A proportional-integral (PI) controller is still the workhorse in the industry due to its ease of commissioning and reliability. Therefore, this paper introduces an exponential PI (EXP-PI) controller as a potential alternative. In the proposed scheme, two tuneable EXP functions acting nonlinearly on the error and the rate of change of the error are incorporated in cascade with the PI control architecture. This controller is implemented as a speed controller on a permanent magnet DC motor drive system. Five recent intelligent algorithms, namely stochastic fractal search (SFS), snake optimizer (SO), dragonfly search algorithm (DSA), symbiotic organisms search (SOS) and reptile search algorithm (RSA) are employed to identify the best performer for calibrating the controller gains. According to the statistical results, SFS is found to provide controller gains of higher quality, reducing the designed cost function value to 48.19. The superiority of SFS is verified by the nonparametric Wilcoxon rank-sum test. Several experimental results with SFS-calibrated EXP-PI controller and other existing control schemes are presented using the DSP of TMS320F28335. The results show that our proposal performs better than its competing opponents in terms of various performance metrics, including integral-based error criteria, stability margin, overshoot and settling time for plants with and without dead time.

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.

This paper introduces a novel cascaded softsign function-based PID (CSoft-PID) controller designed for precise pressure regulation in highly nonlinear shell-and-tube steam condenser systems. For the first time in the literature, the classical PID control structure is enhanced through a cascaded nonlinear transformation using the softsign function, which dynamically adjusts the controller input according to the magnitude of the error. This architecture allows for high sensitivity near the setpoint while gracefully limiting excessive control efforts during larger deviations, thereby improving stability and transient performance. To optimally tune the six parameters of the proposed controller, a new hybrid optimization algorithm, termed hGASO-PS, is proposed. This method synergistically integrates an adaptive gbest-guided atom search optimization (ASO) strategy with the precision of the pattern search (PS) technique, ensuring both effective global exploration and fine-tuned local exploitation. The controller parameters are optimized by minimizing the integral of time-weighted absolute error (ITAE), subject to a step change in the condenser pressure setpoint. Extensive simulations and statistical evaluations demonstrate the superiority of the proposed approach. The hGASO-PS-based CSoft-PID controller achieved the lowest ITAE value of 2.1608, with an average of 2.2746 across 30 runs. It also demonstrated the fastest settling time (12.51 s) and the lowest overshoot (1.98%) among all tested controllers. Comparisons with recent PI, FOPID, and cascaded PI-PDN controllers confirm the consistent outperformance of the proposed method in both transient response and control precision, making it a promising candidate for industrial condenser applications.

Precise pressure regulation in nonlinear shell-and-tube steam condensers is essential for maintaining thermal efficiency and operational safety in power generation plants; however, conventional proportional-integral (PI) and proportional-integral-derivative (PID) controllers struggle with nonlinear dynamics, leading to overshoot, slower settling, and reduced robustness. In this regard, a novel hyperbolic tangent-based PID (tanh-PID) controller is developed in this study to introduce smooth nonlinear gain modulation, enabling enhanced damping behavior and improved transient shaping. The recently introduced artificial lemming algorithm (ALA) is employed to optimally tune the proposed controller for integral of time-weighted absolute error minimization. Extensive simulation studies are performed using a comprehensive nonlinear condenser model incorporating steam–air interactions and hot-well dynamics. The proposed strategy is benchmarked against four competitive optimization algorithms (coati optimization algorithm, dandelion optimizer, success-history based adaptive differential evolution with linear population size reduction, and adaptive artificial electric field algorithm) and compared with state-of-the-art PI and fractional-order PID (FOPID) controllers reported in the literature. The ALA-tuned tanh-PID achieves the lowest integral of time-weighted absolute error (2.1189), fastest rise time (0.5960 s), minimal settling time (12.4799 s) and overshoot (5.8056

DC-DC buck converters are inherently nonlinear systems that often operate under dynamically changing conditions, parameter uncertainties, and external disturbances, posing significant challenges for conventional control strategies. This paper introduces a novel cascaded proportional-integral and proportional-derivative (PI-PD) controller architecture, in which all controller parameters are optimally tuned using the recently developed Electric Eel Foraging Optimizer (EEFO), a bio-inspired metaheuristic algorithm modeled on the electrolocation and hunting behaviors of electric eels. The proposed control structure uniquely integrates a dual-loop configuration: the inner PI loop eliminates steady-state error, while the outer PD loop enhances dynamic response and mitigates rapid transient fluctuations. This cascaded arrangement enables decoupled tuning of steady-state and transient characteristics, offering superior control flexibility compared to conventional single-loop PID designs. To calibrate the controller, EEFO is employed to minimize a composite performance objective function that simultaneously considers settling time and overshoot, ensuring well-damped and rapid system behavior. A comprehensive set of simulation experiments was conducted in a MATLAB/Simulink environment to evaluate the proposed method against multiple benchmark algorithms-including the flood algorithm, gazelle optimization algorithm, and artificial hummingbird algorithm-as well as classical PID, PID acceleration (PIDA), and fractional-order PID (FOPID) controllers optimized by state-of-the-art metaheuristics. Across all key performance metrics-including rise time, settling time, percentage overshoot, peak time, and steady-state error-the EEFO-tuned cascaded PI-PD controller demonstrated consistently superior results, achieving near-zero overshoot, ultra-fast convergence, and minimal output deviation. Beyond nominal conditions, extensive robustness analyses were conducted to validate the controller's effectiveness under realistic disturbances, such as abrupt load changes, high-frequency measurement noise, time-delay effects in feedback channels, and +/- 10%-15% parametric variations in inductance and capacitance. In all scenarios, the controller retained stable output regulation, confirming its resilience and practical viability. To the best of our knowledge, this is the first study to deploy a cascaded PI-PD control structure specifically designed for DC-DC buck converters and optimized using the EEFO algorithm. The integration of a biologically inspired optimization framework with a decoupled dual-loop control scheme offers both architectural and algorithmic novelty. The proposed strategy addresses critical demands in nonlinear converter regulation and provides a robust, high-performance solution suitable for dynamic and uncertain power electronic environments.

This study presents a novel exponential proportional-derivative controller with filter (exp-PDN) for stabilising the nonlinear and underactuated ball and beam system. Unlike conventional PID-based approaches, the proposed controller removes the integral term, resulting in faster transient responses and improved robustness. It incorporates nonlinear exponential shaping of both the error and its derivative, along with a filtered derivative path for enhanced noise handling. A custom multi-objective cost function, comprising the squared error, settling time, and percent overshoot, is proposed to evaluate control performance. The quadratic interpolation optimiser (QIO), a recently developed metaheuristic based on analytical interpolation, is employed to optimise the controller parameters. To validate its effectiveness, the exp-PDN controller is compared against five state-of-the-art metaheuristic algorithms: QIO, spider wasp optimiser, komodo mlipir algorithm, golden eagle optimiser, and slime mould algorithm. The QIO-optimised exp-PDN achieves the best performance, with the lowest cost value (0.3211), minimal overshoot (5.52%), fast rise time (0.97 s), and smallest steady-state error (4.1643 x 10- 4). Further comparisons with QIO-optimised phase-lead and PID-with-filter controllers demonstrate the superiority of the proposed method in both transient and steady-state behaviour. In summary, this work advances the control of nonlinear unstable systems by delivering a structurally simple yet highly responsive control architecture. The combination of dual-channel exponential shaping and efficient metaheuristic optimisation results in state-of-the-art closed-loop performance, highlighting the practical value of the proposed exp-PDN framework for real-world control applications.

Power inconsistency between generation and demand causes to swing the frequency and tie-line power across the grid. Power-frequency swings undermine the reliability, security and stability of the grid, and may even cause power blackouts. The employment of an effective controller within load frequency management loop is therefore an inevitable necessity. An adaptive nonlinear PID (ANPID) controller enjoying interesting abilities is proposed in this article. Two nonlinear gains based on configurable hyperbolic functions of the error and the rate-of-error are utilized in cascade with the classical PID controller. The nonlinear characteristics of these gains make it possible to obtain a fast yet non-oscillatory response without excessive overshoots. Further, through a mathematical framework, it is revealed that the ANPID controller is equivalent to the PIDD2 controller with adaptive gains. Gains of the ANPID controller are prolifically calibrated using stochastic fractal search (SFS) algorithm. Performance achieved is tested for various power grids and a practical speed servo system under different circumstances. Furthermore, a comprehensive comparison against the state-of-the-art is also established to appraise the literal contribution of SFS calibrated ANPID controller. The results affirm the supremacy of our proposal over previously published control architectures concerning minimum values of settling time/undershoot/error criterion of the frequency and tie-line power swings.

Response Surface Methodology (RSM) is a powerful statistical technique that explores the relationship between input and output response variables using statistical methods and mathematical tools throughout the process. Optimization in the RSM is carried out using deterministic models that usually fall into local optima, losing the possibility of finding parameters that achieve better results. To overcome this problem, this article proposes applying metaheuristic algorithms (MA) in the optimization phase of RMS. Here MA offers a solution by optimizing the models derived from RSM. Three real problems are used to verify the performance of the combination of MA with RSM: removal of chemical oxygen demand, biodiesel synthesis from Ceiba pentandra oil, and biodegradation yield of reactive blue. The experimental results validate that the RSM with MA optimize with better results than the models obtained from the analysis of variance. For experimental purposes nine MA were used: Covariance Matrix Adaptation Evolution Strategy (CMAES), Differential Evolution (DE), Estimation of Distribution Algorithm (EDA), Particle Swarm Optimization (PSO), Comprehensive Learning PSO (CLPSO), Runge Kutta Optimizer (RUN), Dung Beetle Optimizer (DBO) Liver Cancer Algorithm (LCA), and Sea-Horse Optimizer (SHO). The metaheuristic with the best results in solving the three problems was the DE. The DE obtained an improvement of 0.56% over the removal of the first problem, for the second problem it obtained the same result as the deterministic technique, but in the third problem that showed surfaces with greater complexity, an improvement of 5.92 % was obtained. This research is a starting point for work in which RSM is applied to solve real-world problems that generate complex models.

The growing penetration of renewable energy sources in modern power systems has significantly complicated the challenge of load frequency control (LFC). The intermittent nature of solar and wind generation, coupled with increasingly unpredictable residential consumption patterns, undermines the effectiveness of traditional control mechanisms. Conventional proportional-integral-derivative (PID) controllers — including fractional-order, tilted, and filtered variants — are commonly employed but often fail to maintain frequency stability under such dynamic and nonlinear conditions. To overcome these limitations, this study proposes a novel Tilted Proportional Integral Filtered-Derivative Filtered-Accelerative (TPIDnAn) controller specifically designed to enhance LFC performance in renewable-dominated environments. The controller parameters are optimized using the Snake Optimizer (SO) algorithm, which offers robust tuning capabilities and improved adaptability. The proposed control strategy is rigorously tested on a two-area power system integrating solar photovoltaic (PV) and wind energy sources. Its performance is compared against other advanced controllers across multiple scenarios, including step load changes, random disturbances, generation rate constraint (GRC) non-linearity, and hybrid renewable integration. Evaluation metrics such as overshoot/undershoot (p.u.), transient time (s), peak time (s), and the integral of time-weighted absolute error (ITAE) confirm the superior effectiveness and resilience of the TPIDnAn controller in maintaining frequency stability and meeting LFC standards under diverse operating conditions.

Particle Swarm Optimization (PSO) is a widely used metaheuristic inspired by the collective behavior of bird flocks. However, its performance is susceptible to parameter tuning, particularly the inertia weight (ω) and acceleration coefficient (c1) that control the exploration process. This work proposes a fuzzy logic-based controller as an additional module to dynamically tune these parameters, improv­ing convergence and solution quality in different variants of recent generation PSO. The proposed fuzzy controller is designed to be adaptable to any PSO vari­ant without requiring modifications to its core structure. To evaluate its effective­ness, the controller was integrated into three PSO variants: Biogeography-Based Learning (BLPSO), Comprehensive Learning (CLPSO), and PSO with Gravita­tional Search Algorithm (PSOGSA). The enhanced versions (BLPSO FUZZYC, CLPSO FUZZYC, and PSOGSA FUZZYC) were compared with their standard counterparts using 40 unconstrained test functions, covering unimodal, multi-modal, hybrid, and shifted landscapes. Experimental results demonstrate that the fuzzy logic add-on improves the exploration-exploitation capability as required by the problem and the quality of solutions while maintaining algorithmic sta­bility. The results highlight the potential of fuzzy logic as a robust parameter adaptation strategy for PSO, making it a valuable enhancement for a wide range of optimization problems.

A new adaptive configuration of fuzzy logic controller (FLCh) based on the hyperbolic function is introduced to improve the performance of control systems. The presented configuration is named adaptive because its input scaling factors (SFs) are dynamically changed while the controller is servicing. This is accomplished by employing two hyperbolic functions with tunable slope and magnitude parameters to act on the input error signal and its derivative nonlinearly. The efficacy of our proposal is explored on a classical PID type FLC (C-PID-FLCh) and the controller parameters are simultaneously tuned using the stochastic fractal search (SFS) algorithm for proper functioning. Extensive simulations are conducted to assess the performance of the presented control scheme. A comparison study is also realised against the existing solutions to prove the true contribution of the work. The results show that thanks to the transient change in input SFs, the C-PID-FLCh exhibits faster yet nonoscillatory behaviour with reference to the reported schemes. The presented configuration does not cause major changes as far as the structure of the classical FLC is concerned, evolving C-PID-FLCh as a potential contender in control systems design.

Maintaining voltage stability within acceptable limits is crucial in power systems, with Automatic Voltage Regulation (AVR) ensuring consistent performance. Traditionally, PID controllers have been widely used; however, they struggle in complex, nonlinear environments with fluctuating conditions and disturbances. This study proposes an Extended PID-Acceleration (ePIDA) controller incorporating a novel state observer-based Disturbance Observer (DOB) for enhanced voltage regulation. The Snake Optimiser (SO) is introduced for the first time in AVR tuning, leveraging its dynamic leader-follower mechanism to achieve faster convergence and optimal controller gains. The SO-ePIDA framework extends the traditional PIDA structure with a three-degree-of-freedom (3DOF) approach, enhancing setpoint tracking and disturbance rejection. The proposed approach is evaluated against six widely used optimisation strategies through comparative statistical and graphical analyses, considering step-load variations and system parameter settings. Results demonstrate that the SO-ePIDA controller achieves a rise time of 0.1679 s, a settling time of 0.3123 s, and the lowest ISTAE value of 0.0046, ensuring superior transient response and steady-state accuracy. Furthermore, under a 30 % step-load disturbance, the proposed controller exhibits the fastest recovery time of 0.1065 s, significantly outperforming other methods. The AVR system was tested with ±25 % and ±50 % variations in system parameters to assess robustness under parametric uncertainty. The results confirm that the SO-ePIDA controller maintains stability, with rise time deviations limited to 0.1577 and 0.2004 s and ISTAE variations between 0.0116 and 0.1891, demonstrating strong adaptability under extreme operating conditions. These findings establish the SO-ePIDA framework as a robust, high-performance solution for real-world AVR applications.

In this study, a novel cascaded exponential proportional-integral-derivative (exp-PID) controller tuned by the starfish optimization algorithm (SFOA) is proposed for enhancing the transient and steady-state performance of nonlinear dynamic systems. The design objective is to achieve improved adaptability, robustness, and precision under varying operating conditions and external disturbances. The exponential PID structure introduces nonlinear modulation in the proportional and derivative components, enabling smoother control action and superior damping characteristics compared to conventional PID and fractional-order PID designs. The proposed SFOA-based exp-PID controller is validated on two benchmark systems: a DC motor speed control system and a three-tank liquid-level process. Across multiple independent trials, the controller achieved outstanding results, with the DC motor system attaining a rise time of 0.0039 s, settling time of 0.0083 s, and zero overshoot, while the three-tank system reached a rise time of 1.72 s, settling time of 2.47 s, overshoot of 1.5%, and steady-state error of 9.22 × 10⁻⁵%. Comparative analyses with recently developed algorithms (including the flood algorithm, greater cane rat algorithm, mantis search algorithm, and dandelion optimizer) as well as previously reported methods demonstrate the superior convergence behavior, stability, and accuracy of the proposed controller. Statistical evaluations further confirm the method's robustness and consistent performance across repeated runs.

This study employs Monte Carlo Simulation (MCS) within the structure of the Stochastic Fractional Search Algorithm (SFSA) to address circumstances involving uncertainty. The goal is to improve the system's performance by creating probability distribution functions for bus voltages and branch currents. We will use the resultant distribution in chance-constrained stochastic scheduling. The objective of the present research is to analyze the impact of uncertainties in the operation of photovoltaic (PV) systems, specifically in relation to different solar radiation conditions, on the amount of power loss. The approach focuses on including stochastic constraints in distribution systems instead of depending solely on precise deterministic boundaries. The goal is to enhance efficiency and ensure optimal consumption of power. This research enhances the knowledge base on PV unit positioning in distribution systems by integrating meta-heuristic optimization and MCS into a comprehensive framework. The investigation centers on the implementation of a chance-constrained method. We evaluate the optimization results using MCS under various uncertainty scenarios to demonstrate the effectiveness of the recommended approach. Furthermore, we conduct an analysis to assess the likelihood of exceeding the system's boundaries. The strategy's effectiveness is assessed by comparing the results of the SFSA with the Firefly algorithm (FA) utilizing probabilistic evaluation and simulation.

This research introduces a novel multi-objective version of the recently proposed prairie dog optimizer, the multi-objective prairie dog optimizer (MOPDO). Inspired by the foraging and burrowing activities of prairie dogs, which entail search exploration and particular responses to distinctive alarms for exploitation, MOPDO is proposed. This is a Pareto dominance-based approach to a modified and enhanced version of its single objective counterpart. MOPDO is able to deal with multiple objectives, explore, and exploit promising regions in the optimization landscape, and identify non-dominated solutions, providing decision makers with valuable trade-off choices. To demonstrate its practical applicability, MOPDO is applied to tackle five challenging structural design problems, each characterized by two conflicting objectives: two objectives, minimizing structure weight and minimizing maximum nodal displacement. The algorithm is compared against two other state-of-the-art multi-objective algorithms and rigorous evaluation is conducted using Hypervolume testing. The results show that MOPDO performs better than the comparison algorithms and is able to find a diverse set of non-dominated solutions. Statistical analysis of the experimental results using Friedman’s rank test is conducted to further investigate the experimental results. MOPDO’s solutions and convergence behaviour show that MOPDO is a very efficient method to solve complex design problems and is superior to the existing multi-objective algorithms in terms of effectiveness and efficiency.

Proper modeling of PV cells/modules through parameter identification based on the real current-voltage (I-V) data is important for the efficiency of PV systems. Most related works have concentrated on the classical single-diode model (SDM) and double-diode model (DDM) and their parameter extraction by various metaheuristic algorithms. In order to render more accurate and representative modeling, this paper adds a small resistance in series with the diodes in SDM and DDM. The new models are named reconfigured SDM (Reconfig-SDM) and reconfigured DDM (Reconfig-DDM), and they have not been studied so far as we know. A squirrel search algorithm (SSA) is employed to globally find the parameters of the new models. The performance achieved is experimentally tested on both a commercial RTC France solar cell and a CS6P-220P polycrystalline PV module located at Düzce University in Türkiye. A vivid comparison of experimental findings, observation, and analysis clearly demonstrates that the proposed Reconfig-SDM and Reconfig-DDM tuned by the SSA have better capacity and effectiveness for modeling PV devices than some cutting-edge approaches. Specifically, compared with the best-performing approach in the literature, Reconfig-SDM and Reconfig-DDM could reduce the error rate up to 0.37% and 2.58% for the solar cell, and 3.21% and 29.0% for the solar module.

The Dung Beetle Optimization (DBO) algorithm is a relatively recent metaheuristic known for its simplicity, versatility, and low parameter dependence, making it a valuable tool for solving complex optimization problems. Despite its potential, DBO suffers from limitations such as slow convergence and premature stagnation in local optima. To address these critical issues, this paper introduces a novel enhanced variant named Elite Bernoulli-based Mutated Dung Beetle Optimizer with Local Escaping Operator (EBMLO-DBO), specifically designed to improve the convergence speed, search capability, and robustness of the original DBO algorithm. The motivation for this enhancement stems from DBO’s limited performance in high-dimensional and non-convex problems, where it often fails to maintain an effective balance between exploration and exploitation. The novelty of the proposed EBMLO-DBO lies in the integration of four key strategies tailored to overcome these weaknesses: (i) Bernoulli map-based initialization to enhance population diversity and ensure a better global search foundation; (ii) Morlet Wavelet mutation to introduce adaptive local refinements and help the algorithm escape local optima; (iii) elite guidance to accelerate convergence by directing the population toward high-quality regions; and (iv) a local escaping operator (LEO) to dynamically refine the search process and strengthen exploitation without sacrificing exploration. The performance of EBMLO-DBO is rigorously validated using the CEC2017 and CEC2022 benchmark suites, where it achieves Friedman ranks of 1.83 and 2.7 respectively, consistently surpassing eleven state-of-the-art algorithms including PSO, HHO, WOA, and advanced methods like CMAES and IMODE. In benchmark function optimization, EBMLO-DBO demonstrates superior performance by achieving first rank in 50% of CEC2022 functions and obtaining the lowest average fitness values in 18 out of 29 CEC2017 functions. For photovoltaic parameter estimation applications, EBMLO-DBO exhibits exceptional accuracy with RMSE values of 9.8602E-4 for single diode models, 9.81307E-4 for double diode models, and 2.32066E-3 for PV module models, achieving top performance ranks of 1.45, 1.42, and 1.74, respectively. Statistical analysis using Wilcoxon signed-rank test at significance level $$\alpha =0.05$$ confirms the significant superiority of EBMLO-DBO over all compared algorithms, thereby validating the effectiveness and reliability of the proposed enhancements. Overall, the results state that EBMLO-DBO offers a significantly improved search performance and solution quality compared to the original DBO and related methods, thereby justifying the necessity and effectiveness of the proposed enhancements.

It is significantly challenging for design engineers to optimize a truss structure's topology, size, and shape. The improvement problem is then modeled as a multiobjective problem with objectives such as minimizing the structure's weight and maximizing reliability. This paper proposes a robust quality-based multiobjective crayfish optimization algorithm (MOCOA). Six different truss designs are used to test the proposed algorithm. It reveals that in the context of consistency and precision, MOCOA is a better algorithm when compared with recent algorithms, such as MOALO, MOBA, MODA, NSGA-II, DEMO, MOWCA, and MOEA-D, overall Friedman rank. Results are reported as superior in Pareto front, hypervolume, generational distance, and spacing metric. The research paper's finding indicates that MOCOA generates suitable Pareto-optimal solutions possessing strong convergence properties with excellent spread. These findings establish a robust foundation for forthcoming research on the optimization of truss structures.

This work presents a novel method for integrating the Load Frequency Control (LFC) and Automatic Voltage Regulator (AVR) processes to enhance frequency and voltage stability in two-area non-reheat thermal power systems. In this study, we present a novel Proportional Derivative-(1+Double Integral) (PD-(1+II)) controller, which is optimized through the utilization of the recently created Rime Optimization Algorithm (RIME). This represents the first time that the RIME algorithm and the PD-(1+II) controller are used in the context of coupled LFC-AVR systems. Our comprehensive research encompasses six distinct scenarios, including AVR system tuning, LFC system tuning, combined LFC-AVR system tuning, disturbance analysis, nonlinearity analysis, and parameter sensitivity analysis. A comparative analysis is conducted between the proposed RIME-tuned PD-(1+II) controller and established techniques such as the Nonlinear Threshold Accepting (NLTA) algorithm and its multi-objective version (MONLTA) tuned PID controllers, i.e. MONLTA-PID and NLTA-PID controllers. The simulation results demonstrate that the RIME-tuned PD-(1+II) controller consistently outperforms existing techniques. It exhibits superior performance in terms of overshoot reduction (100 % decrease in frequency deviation and 30 % decrease in terminal voltage) and faster settling times (50 % decrease in frequency control and 30 % decrease in voltage control) when compared to current methods. Furthermore, the controller demonstrates resilience in the presence of a diverse range of disturbances, nonlinearities, and parameter variations, highlighting its adaptability and reliability in a multitude of operational scenarios. The efficacy and reliability of the proposed methodology are further substantiated by statistical analysis, which demonstrates that it outperforms existing optimization algorithms, including the Gorilla Troops Optimizer (GTO) and the Whale Optimization Algorithm (WOA), with the RIME algorithm achieving an average ITSE value of 0.0881 compared to 0.1023 for GTO and 0.1057 for WOA.