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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Hamidzadeh, Seyed Mohamad
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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CHAOS CONTROL IN PERMANENT MAGNET SYNCHRONOUS MOTOR BY SLIDING MODEL CONTROLLER WITH LYAPUNOV OBSERVER UNDER UNKNOWN INPUTS Hamidzadeh, Seyed Mohamad; Aziz, Amiral; Mohamed, Mohamad Afendee; Vaidyanathan, Sundarapandian; Johansyah, Muhamad Deni
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0541-0556

Abstract

The control of chaotic and hyper-chaotic systems represents a crucial area of research in the field of nonlinear dynamic systems. In this study, we focus on applying chaos control techniques to a permanent magnet synchronous motor (PMSM), a system known to exhibit chaotic behavior under certain conditions. To achieve this, a sliding mode control (SMC) strategy integrated with a Lyapunov-based observer is proposed. The core concept involves designing a candidate Lyapunov function that governs the application of the control law, ensuring system stability while effectively suppressing chaotic dynamics. Through numerical simulations, the proposed sliding mode controller demonstrates its effectiveness in rapidly eliminating chaotic behavior and stabilizing the PMSM system toward a predefined reference trajectory. Notably, the system achieves error convergence within approximately 0.7 seconds under full control (four channels). When control channels are reduced to two, the system still maintains stability, showing flexibility and cost efficiency. In a further simulation, the chaotic PMSM is subjected to two unknown external disturbances, and the proposed controller continues to maintain stability with only a slight increase in convergence time. These quantitative results affirm the robustness, accuracy, and practicality of the proposed control method. This research confirms that integrating sliding mode control with a Lyapunov observer is an effective approach for chaos suppression in PMSMs, offering promising insights for the development of advanced control strategies in nonlinear electromechanical systems.
DESIGN AND IMPLEMENTATION OF ANFIS CONTROLLERS FOR STABILIZING FINANCIAL SYSTEMS: A COMPARATIVE STUDY WITH NONLINEAR FEEDBACK CONTROL Patria, Lintang; Hamidzadeh, Seyed Mohamad; Mohamed, Mohamad Afendee
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1317-1330

Abstract

The study revisits the well-known Bouali chaotic financial model, which is characterized by nonlinear dynamics. As a benchmark, the nonlinear feedback control method is implemented and compared with an Adaptive Neuro-Fuzzy Inference System (ANFIS) controller. The ANFIS model is trained using 250 data samples derived from the nonlinear feedback controller and divided into training, validation, and testing subsets. The proposed ANFIS controller demonstrates superior stabilization performance by effectively eliminating chaotic behavior, ensuring stability, and achieving faster convergence than the traditional nonlinear feedback method. Quantitative results confirm this improvement: the ANFIS controller achieved very low Root Mean Square Error (RMSE) values, such as 8.78×10−5 for training and 1.37×10−4 for validation in the profit control input, highlighting its learning accuracy. Additionally, the ANFIS maintained stability even with a reduced number of controllers, demonstrating robustness and adaptability. These findings emphasize the potential of ANFIS controllers to provide efficient and reliable chaos control in complex financial systems.
Co-Authors Amiral Aziz Lintang Patria Mohamed, Mohamad Afendee Muhammad Deni Johansyah Vaidyanathan, Sundarapandian