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6: Non-Linear Systems

Last updated

Aug 15, 2021
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- 5.3: Feedback Compensation
- 6.1: Introduction to Non-Linear Systems

James K. Roberge
Massachusetts Institute of Technology via MIT OpenCourseWare

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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

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