Control of large-scale dynamic systems by aggregation
TL;DR: Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived and questions of performance degradation and of stability of such suboptimally controlled systems are answered.
Abstract: A method is proposed to obtain a model of a dynamic system with a state vector of high dimension. The model is derived by "aggregating" the original system state vector into a lower-dimensional vector. Some properties of the aggregation method are investigated in the paper. The concept of aggregation, a generalization of that of projection, is related to that of state vector partition and is useful not only in building a model of reduced dimension, but also in unifying several topics in the control theory such as regulators with incomplete state feedback, characteristic value computations, model controls, and bounds on the solution of the matrix Riccati equations, etc. Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived. Questions of performance degradation and of stability of such suboptimally controlled systems are also answered in the paper.
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DOI•
01 Jan 1984TL;DR: In this article, a decomposition method for large power systems is proposed, by analyzing and quantifying the dynamic interactions among the generating units on the basis of a linearised model, a natural subdivision which reflects the structural features of the system.
Abstract: The paper describes the development of a decomposition method which exploits the structure of large power systems. As large power systems are almost invariably composed of weakly connected subsystems, each consisting of strongly interacting machines, the proposed decomposition technique provides, by analysing and quantifying the dynamic interactions among the generating units on the basis of a linearised model, a natural subdivision which reflects the structural features of the system. The method is rigorous and can be carried out systematically. The resulting decomposition scheme can be used to simplify the stability analysis of large power systems under both small and large disturbances. The capability and the usefulness of the proposed method are illustrated by carrying out simulation studies on a sample power system.
2 citations
TL;DR: A time decomposition technique is suggested for large-database (DB) models and the problem of network aggregation is studied and the results used to create a meaningful decomposed model are studied.
Abstract: A time decomposition technique is suggested for large-database (DB) models. The problem of network aggregation is studied and the results used to create a meaningful decomposed model. Decomposition conditions and assumptions are discussed and illustrated by examples. A practical operating schedule is presented for the time-separated DB model. The schedule uses a sequence of decomposed models, which are to be constructed recursively. The application of the time separation technique for large-DB models is presented in the form of a closed-loop algorithm. The problem of decomposition stability with respect to variations in time constants is considered as well. Two alternative approaches to the problem are suggested. For a probabilistic approach, practical approximate formulas are obtained for subsystem time constants and recommendations are made with respect to the decomposition structure. An approximate performance analysis is done for both standard and time-decomposed models. A comparison of the results is given.
2 citations
01 Sep 2015
TL;DR: In this article, a new method of model order reduction technique for interval system is proposed, where the reduced order denominator coefficients are determined by combined benefits of reciprocal transformation, principal pseudo break frequency and a method of eigen spectrum analysis.
Abstract: A new method of model order reduction technique for interval system is proposed here. The reduced order denominator coefficients are determined by combined benefits of reciprocal transformation, principal pseudo break frequency and a new method of eigen spectrum analysis. Then the reduced order numerator coefficients are obtained using polynomial coefficient matching method. Optimization method can also be used for determining the coefficients of reduced order numerator. In this paper Luus -- Jaakola optimization technique is tried. This method guaranteed a stable reduced order model for the stable higher order system along with performance matching. The illustrated examples using MATLAB simulation show the effectiveness of the proposed method.
2 citations
Cites methods from "Control of large-scale dynamic syst..."
...Pade approximation [4], Routh approximation [5], Aggregation method [6] etc....
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Dissertation•
24 Nov 2010
TL;DR: In this paper, the authors propose an approach to estimate the position of a source by using the notion of transmittance entre deux capteurs, which correspond to the response of a capteur quelconque.
Abstract: Cette etude est consacree au probleme inverse d’estimation de l’intensite et de la position d’une source de polluant. Nous inversons tout d’abord des mesures de concentration a l’interieur d’une chambre a sable(extension des egouts souterrain) en utilisant la methode d’identification modale pour estimer l’intensite d’emission du gaz H2S. Une approche originale est ensuite proposee pour estimer la position d’une source en utilisant la notion de transmittance entre deux capteurs. Des outils de regularisation sont utilises afin d’estimer chaque transmittance, dont le produit de convolution avec la concentration d’un capteur choisi comme reference correspond a la reponse d’un capteur quelconque. Les transmittances estimees a partir des signaux de concentration simules dans une configuration d’un ecoulement tunnel avec source ponctuelle sont ensuite comparees a la sortie d’un modele analytique 1D de l’equation de transport.L’utilisation d’un algorithme de minimisation non lineaire a permis d’estimer d’abord la vitesse et le coefficient de diffusion de l’ecoulement et ensuite la position de la source, sous certaines hypotheses
2 citations
Cites background from "Control of large-scale dynamic syst..."
...De nombreuses méthodes de réduction de systèmes linéaires ont été développées au cours des dernières décennies, on peut ainsi citer les travaux de [Marshall, 1966], [Aoki, 1968], [Litz, 1981], [Moore, 1981], [Eitelberg, 1982], [Oulefki and Neveu, 1993], [Petit et al., 1997]....
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...De nombreuses méthodes de réduction de systèmes linéaires ont été développées au cours des dernières décennies, on peut ainsi citer les travaux de [Marshall, 1966], [Aoki, 1968], [Litz, 1981], [Moore, 1981], [Eitelberg, 1982], [Oulefki and Neveu, 1993], [Petit et al....
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TL;DR: In this paper, a new reduction method is proposed to reduce the higher order interval system, which is achieved based on the differentiation method using the Kharitonov's theorized method.
Abstract: A new reduction method is proposed to reduce the higher order interval system. The proposed reduced-order interval model is achieved based on the differentiation method using the Kharitonov’s theor...
2 citations
References
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TL;DR: A technique is presented for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs representing its several parts and a coordinating program that is obtained from the parts by linear transformations.
Abstract: A technique is presented for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs representing its several parts and a coordinating program that is obtained from the parts by linear transformations. The coordinating program generates at each cycle new objective forms for each part, and each part generates in turn from its optimal basic feasible solutions new activities columns for the interconnecting program. Viewed as an instance of a “generalized programming problem” whose columns are drawn freely from given convex sets, such a problem can be studied by an appropriate generalization of the duality theorem for linear programming, which permits a sharp distinction to be made between those constraints that pertain only to a part of the problem and those that connect its parts. This leads to a generalization of the Simplex Algorithm, for which the decomposition procedure becomes a special case. Besides holding promise for the efficient computation of large-scale systems, the principle yields a certain rationale for the “decentralized decision process” in the theory of the firm. Formally the prices generated by the coordinating program cause the manager of each part to look for a “pure” sub-program analogue of pure strategy in game theory, which he proposes to the coordinator as best he can do. The coordinator finds the optimum “mix” of pure sub-programs using new proposals and earlier ones consistent with over-all demands and supply, and thereby generates new prices that again generates new proposals by each of the parts, etc. The iterative process is finite.
2,281 citations
01 Jan 1960
TL;DR: In this article, the authors considered the problem of least square feedback control in a linear time-invariant system with n states, and proposed a solution based on the concept of controllability.
Abstract: THIS is one of the two ground-breaking papers by Kalman that appeared in 1960—with the other one (discussed next) being the filtering and prediction paper. This first paper, which deals with linear-quadratic feedback control, set the stage for what came to be known as LQR (Linear-Quadratic-Regulator) control, while the combination of the two papers formed the basis for LQG (Linear-Quadratic-Gaussian) control. Both LQR and LQG control had major influence on researchers, teachers, and practitioners of control in the decades that followed. The idea of designing a feedback controller such that the integral of the square of tracking error is minimized was first proposed by Wiener [17] and Hall [8], and further developed in the influential book by Newton, Gould and Kaiser [12]. However, the problem formulation in this book remained unsatisfactory from a mathematical point of view, but, more importantly, the algorithms obtained allowed application only to rather low order systems and were thus of limited value. This is not surprising since it basically took until theH2-interpretation in the 1980s of LQG control before a satisfactory formulation of least squares feedback control design was obtained. Kalman’s formulation in terms of finding the least squares control that evolves from an arbitrary initial state is a precise formulation of the optimal least squares transient control problem. The paper introduced the very important notion of c ntrollability, as the possibility of transfering any initial state to zero by a suitable control action. It includes the necessary and sufficient condition for controllability in terms of the positive definiteness of the Controllability Grammian, and the fact that the linear time-invariant system withn states,
1,451 citations
TL;DR: A method is proposed for reducing large matrices by constructing a matrix of lower order which has the same dominant eigenvalues and eigenvectors as the original system.
Abstract: Often it is possible to represent physical systems by a number of simultaneous linear differential equations with constant coefficients, \dot{x} = Ax + r but for many processes (e.g., chemical plants, nuclear reactors), the order of the matrix A may be quite large, say 50×50, 100×100, or even 500×500. It is difficult to work with these large matrices and a means of approximating the system matrix by one of lower order is needed. A method is proposed for reducing such matrices by constructing a matrix of lower order which has the same dominant eigenvalues and eigenvectors as the original system.
614 citations
TL;DR: In this article, a constructive design procedure for the problem of estimating the state vector of a discrete-time linear stochastic system with time-invariant dynamics when certain constraints are imposed on the number of memory elements of the estimator is presented.
Abstract: The paper presents a constructive design procedure for the problem of estimating the state vector of a discrete-time linear stochastic system with time-invariant dynamics when certain constraints are imposed on the number of memory elements of the estimator. The estimator reconstructs the state vector exactly for deterministic systems while the steady-state performance in the stochastic case may be comparable to that obtained by the optimal (unconstrained) Wiener-Kalman filter.
68 citations
67 citations