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The question of PIλDδ controller hardware implementation based on three-layer fractal RC-structure

Keywords:

V.V. Petrovskiy – Ph.D. (Eng.), Associate Professor, Department of Radioelectronics and Information-Measuring Engineering, Kazan National Research Technical University named after A.N. Tupolev (KNRTU-KAI)
E-mail: vvpetrovskiy@kai.ru
M.V. Petrovskaya – Senior Lecturer, Department of Radioelectronics and Information-Measuring Engineering, Kazan National Research Technical University named after A.N. Tupolev (KNRTU-KAI)
E-mail: mvpetrovskaya@kai.ru
D.V. Shakhturin – Ph.D. (Eng.), Associate Professor, Department of Radioelectronics and Information-Measuring Engineering, Kazan National Research Technical University named after A.N. Tupolev (KNRTU-KAI)
E-mail: dvshakhturin@kai.ru


Questions of PIλDδ fractional order controller implementation are considered, based on the use of devices that implement integral-differential arbitrary order operator. This problem is reduced to solving the problem of synthesis of two-terminal based on canonical Cauer circuit.
It was shown that the synthesis results are invariant with respect to a particular frequency range. Within a given frequency range amplitude and phase response deviation from the ideal does not exceed the specified error. The positive synthesis results of the entire range of fractional order for frequency range are to seven decades.
The optimization of ladder circuit parameters in terms of minimizing the number of links, while maintaining the requirements of amplitude and phase response fidelity and the frequency range was carried out. The results show that the frequency range with the same number of links is wider than in similar works. It shows good convergence of results of mathematical modeling and experiments.

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