Caputo fractional derivative operational matrices of Legendre and Chebyshev wavelets in fractional delay optimal control

Malmir, Iman

doi:10.3934/naco.2021013

Cited by 4 publications

(2 citation statements)

References 33 publications

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“…By directly deriving the derivative operation matrices of arbitrary scale Legendre and Chebyshev wavelets, their properties were introduced. The derivative operation matrix was used for quadratic optimization [14].…”

Section: Related Workmentioning

confidence: 99%

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Construction and simulation of a joint scale model for power electronic converters based on wavelet decomposition and reconstruction algorithms

2024

PLoS ONE

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In power electronics systems, system design and operation often involve multiple time and space scales, ranging from nanosecond switching dynamics to hour-level system operation behavior. Due to the complexity of these systems and the rise of wide-gap semiconductor technology, a series of multi-scale phenomena have emerged that are difficult to ignore. The high frequency of switching operations makes multi-scale effects particularly significant, including the fast dynamic response of the power loop, EMI, and heat conduction problems. They are key factors that must be considered in the design to ensure the efficient and reliable operation of power electronic devices. This study proposes the construction and simulation of a joint scale model for power electronic converters based on wavelet decomposition and reconstruction algorithms to address the multi-scale phenomenon and limitations of single-scale power electronic converters. Firstly, a joint scale model for power electronic converters at both macro and micro-scales was established, targeting both single-scale models and simple combinations of multiple scale models for power electronic converters. The traditional single-scale model is sufficient to describe the average behavior of the converter, but it has serious limitations in capturing fast transient processes and high-frequency switching behavior in power electronic systems. These limitations often manifest themselves when there is a need to capture fine timescales of detail. By transforming between the time domain and the frequency domain, wavelet decomposition enables the model to capture both macroscopic average characteristics and microscopic transient dynamics. The wavelet reconstruction algorithm can simulate all kinds of fast changes in the actual working process more accurately and compress irrelevant information while retaining key signal features, so as to optimize the simulation performance of the model. Secondly, this algorithm is used to analyze BC in short time scale. Finally, the short time scale characteristics of power electronic converters are analyzed. Experimental results show that the fusion of wavelet decomposition and reconstruction algorithm enhances the accuracy of the power electronic converter model and improves the performance of the system. The model achieves an error reduction of nearly 3% in the calculation step size of 10-7s, which has a significant impact on the high precision requirements of high-frequency operations. In addition, the optimal calculation step size of 8×10-8s achieves an error reduction of more than 14%, making an important contribution to the transient analysis and fine structure simulation. The wavelet algorithm can improve the accuracy of multi-scale modeling in power electronic system and reduce the simulation time. The reduction of error not only shows the improvement of the accuracy of the model, but also shows its practical significance in the design and test of the actual power electronic system. The reduction in error reveals the ability to more accurately predict and mitigate potential performance problems in matching tests with actual hardware, as well as its ability to adapt to emerging wide bandgap semiconductor materials and structures.

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Section: Related Workmentioning

confidence: 99%

“…N 1 and N 2 are the primary winding turns and secondary winding turns of high-frequency transformer, respectively. The DAB-SST state equation can be obtained in Eq (14).…”

Section: Plos Onementioning

confidence: 99%

Construction and simulation of a joint scale model for power electronic converters based on wavelet decomposition and reconstruction algorithms

2024

PLoS ONE

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An efficient method for a variety of fractional time-delay optimal control problems with fractional performance indices

Malmir

2023

Int. J. Dynam. Control

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Extended Chebyshev cardinal wavelets for nonlinear fractional delay optimal control problems

Heydari

Razzaghi

2021

International Journal of Systems Science

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Caputo fractional derivative operational matrices of Legendre and Chebyshev wavelets in fractional delay optimal control

Cited by 4 publications

References 33 publications

Construction and simulation of a joint scale model for power electronic converters based on wavelet decomposition and reconstruction algorithms

Construction and simulation of a joint scale model for power electronic converters based on wavelet decomposition and reconstruction algorithms

An efficient method for a variety of fractional time-delay optimal control problems with fractional performance indices

Extended Chebyshev cardinal wavelets for nonlinear fractional delay optimal control problems

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