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: This study proposes a coordination of load frequency control and superconducting magnetic energy storage technology using a new optimal PID controller-based moth swarm algorithm in Egyptian Power System (EPS) considering high wind power penetration (HWPP) (as a future planning of the EPS).
Abstract: This study proposes a coordination of load frequency control (LFC) and superconducting magnetic energy storage (SMES) technology (i.e. auxiliary LFC) using a new optimal PID controller-based moth swarm algorithm (MSA) in Egyptian Power System (EPS) considering high wind power penetration (HWPP) (as a future planning of the EPS). This strategy is proposed for compensating the EPS frequency deviation, preventing the conventional generators from exceeding their power ratings during load disturbances, and mitigating the power fluctuations from wind power plants. To prove the effectiveness of the proposed coordinated control strategy, the EPS considering HWPP was tested by the MATLAB/SIMULINK simulation. The convention generation system of the EPS is decomposed into three dynamics subsystems; hydro, reheat and non-reheat power plants. Moreover, the physical constraints of the governors and turbines such as generation rate constraints of power plants and speed governor dead band (i.e. backlash) are taking into consideration. The results reveal the superior robustness of the proposed coordination against all scenarios of different load profiles, and system uncertainties in the EPS considering HWPP. Moreover, the results have been confirmed by comparing it with both; the optimal LFC with/without the effect of conventional SMES, which without modifying the input control signal.
84 citations
TL;DR: Fifteen distinct simplification procedures for simulation models are presented with citations to their application and a guide to the application indicates the order in which they are to be used in a given simplification exercise.
Abstract: Fifteen distinct simplification procedures for simulation models are presented with citations to their application. A guide to the application of those techniques indicates the order in which they ...
81 citations
TL;DR: In this article, the poles and zeros of the original system in the s-plane are clustered using a newly defined inverse distance measure, and a tuning factor k is used to minimize the cumulative square of the time response deviations between the original systems and the reduced order approximant.
78 citations
TL;DR: In this article, the problem of constructing a reduced-order model induced by the information structure is considered and a new system representation, denoted as the Generalized Hessenberg Representation (GHR), is introduced and chained aggregation which transforms the system representation into GHR is described.
Abstract: The problem of constructing a reduced-order model induced by the information structure is considered A new system representation, denoted as the Generalized Hessenberg Representation (GHR), is introduced and chained aggregation which transforms the system representation into the GHR is described A ninth-order model of a two-thermal plant power system used in load-frequency studies is presented to demonstrate the potential of the GHR in model reduction The role of GHR in identifying model structure and suggesting appropriate subsets of adjustable parameters is established
70 citations
TL;DR: For continuous-time systems the class includes an infinite set, whereas for discrete-time the class has only two members as mentioned in this paper, which illustrates the freedom available in a model reduction procedure.
Abstract: Recently developed model-reduction procedures lead (for the single input-output case) to qth degree systems with first q-Markov parameters and first q-covariance parameters (Markov parameters of the causal part of the power spectrum) taking prescribed values. The class of all such systems is parameterized. For continuous-time systems the class includes an infinite set, whereas for discrete-time the class has only two members. The result is important in that it illustrates the freedom available in a model reduction procedure. >
70 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