This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material. The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the engineering properties of the regulator. Topics include degree of stability, phase and gain margin, tolerance of time delay, effect of nonlinearities, asymptotic properties, and various sensitivity problems. The third section explores state estimation and robust controller design using state-estimate feedback. Numerous examples emphasize the issues related to consistent and accurate system design. Key topics include loop-recovery techniques, frequency shaping, and controller reduction, for both scalar and multivariable systems. Self-contained appendixes cover matrix theory, linear systems, the Pontryagin minimum principle, Lyapunov stability, and the Riccati equation. Newly added to this Dover edition is a complete solutions manual for the problems appearing at the conclusion of each section.

Optimal Control: Linear Quadratic Methods

A broad generalization of memristors--a recently postulated circuit element--to an interesting class of nonlinear dynamical systems called memristive systems is introduced. These systems are unconventional in the sense that while they behave like resistive devices, they can be endowed with a rather exotic variety of dynamic characteristics. While possessing memory and exhibiting small-signal inductive or capacitive effects, they are incapable of energy discharge and they introduce no phase shift between the input and output waveforms. This zero-crossing property gives rise to a Lissajous figure which always passes through the origin. Memristive systems are hysteretic in the sense that their Lissajous figures vary with the excitation frequency. At very low frequencies, memristive systems are indistinguishable from nonlinear resistors while at extremely high frequencies, they reduce to linear resistors. These anomalous properties have misled and prevented the identification of many memristive devices and systems-including the thermistor, the Hodgkin-Huxley membrane circuit model, and the discharge tubes. Generic properties of memristive systems are derived and a canonic dynamical system model is presented along with an explicit algorithm for identifying the model parameters and functions.

Memristive devices and systems

This paper describes an algorithm for generating provably passive reduced-order N-port models for RLC interconnect circuits. It is demonstrated that, in addition to macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and passive driver/load models are connected. The approach proposed here, PRIMA, is a general method for obtaining passive reduced-order macromodels for linear RLC systems. In this paper, PRIMA is demonstrated in terms of a simple implementation which extends the block Arnoldi technique to include guaranteed passivity while providing superior accuracy. While the same passivity extension is not possible for MPVL, comparable accuracy in the frequency domain for all examples is observed.

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PRIMA: passive reduced-order interconnect macromodeling algorithm

The paper is concerned with the problem of synthesis of (passive) mechanical one-port networks. One of the main contributions of the paper is the introduction of a device, which win be called the inerter, which is the true network dual of the spring. This contrasts with the mass element which, by definition, always has one terminal connected to ground. The inerter allows electrical circuits to be translated over to mechanical ones in a completely analogous way. The inerter need not have large mass. This allows any arbitrary positive-real impedance to be synthesized mechanically using physical components which may be assumed to have small mass compared to other structures to which they may be attached. The possible application of the inerter is considered to a vibration absorption problem, a suspension strut design, and as a simulated.

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Synthesis of mechanical networks: the inerter

The basic concepts and building blocks in multirate digital signal processing (DSP), including the digital polyphase representation, are reviewed. Recent progress, as reported by several authors in this area, is discussed. Several applications are described, including subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion (such as in digital audio), digital crossover networks, and multirate coding of narrowband filter coefficients. The M-band quadrature mirror filter (QMF) bank is discussed in considerable detail, including an analysis of various errors and imperfections. Recent techniques for perfect signal reconstruction in such systems are reviewed. The connection between QMF banks and other related topics, such as block digital filtering and periodically time-varying systems, is examined in a pseudo-circulant-matrix framework. Unconventional applications of the polyphase concept are discussed. >

/pdf/multirate-digital-filters-filter-banks-polyphase-networks-3tw69k99m1.pdf

Louis Weinberg

Papers

Network Analysis and Synthesis