On limit cycles in feedback polynomial systems

Genesio, R.; Tesi, A.

doi:10.1109/31.9915

Cited by 11 publications

(2 citation statements)

References 7 publications

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“…When a closed loop system exhibits limit cycles, the signal at any point of the loop is transmitted around the loop to that point without any change in amplitude and phase. Thus, a system exhibits a limit cycle when the loop gain is one and the loop phase shift is ± 2nπ, [21], [51], when n is an integer.…”

Section: Graphicalmentioning

confidence: 99%

“…The importance of this problem was well felt among the researchers, [2], [3], [4], [5], [6], where the people were mostly focusing on single input single output systems. However, for the last five decades, the analysis of 2x2 nonlinear multivariable systems gained importance, particularly for the prediction of limit cycles and quite a good amount of literature is available addressing this area of research, [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [37], [38], [39], [40], [41] [51]. Prediction of limit cycle and its analysis in both single as well as two dimensional nonlinear systems, a means of increasing the reliability of t...…”

Section: Introductionmentioning

confidence: 99%

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Investigation of the Existence of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems

Patra

Patnaik

2023

International Journal of Applied Mathematics, Computational Science and Systems Engineering

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The proposed work addresses the dynamics of a general system and explores the existence of limit cycles (LC) in multi-variable Non-linear systems with special attention to 3x3 nonlinear systems. It presents a simple, systematic analytical procedure as well as a graphical technique that uses geometric tools and computer graphics for the prediction of limit cycling oscillations in three-dimensional systems having both explicit and implicit nonlinear functions. The developed graphical method uses the harmonic balance/harmonic linearization for simplicity of discussion which provides a clear and lucid understanding of the problem and considers all constraints, especially the simultaneous intersection of two straight lines & one circle for determination of limit cycling conditions. The method of analysis is made simpler by assuming the whole system exhibits the limit cycling oscillations predominantly at a single frequency. The discussions made either analytically/graphically are substantiated by digital simulation by a developed program as well as by the use of the SIMULINK Toolbox of MATLAB Software.

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Section: Graphicalmentioning

confidence: 99%