Subsystems, time scales and multimodeling

Abstract

-Through a couple of naive examples the control theorists are invited to re-examine the role of modeling in the study of large scale dynamic systems. Instead of assuming the existence of 'N diagonally dominant blocks', it is possible to justify one strongly coupled slow core and N weakly coupled fast subsystems. This structure is exhibited with a physically meaningful choice of state variables. The controls are introduced following the recent concept of multimodeling. INTRODUCTION MOST control studies of large-scale systems assume that a model is given possessing some known diagonal dominance properties. This assumption, which avoids the task of modeling, may be acceptable in small size systems. However, the phenomena occurring in large-scale systems are too rich to be handled by all-purpose models. Consider, for instance, the stabilization strategies based on the assumption of diagonal dominance and designed by vector Lyapunov function methods (Siljak, 1978). As power system examples show, the success of these strategies critically depends on what is modeled as a subsystem. If the subsystems are simply taken to be the individual generating units, the results are extremely conservative. With a choice of 'coherent areas' as subsystems, the results become more meaningful. Instead of assuming that an 'off-the-shelf model is already available in a diagonally dominant form, a deeper understanding of the causes for weak coupling is essential in the modeling of sybsystems. In this paper an attempt is made in this direction. Firstly the relationship of diagonal dominance and time scales in electrical networks and in aggregation of Markov chains is examined (Pervozvanski and Smirnov, 1974; Gaitsgori and Pervozvanski, 1975; Delebecque and Quadrat, 1978, 1981). Secondly a grouping procedure for determination of subsystems and separation of time scales is outlined (Avramovic and colleagues, 1980). A general property of the considered systems is that they are strongly coupled in the slow time scale and weakly coupled in the fast time scale. Due to this property every subsystem controller can neglect all other fast subsystems except for his own. This multimodeling situation is discussed in the last section of the paper. To highlight the ideas the paper is written as an informal discussion of representative examples. More general and rigorous treatment can be found in quoted references. NETWORKS, SUBNETWORKS, AND TIME SCALES We begin by considering a simple RL-network [Fig. l(a)] where all the inductors are of the same order of magnitude, and the nonuniformity of their interactions is due to the fact that the resistors R are much larger than the resistors r.

DOI: 10.1016/0005-1098(81)90066-2

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Cite this paper

@article{Kokotovic1981SubsystemsTS, title={Subsystems, time scales and multimodeling}, author={Petar V. Kokotovic}, journal={Automatica}, year={1981}, volume={17}, pages={789-795} }