Search Results (170)

Photovoltaic (PV) generation and electric vehicle (EV) charging infrastructure are changing the dynamic behavior of current power systems, especially in terms of voltage stability and LVRT capabilities. In this work, 50% PV penetration on a modified Kundur two-area power system was tested to mitigate transient instability under severe fault circumstances. With PV units running at unity power factors under steady-state conditions, 50% PV penetration was defined relative to the system’s total active load demand. A steady-state power-flow study ensured generation–load balance before MATLAB/Simulink dynamic simulations. Controllable reactive power compensation was used as an EV aggregator on Bus 7. We constructed and evaluated a genetic algorithm (GA)-optimized fractional-order proportional–integral–derivative (FOPID) controller with a traditional PID controller utilizing identical optimization conditions. An inter-area tie-line critical three-phase fault was applied and removed after 100 ms to evaluate system performance. While the GA-PID controller increased transient performance, it did not restore system stability. Instead, the GA-FOPID controller provided superior dynamic support by restoring Bus 7 voltage to 0.9–1.1 pu within 250 ms after fault clearance and maintaining about 95% LVRT compliance. The suggested controller also reduced rotor angle oscillations and enhanced inter-area damping. Fractional-order control increased EV aggregators’ reactive power response during transient shocks. Thus, in renewable-energy-dominated power systems, the GA-FOPID-controlled EV support technique may improve voltage stability and LVRT compliance. Full article

Automatic voltage regulation (AVR) systems play an important role in maintaining voltage stability, ensuring efficiency, and enhancing the reliability of synchronous generators. Although conventional PID (proportional-integral-derivative) controllers are widely adopted for AVR systems due to their simplicity and robustness, their performance is still limited under dynamic operating conditions. In this paper, this problem is addressed by developing an intelligent controller using a deep reinforcement learning (DRL)-based PID controller, which integrates PID with a reinforcement learning agent to create an adaptive intelligent controller for AVR systems. A comprehensive evaluation of AVR system performance under four control configurations is presented: (1) a conventional PID controller optimised using three recent hybrid optimisation algorithms, (2) a fractional-order proportional-integral-derivative (FOPID) controller tuned with the same hybrid algorithms, (3) a proposed DRL-based FOPID controller, and (4) a proposed DRL-based PID controller. The DRL-based PID controller parameters are adapted by using the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, which allows the improvement of generalisation and adaptive learning. The simulation results demonstrate that the proposed DRL-FOPID controller significantly improves performance compared to both the conventional PID and conventional FOPID controllers that were tuned using a hybrid optimisation algorithm. The results emphasise the DRL-based controller in the development of intelligent controllers for AVR systems. Full article

This paper investigates the synchronization problem for a class of proportional Caputo fractional-order neural networks with respect to another function. A master–slave framework is formulated, and a linear state-feedback controller is proposed for the response system. Under a standard Lipschitz condition on the activation functions, sufficient conditions ensuring the convergence of the synchronization error to zero are established. The analysis is based on an explicit integral representation of the error system, a generalized Gronwall-type inequality, and asymptotic properties of the Mittag–Leffler function. The obtained criterion explicitly reveals the roles of the fractional order, the proportional parameter, the control gain, and the network interconnection matrix. Numerical experiments based on a benchmark fractional Hopfield neural network illustrate the effectiveness of the proposed approach. In particular, a scaled benchmark satisfying all theoretical assumptions provides a strict validation of the main theorem, while the original benchmark highlights the conservative nature of the derived sufficient conditions. Full article

This paper presents a novel algebraic saturation-based Proportional–Integral–Derivative (ASB-PID) controller for achieving ultra-fast and well-damped dynamic response in automatic voltage regulator (AVR) systems. The proposed controller incorporates an algebraic saturation-based nonlinear transformation applied to both the error signal and its derivative, enabling adaptive control sensitivity across different operating regions. This formulation preserves high sensitivity near the equilibrium point while effectively limiting excessive control action under large transient deviations, thereby overcoming the inherent trade-off between response speed and overshoot observed in conventional PID-based controllers. To address the highly nonlinear and multimodal tuning problem, the controller parameters are optimally determined using the Animated Oat Optimization Algorithm (AOOA), which provides strong global exploration capability and stable convergence behavior. The effectiveness of AOOA is first validated through comparative analysis with widely used metaheuristic algorithms, including Particle Swarm Optimization (PSO), Gray Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), and Sine Cosine Algorithm (SCA). Furthermore, the proposed controller is benchmarked against recently developed high-performance AVR control strategies, including Gudermannian-PID (G-PID), fractional-order PID (FOPID), and higher-order PID-based controllers. Simulation results demonstrate that the proposed AOOA-optimized ASB-PID controller achieves a rise time of 0.0215 s and a settling time of 0.0383 s with zero overshoot and negligible steady-state error, significantly outperforming both competing optimization algorithms and state-of-the-art control designs. Comprehensive benchmarking further confirms that the proposed method consistently delivers superior performance in terms of speed, stability, and robustness, indicating that it provides an effective, computationally efficient, and scalable solution for high-performance AVR systems and broader nonlinear control applications. Unlike conventional nonlinear PID designs based on hyperbolic or sigmoid mappings, the proposed algebraic formulation provides a more explicit and effective saturation mechanism, enabling a superior balance between transient speed and overshoot suppression without increasing controller complexity. Full article

To address the key problems of low-frequency oscillation and insufficient regulation accuracy at the Point of Common Coupling (PCC) in hydro–wind–photovoltaic hybrid systems, which are caused by the randomness of wind and photovoltaic output, the water-hammer effect of hydropower units, and multi-source power coupling, a joint control strategy based on Fractional-Order Proportional Integral Derivative (FOPID) and Co-evolutionary Multi-objective Particle Swarm Optimization (CMOPSO) is proposed. First, a small-signal transfer function model of the system covering photovoltaic inverters, doubly fed induction generators (DFIGs), hydropower units and voltage-source converter-based high-voltage direct current (VSC-HVDC) converter stations is established to accurately characterize the water-hammer effect and multi-source dynamic coupling characteristics. Second, a Caputo-type FOPID controller is designed. Compared with traditional integer-order controllers with limited tuning flexibility, the FOPID controller utilizes its five degrees of freedom to address specific multi-source coupling challenges. This precisely compensates for the non-minimum phase lag caused by the water-hammer effect in hydropower units via the fractional derivative link, and effectively smooths the impact of stochastic wind–solar fluctuations on PCC voltage through the memory characteristics of the fractional integral link. This multi-parameter regulation mechanism prevents a trade-off between response speed and overshoot suppression, achieving effective decoupling of complex multi-source dynamic interactions. Third, a dual-objective optimization framework with the Integral of Time-weighted Absolute Error (ITAE) and Oscillatory Disturbance Risk Index (ODRI) as the objectives is constructed. The multi-population co-evolution mechanism of the CMOPSO algorithm is adopted to solve the Pareto-optimal solution set, realizing the coordinated optimization of dynamic response accuracy and oscillation instability risk. Finally, comparative simulations are carried out on the Simulink platform with traditional PI/FOPI controllers and optimization algorithms such as Multi-objective Particle Swarm Optimization based on the Decomposition/Simple Indicator-Based Evolutionary Algorithm (MPSOD/SIBEA). The results show that the proposed strategy can effectively suppress low-frequency oscillations in the range of 0~30 Hz. Compared with the traditional PI controller, the PCC voltage overshoot is reduced by more than 40%, the oscillation decay time is shortened by 33%, the ITAE and ODRI indices are decreased by 12.58% and 2.47%, respectively, and the stability of DC bus voltage is significantly improved. Its robustness and comprehensive control performance are superior to existing methods, providing an efficient and stable control scheme for power electronics-dominated complex new energy grid-connected systems. Full article

High penetration of converter-based wind generation reduces system inertia. It poses challenges to frequency stability in modern distribution networks, particularly in doubly fed induction generator (DFIG)-based wind-energy-conversion systems (WECSs), where frequency regulation is coupled with point-of-common-coupling (PCC) voltage and power factor (PF) dynamics. This study presents a multi-objective comparative evaluation of proportional–integral (PI), proportional–integral–derivative (PID), fractional-order PID (FOPID), and adaptive neuro-fuzzy inference system (ANFIS) controllers for a DFIG-based WECS connected to a radial distribution feeder. Controller parameters are tuned using multi-objective optimisation, considering frequency deviation, overshoot, settling time, disturbance robustness, control smoothness, and computational cost, while maintaining PCC voltage and PF within acceptable limits. MATLAB/Simulink simulations are conducted under turbulent wind conditions, load variations, voltage disturbances, and measurement noise. The results indicate that conventional PI and PID controllers exhibit limited performance under low-inertia conditions, whereas FOPID improves damping and voltage/PF behaviour. ANFIS achieves the best overall performance, providing reduced frequency deviation, faster settling time (below 3 s), improved disturbance rejection, and significantly lower integral absolute error (up to ~90%) compared to PI control. These findings offer practical guidance for selecting and tuning controllers to enhance frequency-centric stability in wind-integrated distribution networks. Full article

Renewable energy sources (RESs) enable sustainable and environmentally friendly electricity generation. However, their intermittent nature makes it difficult to maintain energy balance. Smart grids (SGs) address this challenge by enabling grid control under variable demand and fluctuating generation. With the growing share of distributed generation, dynamic energy pricing has become increasingly important for sustaining the supply–demand balance in SGs. This study aims to regulate the interaction between variable demand and distributed generation in SGs using control strategies. The dynamic pricing framework was analyzed using closed-loop Proportional–Integral–Derivative (PID), Fractional-Order PID (FOPID)- and Adaptive Neuro Fuzzy Inference System (ANFIS)-based FOPID controllers. PID and FOPID parameters were tuned by pole placement with reference model matching, while the FOPID parameters in the ANFIS-FOPID structure were adaptively optimized using ANFIS. Energy supply–demand models were developed in MATLAB/Simulink, and the effects of each controller on system dynamics and energy prices were comparatively examined. The results indicate that ANFIS-FOPID achieves lower overshoot, shorter settling time, and more stable balancing performance, owing to its fractional-order flexibility and optimized parameters. In the model established in the MATLAB/Simulink environment, the controllers were evaluated based on integral of squared error (ISE), time-weighted integral absolute error (ITAE), root mean square error (RMSE), average unit energy price, price volatility, and coefficient of variation. A virtual energy storage model was added to the system. Disturbance and load change scenarios were also examined. The results showed that the ANFIS-FOPID controller provided the most balanced performance in terms of error reduction, suppression of price fluctuations, and reduction of the average unit energy price. Full article

This paper presents a novel proportional–integral–derivative (PID) control framework for first $\alpha$-order systems evolving in fractal time. The main contribution is the extension of classical control theory to systems exhibiting anomalous temporal scaling by employing local fractal derivatives. In contrast to fractional-order PID (FOPID) approaches, which primarily model memory effects, the proposed fractal PID framework captures time-scaling behavior arising in non-smooth environments, such as viscoelastic friction and irregular contact surfaces. The closed-loop dynamics are formulated as a second $\alpha$-order fractal differential equation, from which a characteristic equation is derived to establish conditions for asymptotic stability. It is shown that, for a constant reference input and positive controller gains, the tracking error converges to zero as $t\to \infty$. In addition, a quantitative performance analysis demonstrates that the fractal-order $\alpha$ governs temporal stretching: smaller values of $\alpha$ lead to increased rise and settling times and reduced oscillation frequency. The effectiveness of the proposed approach is illustrated through applications to a thermal system with fractal heat input and robotic actuators operating in irregular environments. These results highlight the potential of fractal-time control as a systematic framework for modeling and controlling dynamical systems with non-integer temporal structure. Full article

Quadrotor UAVs present a significant control challenge due to their underactuated nature; strong coupling effects; nonlinear dynamics; and high sensitivity to unknown effect parameters, external disturbances, and uncertainties. To address this issue, this study proposes a Lyapunov-based backstepping (LYP) controller that ensures robust stability and precise trajectory tracking. The controller employs an inner- and outer-loop architecture for coupled position and attitude control. Its performance is compared with Proportional–Integral–Derivative (PID) and Fractional-Order PID (FOPID) controllers under three scenarios: nominal conditions, external disturbances, and model parameter uncertainties. All controller gains are optimized using Particle Swarm Optimization (PSO). Simulation results, which are evaluated using time-domain metrics and root mean square error (RMSE), demonstrate that the proposed LYP controller achieves superior robustness, faster disturbance rejection, and improved tracking accuracy compared to both PID and FOPID controllers. Full article

The global shift toward decentralized generation has established standalone energy supply systems as a vital solution for remote regions. However, the integration of intermittent renewable sources and the inherent lack of rotational inertia in power electronic interfaces create significant challenges for frequency stability. This study addresses these issues by introducing an original Two-Tier Fractional-Order PID (TTFOPID) controller designed for robust Load Frequency Control (LFC) in a hybrid system comprising solar, diesel, biodiesel, and battery energy storage (BESS). The research utilizes the Multi-Objective Imperialist Competitive Algorithm (MOICA), enhanced with an attractive and repulsive assimilation phase, to navigate the high-dimensional parameter space. A unique framework is established to simultaneously tune controller gains and high-level system parameters, specifically BESS sizing and droop settings. Results demonstrate that the MOICA-tuned TTFOPID provides superior performance, achieving a 72% improvement in the Integral of Time-Weighted Absolute Error (ITAE) compared to NSGA-II and a 56% improvement in the Integral of the Square of Control (ISC) compared to MOPSO. Furthermore, robustness analysis validates the controller’s stability against significant parametric variations. The study concludes that the integrated TTFOPID-MOICA approach provides a superior pathway for stabilizing autonomous energy supply systems while protecting hardware longevity through optimized control effort. Full article

The increasing need for energy-efficient and environmentally friendly electricity generation has led to the extensive use of hybrid electric systems. These systems integrate different energy sources in an effort to take advantage of the positives of each technology, as using a single source of energy comes with many limitations and disadvantages; hence, the popularity of hybrids has increased in recent times. In this regard, this paper proposes a lithium-ion battery (LIB) and ultracapacitor (UC)-based hybrid architecture considering an optimal energy management framework. In the transportation sector, hybrid vehicles (LIB and UC-based vehicles) effectively utilize the high energy density and power density of LIBs and UCs. This LIB and UC-based hybrid architecture provides an efficient power management solution considering the high power density of the LIB for smooth road profiles, and the high power density of the UC is driven during sudden spikes in load demand because the LIB will not function optimally during the sudden spikes due to lower power density. Furthermore, in order to achieve efficient utilization of the proposed hybrid system, an optimal energy management framework is used. In this regard, in this study, a fractional-order proportional–integral–derivative (FOPID) controller has been designed for effective and optimal energy management. Furthermore, the designed FOPID has been optimized using a metaheuristic technique, namely particle swarm optimization (PSO), to enhance LIB and UC-based hybrid electric vehicle energy management performance. Employing dynamic and optimal energy flow control, the FOPID-based system improves energy consumption, extends LIB life, and improves overall system performance and reliability. Full article

Desertification is one of the main threats to high Andean ecosystems, particularly in arid and semi-arid regions subject to increasing climatic and anthropogenic pressures. This study evaluated the spatial-temporal dynamics of desertification in the province of Candarave (Tacna, Peru) by integrating the Remote Sensing-based Desertification Index (RSDI), constructed from a principal component analysis incorporating four biophysical indicators: vegetation greenness, surface moisture, soil grain size, and fraction of solar radiation reflected (albedo), derived from Landsat 5 and 8 satellite images processed in Google Earth Engine. Temporal trends were analyzed using the Mann–Kendall test, while system stability was evaluated using the coefficient of variation, allowing different degrees of stability and environmental degradation to be characterized during the period 2010–2025. The results show that moderate and severe desertification classes predominate in higher altitude areas, covering approximately 92% of the study area, and are characterized by insignificant to weakly significant negative trends associated with high to relatively high temporal volatility. In contrast, stable areas with no significant changes represent 5.3% of the territory, while restoration processes occupy a small proportion, close to 2.7%. The high variability observed in the high Andean sectors is mainly linked to the interaction between reduced water availability, climate variability, and extreme events, as well as anthropogenic pressures, particularly overgrazing and aquifer exploitation. This multitemporal analysis allows us to anticipate the evolution of desertification and highlights the need to strengthen conservation planning in order to reduce the degradation of strategic high Andean ecosystems in the Tacna region. Full article

The fractional Fourier transform (FRFT) serves as an effective tool for linear frequency modulated (LFM) signal parameter estimation, whose performance depends on the search efficiency for the optimal transform order. To address the issues of fixed inertia weight in the standard particle swarm optimization (PSO) algorithm, which tends to fall into local optima and suffers from insufficient convergence accuracy, this paper introduces a proportional-integral-derivative (PID) control strategy and proposes a PID-PSO-FRFT-based LFM signal parameter estimation method. This approach introduces a PID controller, which takes the deviation between the particle’s current position and the global best position as input and dynamically adjusts the inertia weight through proportional, integral, and derivative regulation, thereby achieving an adaptive balance between global exploration and local exploitation capabilities of the particles. Simulation results demonstrate that, compared with the basic PSO-FRFT algorithm, the proposed method significantly improves the estimation accuracy of the center frequency and chirp rate of LFM signals under SNR conditions ranging from −9 dB to −7 dB, while considerably reducing computation time, exhibiting superior noise resistance, and exhibiting superior robustness. Full article

Robust controller tuning is essential for the accurate regulation of nonlinear dynamic plants operating under variable conditions. This study proposes an enhanced gradient-based optimizer, termed the quadratic wavelet–enhanced gradient-based optimizer (QWS–GBO), which integrates quadratic interpolation mutation (QIM) and a wavelet mutation strategy (WMS). QIM reinforces population diversity, while WMS mitigates stagnation and strengthens local refinement through adaptive perturbations, yielding a more effective balance between global exploration and local exploitation. QWS–GBO is employed in a reference–follower control framework based on Bode’s ideal response, where the follower is realized by a fractional-order proportional–integral–derivative (FOPID) controller. The FOPID parameters are optimized using QWS–GBO and evaluated in two stages. First, performance is assessed on the CEC2020 benchmark suite under a uniform protocol. Second, the approach is applied to DC motor speed regulation. On the CEC2020 functions, QWS–GBO consistently achieves lower mean objective values and faster convergence than GBO, dwarf mongoose optimization (DMO), the arithmetic optimization algorithm (AOA), and the salp swarm algorithm (SSA) with only minor computational overhead (35.90 s per trial versus 34.00 s for GBO). In the DC motor case, the QWS–GBO–tuned FOPID controller attains a rise time of 0.0216 s, settling time of 0.0350 s, zero overshoot, and peak time of 0.0509 s. Robustness tests under four operating conditions showed limited deviations (maximum 0.0058 s in rise time, 0.0113 s in settling time, 0.465% in overshoot, and 0.0131 s in peak time). Additional analyses confirmed that both QIM and WMS individually contribute measurable gains, validating their joint integration. Implementation details and parameter settings are provided to ensure reproducibility. Full article

Magnetic ball suspension (MBS) systems are widely used as benchmark platforms in control engineering due to their nonlinear dynamics and inherent open-loop instability, which pose substantial challenges for conventional linear control strategies. The objective of this study is to investigate a hyperbolic tangent–based proportional–integral–derivative (tanh-PID) control structure for MBS systems and to assess the suitability of the artificial lemming algorithm (ALA) for tuning its parameters within a simulation-based benchmark framework. The proposed approach embeds smooth nonlinear signal shaping through the hyperbolic tangent function directly into the classical PID structure, while controller parameters are obtained via metaheuristic optimization using ALA. A performance index balancing overshoot suppression and tracking error minimization is adopted, and the controller is evaluated on a linearized MBS model to ensure comparability with existing studies. Simulation results demonstrate that the optimized tanh-PID controller achieves improved transient and steady-state performance, including a rise time of 0.0144 s, settling time of 0.0275 s, overshoot of 2.98%, and a steady-state error of 2.69 × 10⁻⁵, when compared with classical PID, fractional-order PID (FOPID), and real PID with second-order derivative (RPIDD²) controllers under identical conditions. The results indicate that bounded nonlinear preprocessing combined with metaheuristic-based parameter tuning can provide an effective and practical control alternative for unstable nonlinear systems such as magnetic ball suspension systems. Full article