Comparative analysis of Bootan's and Axelby's describing functions

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1970

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Abstract

Linearization of nonlinear systems with random inputs using the describing function technique is discussed. Using Bootan's and Axelby's definitions the expressions for the equivalent describing function K[subscript n] for several types of nonlinearities are derived and the difference in the values of K[subscript n] which result from the two approaches is illustrated. A particular nonlinearity combined with a third order linear system is considered for analysis using both definition of K[subscript n]. The discrepancies that arise in the design or analysis of a control system using the two definitions is clearly presented and the for this nonlinearity that provides the best approximation of the actual system behavior is determined by simulating the physical model on an analog computer.

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