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The doubly fed induction generator (DFIG)-based wind energy conversion systems (WECSs) are prone to certain uncertainties, nonlinearities, and external disturbances. The maximum power transfer from WECS to the utility grid system requires a high-performance control system in the presence of such nonlinearities and disturbances. This paper presents a nonlinear robust chattering free super twisting fractional order terminal sliding mode control (ST-FOTSMC) strategy for both the grid side and rotor side converters of 2 MW DFIG-WECS. The Lyapunov stability theory was used to ensure the stability of the proposed closed-loop control system. The performance of the proposed control paradigm is validated using extensive numerical simulations carried out in MATLAB/Simulink environment. A detailed comparative analysis of the proposed strategy is presented with the benchmark sliding mode control (SMC) and fractional order terminal sliding mode control (FOTSMC) strategies. The proposed control scheme was found to exhibit superior performance to both the stated strategies under normal mode of operation as well as under lumped parametric uncertainties.

This paper suggests a developed virtual inertia-damping control (VIDC) scheme to improve the frequency stability of low-inertia, renewable-dominated power systems. The introduced approach integrates fractional-order control theory into both virtual primary and secondary control loops (FO-VPSC), coordinated with a Battery Energy Storage System (BESS)-based VIDC, to provide richer phase shaping and greater flexibility in mitigating diverse system disturbances. To ensure robustness and adaptability, the FO-VPSC parameters are optimally tuned using the Dandelion Optimizer (DO) algorithm. The effectiveness of the proposed strategy is validated on a two-area interconnected renewable power system comprising heterogeneous sources, including a thermal power plant, solar and wind units, and BESSs. Simulation results reveal that the proposed FO-VPSC significantly enhances the system’s dynamic response, achieving a 35–45% reduction in frequency overshoot, up to a 42% improvement in settling time, and a 30% reduction in frequency deviation magnitude compared with conventional VIDC. Moreover, the proposed control strategy improves inter-area oscillation damping and ensures stable operation under renewable penetration above 60% reduction in system inertia and damping constants. These results confirm that the FO-VPSC-based VIDC provides superior adaptability and resilience for next-generation low-inertia grids.

Currently, a two-level voltage source inverter (2L-VSI) is regarded as the cornerstone of modern industrial applications. However, the control of VSIs is a challenging task due to their nonlinear and time-varying nature. This paper proposes employing the fractional-order controller (FOC) to improve the performance of model-free predictive control (MFPC) of the 2L-VSI voltage control in uninterruptible power supply (UPS) applications. In the conventional MFPC based on the ultra-local model (ULM), the unknown variable that includes all the system disturbances is estimated using algebraic identification, which is insufficient to improve the prediction accuracy in the predictive control. The proposed FO-MFPC uses fractional-order proportional-integral control (FOPI) to estimate the unknown function associated with the MFPC. To get the best performance from the FOPI, its parameters are optimally designed using the grey wolf optimization (GWO) approach. The number of iterations of the GWO is 100, while the grey wolf’s number is 20. The proposed GWO algorithm achieves a small fitness function value of approximately 0.156. In addition, the GWO algorithm nearly finds the optimal parameters after 80 iterations for the defined objective function. The performance of the proposed FO-MFPC controller is compared to that of conventional MFPC for the three loading cases and conditions. Using MATLAB simulations, the simulation results indicated the superiority of the proposed FO-MFPC controller over the conventional MFPC in steady state and transient responses. Moreover, the total harmonic distortion (THD) of the output voltage at different sampling times proves the excellent quality of the output voltage with the proposed FO-MFPC controller over the conventional MFPC controller. The results confirm the robustness of the two control systems against parameter mismatches. Additionally, using the TMS320F28379D kit, the experimental verification of the proposed FO-MFPC control strategy is implemented for 2L-VSI on the basis of the Hardware-in-the-Loop (HIL) simulator, demonstrating the applicability and effective performance of our proposed control strategy under realistic circumstances.

This paper deals with the longitudinal movement control of an airplane (pitch angle) using fractional order adaptive controllers (FOACs). It shows the improvements achieved in the plane’s behavior, in terms of the minimization of a given performance index. At the same time, less control effort is needed to accomplish the control objectives compared with the classic integer order adaptive controllers (IOACs). In this study, fractional order direct model reference adaptive control (FO-DMRAC) is implemented at the simulation level, and exhibits a better performance compared with the classic integer order (IO) version of the DMRAC (IO-DMRAC). It is also shown that the proposed control strategy for FO-DMRAC reduces the resultant system control structure down to a relative degree 2 system, for which the control implementation is simpler and avoids oscillations during the transient period. Moreover, it is interesting to note that this is the first time that an FOAC with fractional adaptive laws is applied to the longitudinal control of an airplane. A suitable model for the longitudinal movement of the airplane related to the pitch angle θ as the output variable with the lifter angle (δe) as the control variable, is first analyzed and discussed to obtain a reliable mathematical model of the plane. All of the other input variables acting on the plane are considered as perturbations. For certain operating conditions defined by the flight conditions, an FO-DMRAC is designed, simulated, and analyzed. Furthermore, a comparison with the implementation of the classical adaptive general direct control (relative degree ≥ 2) is presented. The boundedness and convergence of all of the signals are theoretically proven based on the new Lemma 3, assuring the boundedness of all internal signals ω(t).

Due to the high interest in renewable energy and diversity of research regarding photovoltaic (PV) array, a great research effort is focusing nowadays on solar power generation and its performance improvement under various weather conditions. In this paper, an integrated framework was proposed, which achieved both maximum power point tracking (MPPT) and minimum ripple signals. The proposed control scheme was based on extremum-seeking (ES) combined with fractional order systems (FOS). This auto-tuning strategy was developed to maximize the PV panel output power through the regulation of the voltage input to the DC/DC converter in order to lead the PV system steady-state to a stable oscillation behavior around the maximum power point (MPP). It is shown that fractional order operators can improve the plant dynamics with respect to time response and disturbance rejection. The effectiveness of the proposed controller scheme is illustrated with simulations using measured solar radiation data.

In adaptive control, error models use system output error and adaptive laws to update controller parameters for control or identification tasks. Fractional-order calculus, involving non-integer-order derivatives and integrals, is increasingly important for modeling, estimation, and control due to its ability to generalize classical methods and offer improved robustness to disturbances. This paper addresses the gap in the literature where fractional-order gradient methods have not yet been extensively applied in identification and adaptive control schemes. We introduce a fractional-order error model with fractional-order gradient (FOEM1-FG), which integrates fractional gradient operators based on the Caputo fractional derivative. By using theoretical analysis and simulations, we confirm that FOEM1-FG maintains stability and ensures bounded output errors across a variety of input signals. Notably, the fractional gradient’s performance improves as the order, β, increases with β>1, leading to faster convergence. Compared to existing integer-order methods, the proposed approach provides a more flexible and efficient solution in adaptive identification and control schemes. Our results show that FOEM1-FG offers superior stability and convergence characteristics, contributing new insights to the field of fractional calculus in adaptive systems.

The global shift toward clean production, like using renewable energy, has significantly decreased the use of synchronous machines (SMs), which help maintain stability and control, causing serious frequency stability issues in power systems with low inertia. Fractional order controller-based virtual synchronous machines (FOC-VSMs) have become a promising option, but they rely on communication networks to work together in real time, causing them to be at risk of cyberattacks, especially from false data injection attacks (FDIAs). This paper suggests a new way to detect FDI attacks using a federated physics-informed long short-term memory (PI-LSTM) network. Each FOC-VSM uses its data to train a PI-LSTM, which keeps the information private but still helps it learn from a common model that understands various operating conditions. The PI-LSTM incorporates physical constraints derived from the FOC-VSM swing equation, facilitating residual-based anomaly detection that is sensitive to minor deviations in control dynamics, such as altered inertia or falsified frequency signals. Unlike traditional LSTMs, the physics-informed architecture minimizes false positives arising from benign disturbances. We assessed the proposed method on an IEEE 9-bus test system featuring two FOC-VSMs. The results show that our method can successfully detect FDI attacks while handling regular changes, proving it could be a strong solution.

This paper presents a novel fractional-order field-oriented control (FO-FOC) strategy for induction motor drives in electric vehicles (EVs) powered by an autonomous photovoltaic (PV) battery energy system. The proposed control approach integrates a fractional-order sliding mode controller (FO-SMC) into the conventional FOC framework to enhance dynamic performance, improve robustness, and reduce sensitivity to parameter variations. The originality of this work lies in the combined use of fractional-order control and real-time adaptive parameter updating, applied within a PV battery-powered EV platform. This dual-layer control structure allows the system to effectively reject disturbances, maintain torque and flux tracking, and mitigate the effects of component aging or thermal drift. Furthermore, to address the chattering phenomenon typically associated with sliding mode control, a continuous saturation function was employed, resulting in smoother voltage and current responses more suitable for real-time implementation. Extensive simulation studies were conducted under ideal conditions, with parameter mismatch, and with the proposed adaptive update laws. Results confirmed the superiority of the FO-based approach over classical integer-order designs in terms of speed tracking, flux regulation, torque ripple reduction, and system robustness. The proposed methodology offers a promising solution for next-generation sustainable mobility systems requiring high-performance, energy-efficient, and fault-tolerant electric drives.

This chapter contains sections titled: Fractional Calculus Fractional Order Controls Fractional Order Motion Controls Contributions Organization