Signal Stabilization of Limit Cycling Two Dimensional Memory Type Non Linear Systems by Gaussian Random Signal

Patra, K.C.; Kar, Namrata

doi:10.22541/au.158022324.44338046

Cited by 2 publications

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“…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%

“…If there exit limit cycle oscillations, the possibility of quenching the sustained oscillations using the method of signal stabilization has been investigated, [6], [16], [23], [29], [30], in 2x2 nonlinear systems with non-memory type nonlinear elements. Prediction of limit cycling oscillations and its quenching using signal stabilization technique by a deterministic signal in memory type nonlinear elements for 2x2 multivariable systems has been discussed in [49], and the same has been addressed with Gaussian signals, [50].…”

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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Quenching and Suppression of Limit Cycles in 3x3 Nonlinear Systems

Patra,

Patnaik

2024

Design, Construction, Maintenance

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For several decades, the importance and weight-age of prediction of nonlinear self-sustained oscillations or Limit Cycles (LC) and their quenching by signal stabilization have been discussed which is confined to Single Input and Single Output (SISO) system. However, for the last five to six decades, the analysis of 2x2 Multi Input and Multi Output (MIMO) Nonlinear Systems gained importance in which a lot of literature available. In recent days few literatures are available which addresses the exhibition of LC and their quenching/suppression in 3x3 MIMO Nonlinear systems. Poor performances in many cases like Load Frequency Control (LFC) in multi area power system, speed and position control in robotics, automation industry and other occasions have been observed which draws attention of Researchers. The complexity involved, in implicit nonmemory type and memory type nonlinearities, it is extremely difficult to formulate the problem in particular for 3x3 systems. Under this circumstance, the harmonic linearization/ harmonic balance reduces the complexity considerably. Still the analytical expressions are so complex which loses the insight into the problem particularly for memory type nonlinearity in 3x3 system. Hence in the present work a novel graphical method has been developed for prediction of limit cycling oscillations in a 3x3 nonlinear system. The quenching of such LC using signal stabilization technique using deterministic (Sinusoidal) and random (Gaussian) signals has been explored. Suppression LC using pole placement technique through arbitrary selection and optimal selection of feedback Gain Matrix K with complete state controllability condition and Riccati Equation respectively. The method is made further simpler assuming a 3x3 system exhibits the LC predominantly at a single frequency, which facilitates clear insight into the problem and its solution. The proposed techniques are well illustrated with example and validated/substantiated by digital simulation (a developed program using MATLAB codes) and use of SIMULINK Tool Box of MATLAB software. The Signal stabilization with Random (Gaussian) Signals and Suppression LC with optimal selection of state feedback matrix K using Riccati Equation for 3x3 nonlinear systems have never been discussed elsewhere and hence it claims originality and novelty. The present work has the brighter future scope of: i. Adapting the Techniques like Signal Stabilization and Suppression LC for 3x3 or higher dimensional nonlinear systems through an exhaustive analysis. ii. Analytical/Mathematical method may also be developed for signal stabilization using both deterministic and random signals based on Dual Input Describing function (DIDF) and Random Input Describing Function (RIDF) respectively. iii. The phenomena of Synchronization and De-synchronization can be observed/identified analytically using Incremental Input Describing Function (IDF), which can also be validated by digital simulations.

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Signal Stabilization of Limit Cycling Two Dimensional Memory Type Non Linear Systems by Gaussian Random Signal

Cited by 2 publications

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

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

Quenching and Suppression of Limit Cycles in 3x3 Nonlinear Systems

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