Second Order Systems

Atherton, Derek P (2006) Second Order Systems. In: Control Systems, Robotics, and Automation. Encyclopedia of Life Support Systems, 3 . UNESCO, Paris.

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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.

Item Type: Book Section
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Depositing User: Derek Atherton
Date Deposited: 06 Feb 2012 20:58
Last Modified: 11 Jul 2012 13:06
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