Similarity and dimensional relationships in control systems

Similarity and dimensional relationships in control systems

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The essential theorems of dimensional analysis are reviewed and related to the familiar process of normalizing or ‘non-dimensionizing’, by which the results of calculation or observation of relationships between varying quantities may be expressed so as to be applicable to many possible observations. In recording or cataloguing the behaviour of systems of given kinds having various combinations of values of parameters, it is desirable to express the behaviour in terms of the fewest possible composite parameters. It is shown that, for transfer functions, this is achieved by the usual process of normalizing applied to the transfer function when expressed in the form of a ratio of polynomials in p. In systems with feedback this number of parameters may be smaller than the number of the ratios of independent time-constants of the equations. This implies that systems with feedback may have dynamically similar behaviour, even though their basic time-constants are in different ratios. Consideration is given to systems involving non-linear relationship. In such cases the choice of the products, having dimension zero, in terms of which results may most effectively be recorded is particularly important and may be less obvious. A procedure is outlined, using the concepts of sets of affine curves and representative values, by which the appropriate composite variables may be discovered.


    1. 1)
      • P.W. Bridgman . (1946) , Dimensional Analysis.

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