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6: Non-Linear Systems

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• 6.1: Introduction to Non-Linear Systems
Analytic difficulties arise because most of the methods we have learned are dependent on the principle of superposition, and nonlinear systems violate this condition. Time-domain methods such as convolution and fre­quency-domain methods based on transforms usually cannot be applied directly to nonlinear systems. Similarly, the blocks in a nonlinear block diagram cannot be shuffled with impunity.
• 6.2: Linearization
One direct and powerful method for the analysis of nonlinear systems involves approximation of the actual system by a linear one. If the approxi­mating system is correctly chosen, it accurately predicts the behavior of the actual system over some restricted range of signal levels. This technique of linearization based on a tangent approximation to a nonlinear relationship is familiar to electrical engineers, since it is used to model many electronic devices.
• 6.3: Describing Function
Describing functions provide a method for the analysis of nonlinear sys­tems that is closely related to the linear-system techniques involving Bode or gain-phase plots. It is possible to use this type of analysis to determine if limit cycles (constant-amplitude periodic oscillations) are possible for a given system. Unfortunately, since the frequency response and transient response of nonlinear systems are not directly re­lated, the determination of transient response is not possible via describ

This page titled 6: Non-Linear Systems is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by James K. Roberge (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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