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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TL;DR: In this paper, a synchronous machine with an excitation system and a prime-mover is decomposed into slow and fast subsystems using the iterative separation of time scales.
Abstract: Power system excitation and governor control design using time-scale decomposition and optimal control theoretic concepts are presented A synchronous machine with an excitation system and a prime-mover is decomposed into slow and fast subsystems using the iterative separation of time scales The slow subsystem model is employed as the design model The effectiveness of the proposed controller is studied through digital simulation The simulation results are compared with those obtained via the classical quasi-steady-state (qss) technique The approach presented does not require an explicit knowledge of the perturbation parameter
1 citations
TL;DR: An approach for decomposition-aggregation based on coherence property of the system is described in this article, and stability analysis and control strategies using this technique are illustrated through an example consisting of 11 generators.
1 citations
01 Jan 2005
TL;DR: This paper establishes and characterize simulation relations for arbitrary discrete-time, linear control systems and considers various embeddings into labeled transition systems, that differ in the amount of timing information that is maintained in the transition relation.
Abstract: Simulation relations of labeled transition systems are used in theoretical computer science in order to formally establish notions of modeling abstraction and refinement in hierarchical systems. In this paper, we establish and characterize simulation relations for arbitrary discrete-time, linear control systems. More precisely, given two discrete-time systems, we consider various embeddings into labeled transition systems, that differ in the amount of timing information that is maintained in the transition relation. For each embedding, we obtain necessary and sufficient conditions for one discrete-time system simulating the transitions of the other. Naturally, the simulation characterizations become weaker as more information is abstracted away in the embedding.
1 citations
Cites result from "Control of large-scale dynamic syst..."
...In all cases, however, we abstract away control information, in contrast to model reduction results which reduce systems while preserving control input information (Aoki, 1968)....
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01 Sep 2018
TL;DR: The algorithm can be utilized for reducing the order of the unstable higher-order system and the model order reduction of power plant system by using balanced realization method is successfully obtained.
Abstract: this paper deals with the model order reduction of power plant system by using balanced realization method. The algorithm can be utilized for reducing the order of the unstable higher-order system and we are successfully obtaining stable reduced order models. Balanced realization based model design gives an utmost ideal matching over all the frequencies. The proposed method preserves the important properties such as controllability, observability and balanced form. The power plant system utilized in this paper is inherently unstable and includes several input-output states. This brings complex scenario for reducing the order of the system. Most of the papers deal with the reduction of SISO (Single-Input-Single-Output) large-scale systems, but in this paper we applied balanced realization method for the reduction of MIMO (Multi-Input-Multi-Output) Systems. This paper produces steady & precise results as compared to conventional reduction techniques like Routh’s approximation.
1 citations
Cites methods from "Control of large-scale dynamic syst..."
...Steps for obtaining Balanced Truncated model [2-11]]:1....
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...After that we got controllability and observability gramians such as [5-7]:2018 International Conference on Computing, Power and Communication Technologies (GUCON) Galgotias University, Greater Noida, UP, India....
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TL;DR: A novel aggregation algorithm is proposed to decompose a system into two subsystems and reduce the subsystem which contains only non-dominant eigenvalues in a way that slow-decaying terms in the variables associated with this subsystem could be well preserved.
Abstract: We propose in this paper a novel aggregation algorithm for linear quadratic control problems. The basic idea of our algorithm is to decompose a system into two subsystems and reduce the subsystem which contains only non-dominant eigenvalues in a way that slow-decaying terms in the variables associated with this subsystem could be well preserved. The advantage of the new algorithm will be clearly shown in numeric examples where ninth-order problems are reduced to second-, third- and fourth-order ones which yield suboptimal controls very close to those obtained from full-order Riccati equations.
1 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