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Second Order Systems

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posted on 2023-06-08, 08:22 authored by Derek P Atherton
A significant amount of the research into nonlinear differential equations in the nineteenth and early twentieth centuries done by mathematics was devoted to second order differential equations. There were two major reasons for this, namely that the dynamics of many problems of practical interest could be approximated by these equations and secondly the phase plane approach allowed a graphical examintaion of their solutions. This section gives a brief overview of how the phase plane approach was developed for use in control and design. The major contribution of control engineers was to consider use of the approach for nonlinear elements which could be defined by linear segmented characteristics, good approximations for many of the nonlinear effects in control systems, rather than continuous mathematical functions considered previously. A major advantage of the approach, as illustrated in this section, is that it can be used when more than one nonlinearity are resent in the feedback loop.

History

Publication status

  • Published

Publisher

UNESCO

Volume

3

Book title

Control Systems, Robotics, and Automation

Place of publication

Paris

Series

Encyclopedia of Life Support Systems

Department affiliated with

  • Engineering and Design Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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