Journal
INTERNATIONAL JOURNAL OF CONTROL
Volume 81, Issue 12, Pages 1886-1900Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207170801927163
Keywords
Hamiltonian mechanics; limit cycle; non-linear systems
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Funding
- Sandia National Laboratories
- Sandia Corporation
- Lockheed Martin Company
- U.S. Department of Energy's National Nuclear Security Administration [DE-AC04-94AL85000]
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A limit cycle is the stability boundary for linear and non-linear control systems. Hamiltonian mechanics and power flow control are employed to demonstrate this property of limit cycles. The presentation begins with the concept of linear limit cycles which is extended to non-linear limit cycles. Many examples are used to demonstrate these concepts including linear and non-linear oscillators, power engineering, and an extension to a class of plane differential systems. Power flow control based on Hamiltonian mechanics is shown to be applicable to a large class of non-linear systems. Finally, eigenanalysis and flight stability for linear systems are extended to non-linear systems and is referred to as 'the power flow principle of stability for non-linear systems'.
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