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New improved fractional order differentiator models based on optimized digital differentiators.

Maneesha Gupta¹, Richa Yadav¹

¹Netaji Subhash Institute of Technology, Sector 3, Dwarka, New Delhi 110078, India.

Thescientificworldjournal

|April 2, 2014

Summary

Evolutionary algorithms optimized digital differential operators for improved fractional order differentiators. Optimized operators demonstrated superior performance compared to existing models across the Nyquist frequency range.

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Area of Science:

Signal Processing
Computational Intelligence
Control Systems Engineering

Background:

Fractional order calculus offers enhanced modeling capabilities for complex systems.
Digital differential operators are crucial for implementing fractional order differentiators.
Optimization of these operators is essential for improving differentiator performance.

Purpose of the Study:

To optimize 2nd and 3rd order digital differential operators using evolutionary algorithms.
To discretize optimized operators for fractional order half differentiator models.
To evaluate the performance of the proposed half differentiators against existing methods.

Main Methods:

Utilized particle swarm optimization (PSO), genetic algorithm (GA), and a PSO-GA hybrid.
Minimized error fitness functions using mean, median, and standard deviation metrics.
Discretized optimized operators for half differentiator implementation and simulation.

Main Results:

Optimized operators showed improved accuracy in approximating ideal fractional order differentiators.
Proposed half differentiators outperformed existing models within the full Nyquist frequency range.
PSO-GA hybrid demonstrated effective operator optimization.

Conclusions:

Evolutionary algorithm-optimized digital differential operators significantly enhance fractional order differentiator performance.
The proposed half differentiators offer a robust and efficient solution for signal processing applications.
Further research can explore higher-order operators and different evolutionary strategies.