Showing papers by "Brian D. O. Anderson published in 1993"
TL;DR: In this article, a new approach is given for the design of adaptive robust control in the frequency domain, starting with an initial model of a stable plant and a robust stabilizing controller, the new (windsurfer) approach allows the bandwidth of the closed-loop system to be increased progressively through an iterative controlrelevant system identification and control design procedure.
Abstract: A new approach is given for the design of adaptive robust control in the frequency domain. Starting with an initial model of a stable plant and a robust stabilizing controller, the new (windsurfer) approach allows the bandwidth of the closed-loop system to be increased progressively through an iterative control-relevant system identification and control design procedure. The method deals with both undermodelling and measurement noise issues. Encouraging results are obtained in the simulations that illustrate the new idea.
164 citations
TL;DR: It is suggested that modern controller design packages often fall short of offering what is truly practical: lower order controllers, discrete-time controllers operating in a sampled-data loop, and finite word length realizations of controllers with the FWL property minimally impacting closed-loop performance.
Abstract: It is suggested that modern controller design packages often fall short of offering what is truly practical: lower order controllers, discrete-time controllers operating in a sampled-data loop, and finite word length (FWL) realizations of controllers with the FWL property minimally impacting closed-loop performance. Several methods for achieving these objectives are considered. The methods deal with controller complexity, transfer function matching, stability robustness, signal spectrum matching, fractional representations of open-loop unstable controllers, discrete time controllers, and realizing digital controllers. >
131 citations
TL;DR: In this article, a finite-dimensional state-space representation is obtained where the states are the transverse displacements of the array from linearity in either the horizontal or vertical plane.
Abstract: The dynamical behavior of a thin flexible array towed through the water is described by the Paidoussis equation. By discretizing this equation in space and time a finite-dimensional state-space representation is obtained where the states are the transverse displacements of the array from linearity in either the horizontal or vertical plane. The form of the transition matrix in the state-space representation describes the propagation of transverse displacements down the array. The outputs of depth sensors and compasses located along the array are shown to be related in a simple, linear manner to the states. From this state-space representation a Kalman filter which recursively estimates the transverse displacements and hence the array shape is derived. It is shown how the properties of the Kalman filter reflect the physics of the propagation of motion down the array. Solutions of the Riccati equation are used to predict the mean square error of the Kalman filter estimates of the transverse displacements. >
58 citations
TL;DR: The convergence properties of this class of blind algorithms under practical constraints common to a variety of channel equalization applications that violate these idealized conditions are studied and show that, in practice, when the equalizer is finite-dimensional and/or the input is discrete theequalizer parameters may converge to parameter settings that fail to achieve the objective of approximating the channel inverse.
Abstract: An early use of recursive identification in blind adaptive channel equalization is an algorithm developed by Y. Sato (1975). An important generalization of the Sato algorithm with extensive analysis appears in the work of A. Benveniste et al. (1980). These generalized algorithms have been shown to possess a desirable global convergence property under two idealized conditions. The convergence properties of this class of blind algorithms under practical constraints common to a variety of channel equalization applications that violate these idealized conditions are studied. Results show that, in practice, when the equalizer is finite-dimensional and/or the input is discrete (as in digital communications) the equalizer parameters may converge to parameter settings that fail to achieve the objective of approximating the channel inverse. It is also shown that a center spike initialization is insufficient to guarantee avoiding such ill-convergence. Simulations verify the analytical results. >
41 citations
TL;DR: Dropping the requirement of gain identification allows equalizer anchoring, and results in the elimination of a degree of freedom that causes ill-convergence of conventional blind equalizers, and affords the possibility of using simple update rules based on the stochastic approximation of output energy.
Abstract: Blind equalization up to a constant gain of linear time-invariant channels is studied. Dropping the requirement of gain identification allows equalizer anchoring. This results in the elimination of a degree of freedom that causes ill-convergence of conventional blind equalizers, and affords the possibility of using simple update rules based on the stochastic approximation of output energy. Unlike conventional blind equalizers, truncations of the nonrecursive infinite-dimensional realizations of those equalizers inherit the convergence properties of their infinitely parametrized counterparts. A globally convergent blind recursive equalizer for channels without all-pass sections is obtained based on the exact equalization of the minimum-phase part of the channel and the identification of its nonminimum-phase zeros. >
37 citations
15 Dec 1993
TL;DR: In this article, it is shown that, given a stable strictly proper model, the windsurfer approach to adaptive robust control can improve the performance robustness of the closed-loop system.
Abstract: In this paper it is shown that, given a stable strictly proper model of a stable strictly proper plant, we can improve the performance robustness of the closed-loop system through the windsurfer approach to adaptive robust control if the deterioration in performance robustness caused by increasing the closed-loop bandwidth resulted in a sufficiently high signal-to-noise ratio for a certain closed-loop output error. This is the key conclusion arising from an examination of a series of questions about the procedure that focus on what one would like to do, and what one can do. Situations that may cause the iterative identification and control design process in the windsurfer approach to terminate prematurely are also indicated. >
29 citations
TL;DR: A theory is developed to explain gross convergence properties observed through simulations of the stochastic dynamics of the blind adaptation of decision feedback equalizers and the potential capture by local minima shows the importance of good initialization.
Abstract: SUMMARY An analysis of the stochastic dynamics of the blind adaptation of decision feedback equalizers is presented. The analysis accounts for the presence of decision errors which, under feedback, are propagated. A number of blind algorithms are presented and a theory is developed to explain gross convergence properties observed through simulations. The possibility of and mechanism behind undesirable local minima are highlighted and a detailed case study is given. The potential capture by local minima shows the importance of good initialization. These results superficially resemble those obtained for blind adaptation applied to linear equalizers.
27 citations
TL;DR: In this article, the robustness of interval polynomials is proved using the second method of Lyapunov, where the Hermite matrix is taken as the matrix of the quadratic form, which is used as a LyAPunov function to prove Hurwitz stability.
16 citations
TL;DR: In this article, techniques from the theory of additive Hankel norm approximation and spectral factorization are synthesized to produce a multiplicative approximant of a possibly unstable or non-square plant.
Abstract: In control system design, specifications are commonly given in terms of log-magnitude quantities (i.e. decibels). This description induces a multiplicative or relative error criterion for plant model reduction. Techniques from the theory of additive Hankel norm approximation and spectral factorization are synthesized to produce a multiplicative approximant of a possibly unstable or non-square plant. It is shown that the reduced-order model preserves the unstable poles and right half-plane zeros of the original system. Explicit state-space formulae are provided for the construction of the reduced-order model and its error properties are discussed. The method is illustrated by a numerical example.
12 citations
15 Dec 1993
TL;DR: In this article, a two-degree of freedom filter for the internal model control (IMC) method is proposed to alleviate some disadvantages of the standard IMC filter when applied to unstable plants that do not have nonminimum phase zeros.
Abstract: In this paper we study the design of a two-degree of freedom filter for the internal model control (IMC) method. The new filter alleviates some disadvantages of the standard IMC filter when the IMC method is applied to unstable plants that do not have nonminimum-phase zeros. We show that by employing the new filter, the resulting system has a flatter frequency response and little overshoot in the step response. Furthermore one of the filter's design parameters can be related directly to the closed-loop bandwidth and the other design parameter can be used to control the recovery time of the step response, after an overshoot has occurred. These features are important when the IMC method is employed in a new approach to adaptive robust control. Examples are given in the paper to illustrate the new filter design. >
7 citations
02 Jun 1993
TL;DR: In this paper, necessary and sufficient conditions are derived for the existence of H∞ controllers for a class of linear, time-invariant generalized plants which is excluded by the assumptions generally made in the solution of H ∞ problems.
Abstract: Necessary and sufficient conditions are derived for the existence of H∞ controllers for a class of linear, time-invariant generalized plants which is excluded by the assumptions generally made in the solution of H∞ problems. The assumptions relaxed in this work concern the comparative dimensions of the plant's input and output spaces.
TL;DR: In this paper, a dual-observer-based compensator is proposed to realize the pole-positioning effect of output injection in a discrete-time system, where linear combinations of the output measurements are fed directly into the plant's state.
Abstract: Output injection feedback is a special kind of pole-positioning mechanism whereby linear combinations of the output measurements are fed directly into the plant's state. Using this mechanism, arbitrary closed-loop pole assignment can be achieved so long as the plant is completely observable. In the event that output injection feedback is not possible, a dual-observer-based compensator can be used to realize the pole-positioning effect of output injection. In this paper, we consider discrete-time systems and derive the equivalent dual-observer-based compensator, herein termed a single-rate input compensator. Further, we explore the concept of multirate input sampling and show that a multirate input compensator (employing multirate sampling of the plant input) of dimension much smaller than that of the single-rate input compensator (employing single-rate input sampling of the plant input) can be designed. Necessary and sufficient conditions for the existence of both types of compensators are found....
15 Dec 1993
TL;DR: In this article, it was shown that the set of matrices whose characteristic polynomials also lie in a polytopic set is strictly positive real if the Lyapunov matrices solving the equations featuring the Kalman-Yakubovic-Popov Lemma are multiaffinely parameterized.
Abstract: This paper has three contributions. The first involves polytopes of matrices whose characteristic polynomials also lie in a polytopic set (e.g. companion matrices). We show that this set is Hurwitz or Schur invariant if there exist multiaffinely parameterized positive definite Lyapunov matrices which solve an augmented Lyapunov equation. The second result concerns uncertain transfer functions with denominator and numerator belonging to a polytopic set. We show all members of this set are strictly positive real if the Lyapunov matrices solving the equations featuring the Kalman-Yakubovic-Popov Lemma are multiaffinely parameterized. Moreover, under an alternative characterization of the underlying polytopic sets, the Lyapunov matrices for both of these results admit affine parameterizations. Finally, we apply the Lyapunov equation results to derive stability conditions for a class of linear time-varying systems. >
15 Dec 1993
TL;DR: In this paper, the problem of controller order reduction aimed at preserving the closed-loop performance of a sampled-data closedloop system is investigated, and weighted balanced truncation is used to reduce the controller.
Abstract: The problem of controller order reduction aimed at preserving the closed-loop performance of a sampled-data closed-loop system is investigated. Fast sampling of the system at a multiple of the sampling frequency followed by lifting allows capturing of the system's inter-sample behaviour (albeit with small error) and yields a time-invariant single-rate system; this then permits standard order reduction ideas to be applied. Special weighting functions aimed at preserving the closed-loop transfer function are obtained and weighted balanced truncation is used to reduce the controller. >
TL;DR: In this paper, the controllability indices in a minimal state-space realization of a real rational transfer matrix may be calculated from evaluations of this transfer matrix at a sufficient number of discrete points in the frequency domain.
TL;DR: In this paper, an adaptive control algorithm is proposed for systems with unknown physical element values, where the parameters enter the numerator and denominator polynomials of the system transfer function in a multilinear fashion.
Abstract: An adaptive control algorithm is proposed for systems with unknown physical element values. These parameters enter the numerator and denominator polynomials of the system transfer function in a multilinear fashion. The algorithm developed is shown to be globally stable with uniformly asymptotic parameter convergence.
Book•
01 Jan 1993
TL;DR: The fundamentals of discrete time systems as discussed by the authors have been downloaded hundreds of times for their chosen books like this, but end up in infectious downloads, rather than enjoying a good book with a cup of tea in the afternoon, instead they cope with some malicious bugs inside their computer.
Abstract: Thank you very much for downloading fundamentals of discrete time systems a tribute to professor eliahu i jury. As you may know, people have look hundreds times for their chosen books like this fundamentals of discrete time systems a tribute to professor eliahu i jury, but end up in infectious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they cope with some malicious bugs inside their computer.
TL;DR: The emulation of a nonadaptive, binary, decision-feedback equalizer, operating on a noiseless, finite impulse response channel, by a feedforward multilayer processor is considered to obtain a tight upper bound on the probability of error as a function of the number of layers, using the theory of finite-state Markov processes.
Abstract: The emulation of a nonadaptive, binary, decision-feedback equalizer, operating on a noiseless, finite impulse response channel, by a feedforward multilayer processor is considered. This feedforward perceptron equalizer comprises a triangular array of bandlimiting processing elements. The functional similarity between the two systems is exploited to obtain a tight upper bound on the probability of error as a function of the number of layers, using the theory of finite-state Markov processes. >
02 Jun 1993
TL;DR: This simple problem set-up is prototypical of the interplay between system identification and robust control design and the effect of unmodeled dynamics on the resulting closed-loop system designed on the basis of the estimated transfer function.
Abstract: Precise, finite-data statistical propereties are determined using a least-square estimator baed on an output error model with an affine parameter representation where the true system is of output error form, but is not in the model set. The purpose of the analysis is to show the effect of unmodeled dynamics on the resulting closed-loop system designed on the basis of the estimated transfer function. This simple problem set-up is prototypical of the interplay between system identification and robust control design.
TL;DR: Control engineering is a discipline that has in part been driven by practice, in part by theory as mentioned in this paper, and the earliest drivers were applications problems in the field of time measurement, mills and steam engine speed control.
Abstract: Control engineering is a discipline that has in part been driven by practice, in part by theory. The earliest drivers were applications problems in the field of time measurement, mills and steam engine speed control. Major control tasks included control with zero steady state error, and achieving fast response to a step change, without instability or excessive overshoot. Work late in the 19th century provided the first formal solution to the stability problem, and an understanding of the value of integral control. A seventh order water turbine system had been successfully, and scientifically, controlled, by 1900.In the first half of the 20th century, electronic amplifier design and then the second world war gave much impetus to the development of control engineering. The methods developed for design were predominantly graphical, and involved adjustment of only a few parameters. The role of high gain, proportional, integral and derivative control all became understood and control engineering ideas found applications throught chemical and mineral industries.Theoretical developments in the second half of this century have been substantial. Many took some years to be translated into practice, such as LQG design, adaptive control and sampled data control. Aerospace applications requirements drove some of these developments, many of which are now finding their place also in materials processing and handling systems, as diverse as sugar cane mills and chemical process control.Future developments will arise from applications pressure, and theoretical work. Applications pressure is strong in the areas of robotics, automobiles, discrete-event systems, environmental control ; replacement of existing nonadaptive by adaptive systems will be widespread. Theoretical developments will occur in many areas including nonlinear systems, robust control design and, perhaps, use of time-varying controllers for time-invariant plants.