A novel application for DC motor-generator cascade system by changing signal density of digital chaotic oscillator

Year 2023, Volume: 41 Issue: 2, 396 - 407, 30.04.2023

Ercan Köse , Aydın Mühürcü Serdar Coşkun

Abstract

Presented is a new method for the realization of a chaotic oscillator in a digital environment. First, a two-stroke sampling mathematical regulation is developed for discrete-time oscillator equations to change signal densities of chaotic signals. This proposed mathematical regulation is applied to Lorenz’s chaotic oscillator, which presents a complex dynamical behavior. An application is shown with simulation through a Matlab-Simulink environment with time-de-pendent density changes of x, y and z 1 − D graphics and x, y 2 − D phase space graphics that are dependent on different density changes. Further to this, in an experimental study, Lorenz’s chaotic oscillator’s signals with variable density is applied to a DC motor as armature voltage via an 8-bit microcontroller based hardware environment. Chaotic supply voltage is applied to the motor rotor to generate a chaotic angular velocity. Time-dependent density change results of x, y and z 1 − D graphics are obtained and shown on an oscilloscope by converting chaotic rotor angular velocity to electrical signals, through a tacho-generator. The observed results re-vealed that chaotic signal production with variable density is achieved both in the simulation environment and the experimental environment. Also, it is shown that the proposed program and mathematical equations are feasible in terms of hardware and software implementations.

Keywords

Chaotic Systems, Digital Chaotic Oscillator, Microcontroller

References

• REFERENCES
• [1] Ogorzalek MJ. Taming chaos. i. synchronization. IEEE Trans Circuits Syst I Fundamental Theory Appl 1993;40:693–699. [CrossRef]
• [2] Kose E, Muhurcu A. Realization of a digital chaotic oscillator by using a low cost microcontroller. Eng Rev 2017;37:341–348.
• [3] Behera SK, Das DP, Subudhi B. Functional link artificial neural network applied to active noise control of a mixture of tonal and chaotic noise. Appl Soft Comput 2014;23:51–60. [CrossRef]
• [4] Gholipour R, Khosravi A, Mojallali H. Multi–objective optimal backstepping controller design for chaos control in a rod–type plasma torch system using Bees algorithm. Appl Math Model 2015:39:4432–4444. [CrossRef]
• [5] Adomaitienė E, Mykolaitis G, Bumelienė S, Tamaševičius A. Adaptive nonlinear controller for stabilizing saddle–type steady states of dynamical systems. Nonlinear Dyn 2015;82:1743–1753. [CrossRef]
• [6] Ontañón–García LJ, Campos–Cantón E. Preservation of a two–wing Lorenz–like attractor with stable equilibria. J Frank Inst 2013;350:2867–2880. [CrossRef]
• [7] Peng C, Zhang W. Back‐stepping stabilization of fractional‐order triangular system with applications to chaotic systems. Asian J Control 2021;23:143–154. [CrossRef]
• [8] Balootaki MA, Rahmani H, Moeinkhah H, Mohammadzadeh A. Non–singleton fuzzy control for multi–synchronization of chaotic systems. Appl Soft Comput 2021;99:106924. [CrossRef]
• [9] Mirrezapour SZ, Zare A, Hallaji M. A new fractional sliding mode controller based on nonlinear fractional–order proportional integral derivative controller structure to synchronize fractional– order chaotic systems with uncertainty and disturbances. J Vib Control 2022;28:773–785. [CrossRef]
• [10] Sambas A, Mamat M, Arafa AA, Mahmoud GM, Mohamed MA, Sanjaya WS. A new chaotic system with line of equilibria: dynamics, passive control and circuit design. Int J Electr Comput Eng 2019;9:2365–2376. [CrossRef]
• [11] Handa H. active control synchronization of similar and dissimilar chaotic systems.. 2021 Innovations in Power and Advanced Computing Technologies; 2021 Nov 27–29; Kuala Lumpur, Malaysia: IEEE; 2021. pp. 1–6.
• [12] Bigdeli N, Afshar K. Chaotic behavior of price in the power markets with pay–as–bid payment mechanism. Chaos Solit Fractals 2009;42:2560–2569. [CrossRef]
• [13] Liang Z, Liang J, Zhang L, Wang C, Yun Z, Zhang X. Analysis of multi–scale chaotic characteristics of wind power based on Hilbert–Huang transform and Hurst analysis. Appl Energy 2015;159:51– 61. [CrossRef]
• [14] Shahverdiev EM, Hashimova LH, Bayramov PA, Nuriev RA. Chaos synchronization between time delay coupled Josephson junctions governed by a central junction. J Supercond Nov Magn 2015;28:3499–3505. [CrossRef]
• [15] Gao L, Wang Z, Zhou K, Zhu W, Wu Z, Ma T. Modified sliding mode synchronization of typical three–dimensional fractional–order chaotic systems. Neurocomputing 2015;166:53–58. [CrossRef]
• [16] Aliabadi F, Majidi MH, Khorashadizadeh S. Chaos synchronization using adaptive quantum neural networks and its application in secure communication and cryptography. Neural Comput Appl 2022;34:6521–6533. [CrossRef]
• [17] Nguyen QD, Huang SC. Synthetic adaptive fuzzy disturbance observer and sliding–mode control for chaos–based secure communication systems. IEEE Access 2021;9:23907–23928. [CrossRef]
• [18] Njitacke ZT, Isaac SD, Nestor T, Kengne J. Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption. Neural Comput Appl 2021;33:6733–6752. [CrossRef]
• [19] Manera M. Perspectives on complexity, chaos and thermodynamics in environmental pathology. Int J Environ Res Public Health 2021;18:5766. [CrossRef]
• [20] Taki FA, Pan X, Zhang B. Revisiting chaos theorem to understand the nature of mirnas in response to drugs of abuse. J Cell Physiol 2015;230:2857–2868. [CrossRef]
• [21] Liu MK, Halfmann EB, Suh CS. Multi–dimensional time–frequency control of micro–milling instability. J Vib Control 2014;20:643–660. [CrossRef]
• [22] Tlelo–Cuautle E, Rangel–Magdaleno JJ, Pano–Azucena AD, Obeso–Rodelo PJ, Nuñez–Perez JC. FPGA realization of multi–scroll chaotic oscillators. Commun Nonlinear Sci Numer Simul 2015;27:66–80. [CrossRef]
• [23] Co TB. Methods of applied mathematics for engineers and scientists. 1st ed. Cambridge: Cambridge University Press; 2013.
• [24] Fadali MS, Visioli A. Digital control engineering: analysis and design. 2nd ed. Massachusetts: Academic Press; 2013. [CrossRef]
• [25] Stojković NV, Stanimirović PS. Two direct methods in linear programming. European J Oper Res 2001;131:417–439. [CrossRef]
• [26] Åström KJ, Wittenmark B. Computer–controlled systems: theory and design. 3rd ed. New York: Dover Publications; 2011.
• [27] Sarra SA, Meador C. On the numerical solution of chaotic dynamical systems using extend precision floating point arithmetic and very high order numerical methods. Nonlinear Anal Model Control 2011;16:340–352. [CrossRef]