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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01 Jan 2021
TL;DR: The paper introduced a model reduction algorithm based on Schur analysis to preserve the dominant points of the original system in the reduced system through the use of SchurAnalysis to arrange the polar points in descending order of dominance on the main diagonal of the upper triangular matrix A.
Abstract: The paper introduced a model reduction algorithm based on Schur analysis. The main idea of the algorithm is to preserve the dominant points of the original system in the reduced system through the use of Schur analysis to arrange the polar points in descending order of dominance on the main diagonal of the upper triangular matrix A. The paper also proposed a solution that the model reduction algorithm based on Schur analysis can reduce order for both stable and unstable systems. Illustrative examples demonstrated the correctness of the proposed solutions and algorithms.
3 citations
TL;DR: In this paper, it is pointed out that the "aggregation" matrix proposed in the above paper can only yield an approximate relationship between the system and the reduced-order model.
Abstract: In this comment it is pointed out that the "aggregation" matrix proposed in the above paper can only yield an approximate relationship between the system and the reduced-order model.
3 citations
01 Jan 2015
TL;DR: In this article, a review of previous works based on experimental and model studies have established that nanofluids have great potential for cooling various thermal systems, which is reported by many researcher and nano research centers all over the world.
Abstract: Miniaturization of devices and energy efficiency are two major driving forces to find new materials and improved designs of solar collectors. Nanofluids are innovative fluids getting worldwide attention due to their inherent characteristics. Nanofluids exhibits enhanced heat absorbing and heat transport ability, credited to nanoparicles suspended in base- fluids. The cardinal factor which is responsible for enhanced heat transfer and absorption ability of Nanofluids is multiplication of surface to volume ratio of nanoparicles. Nanofluids are nanoparicles suspended in a base fluids, it can be considered liquid nano-composites (homogeneous solution of suspended nanoparicles in base fluids).These Nanofluids are now being used as working fluids to absorb solar insolence and transfer it to another fluids at appreciably enhanced rate as reported by many researcher and nano research centers all over the world. Our intention behind writing this review is to comprehensively and thoroughly investigate the research work done for improvement of efficiency in Direct absorbing Solar Collectors Using Nanofluids. Review of previous works based on experimental and model studies have established that nanofluids have great potential for cooling various thermal systems. Recent trends also encouraging towards application of nanofluids in PV/T systems to increase overall efficiency of solar energy conversion.
3 citations
01 Nov 2014
TL;DR: A model order reduction technique based on Routh approximation criteria is used to model AGC model of a single area and it is demonstrated that the complexity of the system is reduced to a great extent.
Abstract: The fast development and usage of small digital computers and processors in the design, analysis and implementation of suitable control strategies has led towards proposing the reduced order modeling of large order physical systems As most of the models are too complex to be analyzed in its original form, various techniques have been developed in the past to reduce the order of a complex system The structure of existing power systems is very complex in nature and therefore their resulting mathematical models are of large orders The analysis of such systems becomes a tedious and difficult job In this article, a model order reduction technique based on Routh approximation criteria is used to model AGC model of a single area An AGC model of single area is reduced to third order The system dynamic response plots for both original and reduced order models are obtained for step input and they are compared The investigations of these results carried out in the study demonstrate that the complexity of the system is reduced to a great extent However, the dynamic behavior of all the system states for same step disturbance is within acceptable limit
3 citations
TL;DR: It is shown that it is possible to obtain an approximated model that makes the computation of the Gramian and its interpretation much easier and provides a reliable approximation of the control energy necessary to control the network.
Abstract: In this article, we consider the problem of determining the control energy for large-scale networks. Instead of controlling all the nodes of the network, we are interested in driving the value of some outputs to the desired value, by directly controlling some of the nodes. To do this, we exploit the concept of output controllability and of output controllability Gramian that permits to analyze the properties of the system, both in single-output and multioutput cases. Based on a projection method, we show that it is possible to obtain an approximated model that makes the computation of the Gramian and its interpretation much easier. Simulations show that the reduced model is consistent with the original one and provides a reliable approximation of the control energy necessary to control the network.
3 citations
Cites background from "Control of large-scale dynamic syst..."
...However, the case of D̂ = 0(m+1)×η, commonly referred to as exact projection, holds only in particular cases (see [33] for more details on the subject)....
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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