Society for Industrial and Applied Mathematics249-497 History Submitted:23 September 1963Published online:28 July 2006 InformationCopyright © 1964 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0112041Article page range:pp. 487-496ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

Analysis of linear distributed systems with random parameters and inputs

This paper is concerned with the statistical analysis of first-order linear distributed-parameter systems with random parameters and random inputs. In both cases, Gaussian processes are assumed. This work essentially extends the statistical theory available for analyzing random linear lumped-parameter systems to a restricted class of distributed-parameter systems.

An extension of the Nyquist-Barkhausen stability criterion to linear lumped-parameter systems with time-varying elements

An extension of the Nyquist-Barkhausen stability criterion to linear lumped-parameter systems with time-varying elements

D-decomposition analysis of automatic control systems

Development of the basic theory of D-decomposition by a general polynomial expression, the characteristic function of a linear lumped parameter automatic control system, is followed by account of: the basic theory of parametric stability; unity-feedback variable-gain analysis, with subsequent generalization to numeric and frequency-dependent feedback; transient response determination; and sampled-data system analysis, as effected by D-decomposition theory. Application of theory in practice is illustrated by numerous illustrative examples.