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.
Citations
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01 Oct 2018
TL;DR: A new mixed approach of model order reduction (MOR) for the simplification of higher order linear time-invariant single-input single-output (SISO) systems is presented in this article by combining the benefits of Fuzzy C-means (FCM) along with Jaya optimization algorithm.
Abstract: A new mixed approach of model order reduction (MOR) for the simplification of higher order linear time-invariant single-input single-output (SISO) systems is presented in this article by combining the benefits of Fuzzy C-means (FCM) along with Jaya optimization algorithm. The FCM is a pole clustering based method used for the determination of reduced order denominator polynomial while the numerator polynomial is calculated by the Jaya optimization algorithm. Further, two numerical examples are considered and their performance indices are computed to justify the superiority of the proposed approach.
1 citations
Cites background or methods from "Control of large-scale dynamic syst..."
...Several conventional methods for MOR are aggregation approach [1], Padè approximation method [2], continued fraction expansion (CFE) techniques [3-6], moment matching method [7], Markov parameters and moment matching approach [8] etc....
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...A significant number of approaches for MOR in time domain [36-38] as well as in frequency domain [1-13] are presented in the literature....
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01 Dec 2015
TL;DR: In this article, the balanced realization technique with frequency weights is applied for the order reduction of continuous time uncertain systems, which results in a stable reduced order model corresponding to higher order system.
Abstract: In order reduction, complex systems are approximated by comparatively lower order models by retaining the inherent features of the original systems. The main objective is to design a low order controller with lesser number of states to control the higher order system effectively. In this work, the well established balanced realization technique, with frequency weights, is applied for the order reduction of continuous time uncertain systems. The proposed technique results in a stable reduced order model corresponding to higher order system. Test examples available in the literature are considered to demonstrate the results of the proposed technique and a comparison with other methods for order reduction of uncertain systems is given.
Cites methods from "Control of large-scale dynamic syst..."
...The established order reduction techniques in time domain are modal analysis approach [9], aggregation method [10] and optimal Hankel norm approximation [11-12]....
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Dissertation•
01 Jan 1993
TL;DR: In this article, the authors claim to have constructed an aggregation matrix equivalent to the continued fraction expansion model reduction technique of Chen and Shieh, but the suggested procedure is not equivalent and the correct version is given.
Abstract: In the above paper the authors claim to have constructed an aggregation matrix equivalent to the continued fraction expansion model reduction technique of Chen and Shieh. It is shown that the suggested procedure is not equivalent and the correct version is given.
01 Jan 2021
TL;DR: In this chapter, a comprehensive literature review on the issue of load frequency control (LFC) in the power system has been highlighted and some new research directions in the field of LFC are presented.
Abstract: As the world’s supply of fossil fuels shrinks, there is a great need for clean and affordable renewable energy sources (RES) in order to meet growing energy demands. Furthermore, the conventional plants based on fossil fuel have serious environmental and financial problems, and therefore, the dependency of the distribution networks on the RES such as solar power systems for generating electrical power is significantly promoted. In the past few decades, solar energy systems have been received great attention as an important type of RES. Nowadays, solar energy sources constitute appropriate commercial options for small and large power plants. The two mainstream categories of solar energy systems utilized for this purpose are concentrated solar power (CSP) and photovoltaic (PV). This chapter presents a brief introduction about the role, important need, and advantages of renewable energies for today and the future, especially solar energy such as PV and CSP systems. In addition, it introduces a survey for all types of CSP technologies. As well as, it presents a literature review for the LCOE and cost reduction of CSP and PV systems, CSP modeling, and the application of ANN technologies in various SF systems. Further, it presents the problem definition, objectives, and outlines of this thesis.
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