Publisher : The Korean Institute of Electrical Engineers
DOI : 10.5370/JEET.2011.6.5.697
Title & Authors
State-Space Analysis on The Stability of Limit Cycle Predicted by Harmonic Balance Lee, Byung-Jin; Yun, Suk-Chang; Kim, Chang-Joo; Park, Jung-Keun; Sung, Sang-Kyung;
In this paper, a closed-loop system constructed with a linear plant and nonlinearity in the feedback connection is considered to argue against its planar orbital stability. Through a state space approach, a main result that presents a sufficient stability criterion of the limit cycle predicted by solving the harmonic balance equation is given. Preliminarily, the harmonic balance of the nonlinear feedback loop is assumed to have a solution that determines the characteristics of the limit cycle. Using a state-space approach, the nonlinear loop equation is reformulated into a linear perturbed model through the introduction of a residual operator. By considering a series of transformations, such as a modified eigenstructure decomposition, periodic averaging, change of variables, and coordinate transformation, the stability of the limit cycle can be simply tested via a scalar function and matrix. Finally, the stability criterion is addressed by constructing a composite Lyapunov function of the transformed system.
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