Chaotic Speed Control of a DC Motor Using the Sprott-A System for Robotic End-Effector Applications

Abstract

This study investigates the use of chaotic speed control, based on the Sprott-A chaotic system, for improving the performance and stability of DC motor-driven robotic end-effector mixers. The chaotic differential equations were implemented and numerically solved in MATLAB/Simulink using the fourth-order Runge–Kutta method, and the resulting time series were analyzed. Among the variables generated, the X_t signal was selected for pulse-width modulation (PWM) due to its smooth dynamic characteristics. This signal was scaled to match the 0–100% duty cycle range and applied to the motor driver as a control input. The chaotic control system was realized both through analog circuit simulation in OrCAD and experimentally using an STM32F407 microcontroller. Time series, phase portraits, and oscilloscope outputs confirmed the consistency between simulation and hardware implementations. Compared to chaotic Y_t and Z_t signals, the chaotic X_t based PWM control reduced motor vibrations and provided more stable speed regulation. These results demonstrate the feasibility and effectiveness of chaotic dynamics for real-time motor control in robotic mixing applications, offering a robust alternative to traditional deterministic methods.

Keywords

• Robotics
• Chaos theory
• Motor speed control
• PWM

Ethical Statement

Since this study did not involve any studies on animals or humans, ethics committee approval was not obtained.

References

1. Ahrabi AR, Kobravi H. 2019. Chaos control in chaotic dynamical systems via auto-tuning Hamilton energy feedback. Turk J Forecast, 3(2): 47-53.
2. Al Khudir K, De Luca A. 2018. Faster motion on Cartesian paths exploiting robot redundancy at the acceleration level. IEEE Robot Autom Lett, 3(4): 3553-3560.
3. Chen R, Wang C, Wei T, Liu C. 2022. A composable framework for policy design, learning, and transfer toward safe and efficient industrial insertion. In: 2022 October–2022 IEEE/RSJ Int Conf Intell Robots Syst (IROS), Kyoto, Japan, pp: 8894-8901.
4. Demirsoy MS, El Naser YH, Sarıkaya MS, Peker NY, Kutlu M. 2024. Development of elbow rehabilitation device with iterative learning control and internet of things. Turk J Eng, 8(2): 370-379.
5. El Naser YH, Karayel D, Demirsoy MS, Sarıkaya MS, Peker NY. 2024. Robotic arm trajectory tracking using image processing and kinematic equations. Black Sea J Eng Sci, 7(3): 436-444.
6. Flacco F, De Luca A, Khatib O. 2015. Control of redundant robots under hard joint constraints: Saturation in the null space. IEEE Trans Robot, 31(3): 637-654.
7. Huang Y, Huang Q, Wang Q. 2016. Chaos and bifurcation control of torque-stiffness-controlled dynamic bipedal walking. IEEE Trans Syst Man Cybern Syst, 47(7): 1229-1240.
8. Khan H, Lee MC, Suh J, Kim R. 2025. Enhancing robot end-effector trajectory tracking using virtual force-tracking impedance control. Adv Intell Syst, 7(2): 2400380.

9. Kazemipour A, Khatib M, Al Khudir K, Gaz C, De Luca A. 2022. Kinematic control of redundant robots with online handling of variable generalized hard constraints. IEEE Robot Autom Lett, 7(4): 9279-9286.
10. Li C, Song Y, Wang F, Wang Z, Li Y. 2016. A bounded strategy of the mobile robot coverage path planning based on Lorenz chaotic system. Int J Adv Robot Syst, 13(3): 107.
11. Li S, Xu M, Quo J, Wang B, Hong Y. 2017. Design of fuzzy cross coupling controller for Cartesian robot. In: 2017 Int Conf Appl Math Model Stat Appl (AMMSA), Atlantis Press, pp: 427-431.
12. Liu N, Zhou X, Liu Z, Wang H, Cui L. 2020. Learning peg-in-hole assembly using Cartesian DMPs with feedback mechanism. Assembly Autom, 40(6): 895-904.
13. Mayr M, Salt-Ducaju JM. 2022. A C++ implementation of a Cartesian impedance controller for robotic manipulators. arXiv preprint arXiv:2212.11215 (accessed date: September 2, 2025).
14. Miranda-Colorado R, Aguilar LT, Moreno-Valenzuela J. 2018. A model-based velocity controller for chaotization of flexible joint robot manipulators: Synthesis, analysis, and experimental evaluations. Int J Adv Robot Syst, 15(5): 1729881418802528.
15. Nayak DS, Shivarudraswamy R. 2020. Solar fed BLDC motor drive for mixer grinder using a buck-boost converter. Bull Electr Eng Inform, 9(1): 48-56.
16. Portillo-Vélez RDJ, Rodriguez-Angeles A, Cruz-Villar CA. 2015. An optimization-based impedance approach for robot force regulation with prescribed force limits. Math Probl Eng, 2015: 918301.
17. Ren G, Chen W, Dasgupta S, Kolodziejski C, Wörgötter F, Manoonpong P. 2015. Multiple chaotic central pattern generators with learning for legged locomotion and malfunction compensation. Inf Sci, 294: 666-682.
18. Sarıkaya MS, El Naser YH, Kaçar S, Yazıcı İ, Derdiyok A. 2024. Chaotic-based improved Henry gas solubility optimization algorithm: Application to electric motor control. Symmetry, 16(11): 1435.
19. Sarıkaya MS, Demirel O, Kaçar S, Derdiyok A. 2025. Modelling and chaotic based parameter optimization of sliding mode controller. J Math Sci Model, 8(2): 42-54.
20. Shih CL, Hsu JH, Chang CJ. 2017. Visual feedback balance control of a robot manipulator and ball-beam system. J Comput Commun, 5(9): 8-18.
21. Simanjorang MR, Susanto H, Bukhori ML. 2022. Design and construction of mixer with variable speed for manufacturing nanoparticle composite materials. Teknika STTKD J Tek Electron Eng, 8(2): 257-266.
22. Sprott JC. 1994. Some simple chaotic flows. Phys Rev E, 50(2): R647.
23. Tanaka J, Ogawa A, Nakamoto H, Sonoura T, Eto H. 2020. Suction pad unit using a bellows pneumatic actuator as a support mechanism for an end effector of depalletizing robots. ROBOMECH J, 7: 1-30.
24. Telegenov K, Tlegenov Y, Hussain S, Shintemirov A. 2015. Preliminary design of a three-finger underactuated adaptive end effector with a breakaway clutch mechanism. J Robot Mechatron, 27(5): 496-503.
25. Xiang C, Guo J, Rossiter J. 2019. Soft-smart robotic end effectors with sensing, actuation, and gripping capabilities. Smart Mater Struct, 28(5): 055034.
26. Yagmur D, Kutlu M. 2024. 3D chaotic mixing application for polymer production. Phys Scr, 99(4): 045210.
27. Yang J, Xie Y, Feng M, Li J. 2019. Design and implementation of admittance control for a dual-arm robot under space limitation. In: MATEC Web Conf, 256: 02010.
28. Zang X, Iqbal S, Zhu Y, Liu X, Zhao J. 2016. Applications of chaotic dynamics in robotics. Int J Adv Robot Syst, 13(2): 60.
29. Zhao N, Murakami K, Yamakawa Y. 2024. Vision-based trajectory dynamic compensation system of industrial robot. Int J Adv Manuf Technol, 131(12): 6013-6026.