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AUTHOR(S): Kartik Chandra Patra, Asutosh Patnaik
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ABSTRACT The present work narrates a clear logical approach to estimating Limit Cycles (LC) in 3×3 Nonlinear systems. The estimation of LC is done employing graphical method assuming harmonic balance approximation and are validated by computer simulations. The graphical method is developed using both computer graphics and geometric tools. The computer simulations are done by developing a suitable program with MATLAB code and also using the SIMULINK Toolbox of MATLAB software. Considering the structure of 3×3 nonlinear systems is a bit complex, the estimation of LC is done considering the frequency of LC remains the same at every point of the loop. Once the LC is predicted/detected in an autonomous state, the investigation explores the quenching of the oscillation at high frequency, ten times higher than the frequency of LC applied at the input node, which is normally termed a Signal Stabilization. The process of Signal Stabilization is a type of response which exhibits both transients and steady states. Of course, with the proper amplitude of the dither signal, the synchronizing frequency of the output should be the frequency of the dither signal at the steady state. However, the Signal Stabilization process is made faster and, in minimum time, the steady-state synchronizing value is realized without the transient and any ripples at steady state by a discrete signal which is termed as deadbeat approach to response. In this article, the Signal Stabilization with deadbeat approach has been explored analytically and is validated by computer simulations. |
KEYWORDS Limit Cycles, 3×3 Nonlinear Systems, Signal Stabilizations, Dead Beat response, Describing functions |
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Cite this paper Kartik Chandra Patra, Asutosh Patnaik. (2025) Estimation of Limit Cycles and Signal Stabilization with Deadbeat approach in three Dimensional Nonlinear systems. International Journal of Control Systems and Robotics, 10, 22-38 |
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