Frequency analysis of linear periodical systems. Theory and experiment

Abstract

The frequency methods of mathematical description, analysis and synthesis, using transfer functions and frequency response, have important role in the control system theory. The frequency methods are effective instrument of decision for many theoretical and practical problems. Moreover, important advantage of this methods is principal possibility of using experimental frequency responses, that in many cases essentially simplify the procedure of system design. In this connection, the questions of frequency description of linear nonstationary systems and frequency methods of analysis and synthesis of such systems are at the centre of attention of automatic control literature. The first investigations in this direct belong to L. Zade (1950). A common theory of the finite-dimension continuous nonstationary linear systems was given by Rosenwasser (1994) and for arbitrary periodical continuous systems by Rosenwasser et al. (1997). In the present report we describe common properties of frequency responses for continuous linear periodical systems and consider common ways for their experimental determinations. Analogous ways of theoretical and experimental sampled-data systems investigations are given by Sommer et al. (1994) and Lampe et al. (1999).