Erdem Ilten

Recent developments in fractional calculus reveal that fractional operators enable the emergence of new chaotic behaviors that cannot be observed in integer-order systems. When the characteristics of chaotic systems are combined with fractional calculus, the complexity and unpredictability of the system are further enhanced. This study examines two simple yet topologically similar six-term chaotic systems, namely Sprott H and Sprott K, to explore their application in deep learning within the framework of fractional calculus. Through the analysis of time series data, phase portraits, Lyapunov exponents, and bifurcation diagrams, it is demonstrated that the fractional-order Sprott H (FOS-H) and fractional-order Sprott K (FOS-K) chaotic systems exhibit chaotic behavior under specific system parameters and fractional orders. A dataset of 28,800 time series samples is generated and classified using pre-trained deep learning models, including GoogleNet, MobileNet-v2, DarkNet-19, DarkNet-53, and EfficientNet-b0, with transfer learning techniques applied. Using the SGDM optimizer with a learning rate of 0.0003, all models, except DarkNet-19, achieve high classification accuracy. To assess generalization, a 3160-sample test dataset from lower order fractional chaotic systems (0.8 for FOS-H, 0.82 for FOS-K) is introduced, where DarkNet-53 achieves 100% accuracy and GoogleNet reaches 99.77%, outperforming other models. Additionally, a comparison with classical machine learning methods (Support Vector Machines (SVM), Decision Tree, Random Forest) reveals that while SVM achieves 99.77% validation accuracy, its performance declines for lower fractional orders. Test results confirm that GoogleNet offers the best balance between accuracy and resource efficiency, making it suitable for real-time applications. These findings demonstrate that deep learning models, particularly DarkNet-53 and GoogleNet, can effectively classify chaotic time series with varying fractional orders, even when encountering previously unseen system dynamics.

In this study, a real-time toxic gas measurement and early warning mechanism is proposed to prevent accidents that may occur in underground mining facilities. Temperature, oxygen (O2), hydrogen sulfide (H2S), methane (CH4), carbon monoxide (CO) and dust density sensor data are read via Arduino Mega analog inputs. All sensor data is transferred to the PLC-SCADA (Programmable Logic Controller - Supervisory Control and Data Acquisition) system via ethernet in real time. Thanks to the designed SCADA screen, sensor values can be monitored instantly. In addition, it can be checked whether the system is alarm and whether the ventilation system works. According to the underground coal mine regulations, work cannot be done in places where the mine air contains less than 19% oxygen, more than 2% methane, more than 50 ppm (0.005%) carbon monoxide and other hazardous gases. The highest permissible hydrogen sulfur ratio for 8 hours of operation is 20 ppm (0.002%). An early warning mechanism was created with the algorithm written taking these limits into consideration. The tests of the designed system were carried out in a laboratory environment and successful results were observed.

In this paper, a synchronization study is proposed by using a 4D hyperchaotic system model to be used in secure data transfer applications. Active Disturbance Rejection Control (ADRC) method is used for synchronization process. To prove the success of ADRC method, it is compared with Proportional-Integral-Derivative (PID) control method. The coefficients of both control methods are optimized with Particle Swarm Optimization (PSO) algorithm. Synchronization system is modelled and tested in Matlab/Simulink environment. ADRC and PID methods are tested in simulation environment for the cases without disturbance and under disturbance. It can be seen from the test results that the ADRC method managed to keep the system synchronous without being affected by any disturbances. On the other hand, it is clearly seen that the PID method cannot maintain the synchronization of system under disturbance effects.

This paper focuses on fractional-order modeling and the design of a robust speed controller for a nonlinear system. An induction motor (IM), widely used in Electrical Vehicles (EVs), is preferred in this study as a well-known nonlinear system. The major challenge in designing a robust speed controller for IM is the insufficiency of the machine model due to inherent machine dynamics. Fractional calculus is employed to model the IM using the small-signal method, accounting for model uncertainties. In this context, experimental data is approximated using a fractional-order small-signal transfer function. Consequently, a mixed sensitivity problem is formulated with fractional-order weighting functions. The primary advantage of these weighting functions is their greater flexibility in solving the mixed sensitivity problem by involving more coefficients. Hereby, three robust speed controllers are designed using the PID toolkit of the Matlab program and solving the H_∞ mixed sensitivity problem, respectively. The novelty and contribution of the proposed method lie in maintaining the closed-loop response within a secure margin determined by fractional weighting functions while addressing the controller design. After evaluating the robust speed controllers with Bode diagrams, it is proven that all the designed controllers meet the desired nominal performance and robustness criteria. Subsequently, real-time implementations of the designed controllers are performed using the dsPIC microcontroller unit. Experimental results confirm that the designed H_∞-based fractional-order proportional-integral-derivative (FOPID) controller performs well in terms of tracking dynamics, exhibits robustness against load disturbances, and effectively suppresses sensor noise compared to the robust PID and fixed-structured H_∞ controller.

Liquid level control in industrial applications is one of the classical control problems. The dynamic structure of two couple tank systems resembles many real systems such as boilers and oil refineries. It is the most controlled problem due to its non-linear structure and continuously changing phase properties. The liquid level of the tank is controlled by using a PI controller. The desired level is adjusted by using an ultrasonic sensor on the tank. The closed-loop system is operated by using a control interface designed by the Simulink program. The program prepared by Simulink is downloaded to Raspberry Pi over the Wi-Fi. The experimental input-output data of the system is provided by the external mode of Simulink. The user can adjust the speed of the fluid using the designed interface without a controller or control the liquid level by activating the controller on the same interface. This study provides great convenience to users to control and monitor the liquid level remotely.

This study represents a flux observer application for permanent magnet synchronous motor (PMSM) based electric vehicle (EV) system. Getting rid of speed sensors is very important for reducing EV cost. Firstly, motor control algorithm and observer algorithm are written on Simulink environment and download to TI F28335 DSP over USB by using Simulink Embedded Coder. Then the system is tested at variable speed which is changes every 10 seconds. The results show the performance of the flux observer estimation. It is seen that the flux observer successfully estimates the actual speed in most areas only expect for transients. The effectiveness of flux observer is proven via experimental results.

In recent years, the use of Raspberry Pi as a microcontroller in real-time applications has becomewidespread. In this study, Raspberry Pi is used for DC motor position control system. In addition, wirelesscommunication is provided between the external control panel prepared in the Matlab/Simulink programand the Raspberry Pi. Thanks to this control panel, the system can be turned on and off, the controller gainscan be changed, and the position information of the motor can be displayed on the scope in real-time.

A coupled tank system is designed for liquid level control application with Raspberry Pi 4B board. To control of the liquid level, Active Disturbance Rejection Control (ADRC) method is used. Control algorithm is prepared on Simulink environment by using Simulink Support Package for Raspberry Pi hardware tool of Matlab. Then, the algorithm is loaded to Raspberry Pi board to run as microcontroller. The level control system is tested in real-time and results are obtained. It is seen that the ADRC method works stably in the system.