Fractional Order Extremum Seeking Control Research Articles

Hybrid feedback control of PMSG-based WECS with multilevel flying-capacitor inverter enhanced by fractional order extremum seeking

This paper proposes an original hybrid control strategy for a three-phase multilevel flying capacitor inverter (FCI) used in wind energy conversion system (WECS). A state feedback law, computed using a Lyapunov function and an invariance principle, is designed to manage grid current control and capacitor voltage balancing, guaranteeing the asymptotic stability of the closed-loop system. Additionally, a fractional-order extremum seeking control (FOESC) algorithm for Maximum Power Point Tracking (MPPT) is introduced, which optimizes power capture by adjusting turbine speed from the DC side without requiring a detailed system model (model-free approach). The use of fractional-order calculus leads to improved convergence and more seamless performance while preserving the robust characteristics of the system. The proposed control strategies are validated through simulation, demonstrating improved transient response and stability under varying wind conditions and parameter uncertainties. These results highlight the potential of advanced control algorithms to enhance the efficiency and reliability of wind energy systems, contributing to global efforts to achieve sustainable energy goals.

Fractional-Order Extremum Seeking Method for Maximum Torque per Ampere Control of Permanent Magnet Synchronous Motor

Maximum torque per ampere (MTPA) control of internal permanent magnet synchronous motors (IPMSM) has become integral to high-efficiency motor drives. To minimize the influence of the traditional model-based analytical solution method on the MTPA control strategy due to the parameter variations during the motor operation, an online search MTPA method without model-based fractional-order extremum seeking control (FO-ESC) is proposed. Compared with the traditional integer-order ESC method, the Oustaloup approximation-based fractional-order calculus provides additional factors and possibilities for optimizing controller parameters to improve control performance. At the same time, the proposed approach does not require machine parameters and is thus not influenced by machine and drive nonlinearities. Simulation results show that the proposed method can ensure robust MTPA control under different loading conditions in real-time and improve the system’s dynamic response speed and steady-state accuracy.

An Improved Nonlinear Predictive Control Strategy Enhanced by Fractional Order Extremum Seeking Control of the Antilock Braking System of a Vehicle

Extremum seeking control can search the optimal slip rate of the antilock braking system of a vehicle through a high-frequency sinusoidal excitation signal. However, because of the bandwidth limitation of the braking actuator, the search speed of the optimal slip rate decreases and the stability of the extremum seeking control system becomes worse. To search and control the optimal slip rate, an improved nonlinear predictive control strategy enhanced by fractional order extremum seeking control is proposed for the vehicle antilock braking system. First, the nonlinear dynamic model of the braking system is established. Then, nonlinear prediction control is designed with the prediction of the slip rate response based on the nonlinear model to achieve slip rate control. Using fractional order calculus, a fractional extremum seeking controller is proposed to search for the optimal slip rate. Nonlinear predictive control integrated with fractional extremum seeking control is proposed to achieve the function of vehicle antilock braking. Finally, the effectiveness of the proposed method is verified by simulating the vehicle antilock braking system under different road conditions. The result shows that by considering the actuator available bandwidth, the proposed fractional order extremum seeking control can improve the search speed of the optimal slip rate compared with traditional integer order extremum seeking control. The proposed integrated controller achieves wheel slip rate optimal control regardless of the road conditions.

Fractional Order Extremum Seeking Control: Performance and Stability Analysis

In this paper, a novel extremum-seeking control algorithm called fractional order extremum-seeking control is analyzed and benchmarked against the traditional integer order one. Utilizing fractional order operators in extremum-seeking scheme improves the convergence speed, robustness, and performance of this method without employing additional blocks. Using averaging model, the detailed analysis of fractional order extremum-seeking control is presented. Simulation and experimental results support the mathematical analysis and demonstrate that the proposed scheme outperforms the traditional extremum-seeking algorithm.

Performance analysis of fractional order extremum seeking control

Extremum-seeking scheme is a powerful adaptive technique to optimize steady-state system performance. In this paper, a novel extremum-seeking scheme for the optimization of nonlinear plants using fractional order calculus is proposed. The fractional order extremum-seeking algorithm only utilizes output measurements of the plant, however, it performs superior in many aspects such as convergence speed and robustness. A detailed stability analysis is given to not only guarantee a faster convergence of the system to an adjustable neighborhood of the optimum but also confirm a better robustness for proposed algorithm. Furthermore, simulation and experimental results demonstrate that the fractional order extremum-seeking scheme for nonlinear systems outperforms the traditional integer order one.