Active Realization of Fractional-Order Integrators and Their Application in Multiscroll Chaotic Systems

This paper presents the design, simulation, and experimental verification of the fractional-order multiscroll Lü chaotic system. We base them on op-amp-based approximations of fractional-order integrators and saturated series of nonlinear functions. The integrators are first-order active realizations tuned to reduce the inaccuracy of the frequency response. By an exponential curve fitting, we got a convenient design equation for realizing fractional-order integrators of orders from 0.1 to 0.95. The results include simulations in SPICE of the mathematical description and the electronic implementation and experimental measurements that confirm them. Monte Carlo and sensitivity tests revealed a robust realization. Contrary to its passive counterparts, the suggested realizations significantly reduce design and implementation efforts by favoring resistors and capacitors with commercial values and reducing hardware requirements.

[1]  Mohammed F. Tolba,et al.  FPGA Implementation of the Fractional Order Integrator/Differentiator: Two Approaches and Applications , 2019, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Jing Wang,et al.  Dynamic analysis of seven-dimensional fractional-order chaotic system and its application in encrypted communication , 2020, J. Ambient Intell. Humaniz. Comput..

[3]  M. Sanjuán,et al.  Fractional damping enhances chaos in the nonlinear Helmholtz oscillator , 2020, Nonlinear Dynamics.

[4]  José António Tenreiro Machado,et al.  Complex and Fractional Dynamics , 2017, Entropy.

[5]  YangQuan Chen,et al.  Fractional order control - A tutorial , 2009, 2009 American Control Conference.

[6]  Brent Maundy,et al.  Design of fractional notch filter with asymmetric slopes and large values of notch magnitude , 2013, 2013 IEEE 56th International Midwest Symposium on Circuits and Systems (MWSCAS).

[7]  M. Tabatabaei,et al.  Design of Non-overshooting Fractional-Order PD and PID Controllers for Special Case of Fractional-Order Plants , 2019, Journal of Control, Automation and Electrical Systems.

[8]  J. Valsa,et al.  Comparison of the electronic realization of the fractional-order system and its model , 2012, Proceedings of the 13th International Carpathian Control Conference (ICCC).

[9]  Jesús M. Muñoz-Pacheco,et al.  Circuit synthesis of an incommensurate fractional order multi-scroll PWL chaotic system , 2017, 2017 6th International Conference on Modern Circuits and Systems Technologies (MOCAST).

[10]  Z. Aslipour,et al.  Identification of Wind Turbine using Fractional Order Dynamic Neural Network and Optimization Algorithm , 2020 .

[11]  D. Matignon.  Stability results for fractional differential equations with applications to control processing , 1996 .

[12]  Costas Psychalinos,et al.  Comparative study of fractional-order differentiators and integrators , 2017, 2017 40th International Conference on Telecommunications and Signal Processing (TSP).

[13]  Viet-Thanh Pham,et al.  A fractional-order form of a system with stable equilibria and its synchronization , 2018 .