International Journal of Electrical Engineering and Computer Science
E-ISSN: 2769-2507
Volume 7, 2025
Tracking of Synchronization and Desynchronization during the process of Signal Stabilization in a 3×3 Memory Type Nonlinear Systems
Authors: ,
Abstract: The paper proposes the first harmonic linearization concept leading to a novel graphical technique developed to predict limit cycles (LC) in 3×3 systems with memory-type nonlinearities. This approach leverages computer graphics for ease of visualization and analysis, making the method more accessible and lucid. Under the exhibition of LC, it has been attempted to quench such oscillations by adopting the signal stabilization method with deterministic/random signals. In the process of signal stabilization, tracking of synchronization (alignment of oscillations) and desynchronization (loss of alignment) with deterministic and random signals has been explored. The propositions of the work have been illustrated through an example with backlash type nonlinearities that are commonly present in physical systems on several occasions and in particular in the power system and control system. The proposed graphical method has been validated by digital simulation by means of MATLAB code and with the usage of SIMULINK ToolBox of MATLAB. The developed graphical method in the prediction of LC in 3x3 systems with backlash-type nonlinearities is a novel and significant innovation, making the complex analysis more accessible and interpretable. The work extends to practical applications by proposing ways to stabilize limit cycles using both deterministic and random signals, and tracking synchronization / desynchronization.
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Keywords: Limit cycles, signal stabilization, describing function, incremental input describing function, synchronization, memory type nonlinearities
Pages: 17-32
DOI: 10.37394/232027.2025.7.3