ABSTRACT Existing vehicle lateral control strategies often struggle with nonlinear dynamics across varying speeds, leading to overshoot, slow response, and limited robustness. To address these challenges, this research proposes a novel cascaded Proportional Integral and Fractional Order Proportional Integral Derivative (PI–FOPID–PID) controller, where the outer loop ensures long-term lateral and yaw-error convergence and the inner loop handles actuator dynamics and high-frequency disturbances. This cascaded structure significantly enhances robustness and tracking accuracy compared to conventional single-loop controllers. Optimal controller parameters are obtained using a hybrid Artificial Rabbits Optimization–Bobcat Optimization Algorithm (ARBOA). Simulation results demonstrate rapid convergence with a settling time of approximately 3 s, steady-state error below 0.15 m, and RMSE of 0.18 m. During a high-speed double-lane-change maneuver at 15 m/s, the maximum lateral deviation is limited to 0.12 m. The results confirm improved robustness to tire–road friction variations and superior stability during high-speed autonomous driving.

ABSTRACT This article presents the design of a proportional‐integral‐derivative (PID) controller for a renewable energy (RE) integrated power system using model order reduction (MOR). A test case of an 11th‐order RE‐integrated power system from the literature has been used to validate the applied method. The reduction of the 11th‐order Renewable Energy (RE) integrated power system model to a 2nd‐order model is achieved using a combination of Pade approximation (PA) and direct truncation (DT) (PA‐DT) method. Further, the grey wolf optimization (GWO) technique is employed to determine the optimal parameters for the PID controller for the reduced‐order model. The designed controller is then directly applied to the high‐order system (HOS). This proposed PID design method via PA‐DT MOR for the RE integrated power system is a novel technique because, at this stage, no publications related to this combined method are available. The suggested approach is supported by the time and frequency responses. Time domain specifications (TDSs) and performance error indices (PEIs), and statistical analysis are also provided to demonstrate the efficacy of the suggested method.

Wastewater treatment is essential for environmental sustainability and public health. However, existing control strategies struggle with system nonlinearity, disturbances, and high energy consumption (EC). This study proposes a robust self-organizing fuzzy sliding mode controller (SOFSMC) to enhance effluent quality, energy efficiency, and system adaptability in wastewater treatment plants (WWTPs). By integrating sliding mode control(SMC) with a self-organizing fuzzy logic system (SOFLS), the controller improves adaptability and reduces the chattering effect. The newly developed JAYA optimization algorithm is used to fine-tune control parameters, optimizing both energy use and pollutant removal. Simulation results show SOFSMC outperforms proportional integral derivative (PID), standard SMC, and fuzzy logic controllers (FLCs). EQI is reduced by 48.3% and 28.4% compared to PID and FLC, respectively. EC is significantly optimized, and settling time and chattering amplitude (CA) are reduced by 28% and 75%, respectively. SOFSMC offers a scalable, energy-efficient, and robust solution for advanced wastewater treatment.

High-performance cycling ergometers require precise control systems to ensure smooth operation, dynamic stability, and accurate resistance modulation. Traditional control methods for active magnetic bearings (AMBs) often struggle to manage nonlinear system behavior and external disturbances. This study develops and evaluates a reinforcement learning-based control framework for AMBs to improve stability and responsiveness in cycling ergometers under variable loading conditions. A nonlinear dynamic model of the rotor system is formulated, incorporating magnetic force dynamics, shaft deflection, and disturbances such as pedaling force variation and flywheel imbalance. Two control strategies are implemented and compared: a conventional Proportional-Integral-Derivative (PID) controller and a reinforcement learning controller based on Proximal Policy Optimization (PPO). Both controllers are trained in simulation and evaluated under transient and steady-state conditions. Results show that the PPO controller provides superior rotor stability, reduced angular deviation, and more robust performance under shock inputs compared to PID control. Additionally, the PPO controller adapts effectively to varying operational scenarios without manual tuning. These findings demonstrate the potential of reinforcement learning for real-time adaptive control of AMBs, offering a promising approach to enhance the performance, reliability, and user experience of next-generation sports training equipment.

This paper presents the Fuzzy Gain Tuned Hybrid Posicast Control (FGTHPC) for a Negative Output Buck Boost Converter (NOBBC) operating in Continuous Conduction Mode (CCM). FGTHPC reduces the peak overshoot of the lightly damped NOBBC with step response. Traditional Proportional Integral Derivative (PID) control is highly sensitive to the changing natural frequency of oscillations within NOBBC. In this paper, an FGTHPC has been designed to operate the same converter in a closed loop to reduce the sensitive oscillation and output voltage regulation for the NOBBC. A controller having a posicast structure and a feed-back loop is designed. Here, Fuzzy Logic Controller (FLC) is used to optimize the parameters value of the Hybrid Posicast Control (HPC). The posicast function is designed in order to operate independently of the computational time delays. For performance evaluation, FGTHPC applied to the NOBBC is tested under different operating conditions using an LED string load supplied by a battery and solar panel. Both MATLAB/Simulink simulations and experimental prototypes are developed, and results are compared with those obtained from a PID controller and a HPC. The results will establish the superiority of the designed FGTHPC in comparison with PID control.

Abstract Electro-hydrostatic actuator (EHA) is a self-contained electrically powered hydraulic actuator. This paper deals with the design of high-performance control schemes without demanding complete information about the EHA. The dynamics of EHA is nonlinear, and it is subjected to uncertainties and external disturbances. To deal with these problems, sliding mode control (SMC) is suitable. However, the drawback of SMC is chattering. To meet the high performance of EHA and reduce the chattering of SMC, proportional integral derivative (PID) control is proposed for the inner loop of EHA control. For the outer loop, extended state observer (ESO) and radial basis function neural network (RBFNN) based SMC is designed. ESO is used to estimate the states of EHA whereas RBFNN is used to get the approximate value of the unknown external disturbances, uncertainties and nonlinear dynamics of the EHA. Fixed centers and widths of RBFNN are used and the weights are updated based on an adaptive law derived using a Lyapunov stability analysis. An approximate nonlinear mathematical model of EHA is derived, and a virtual prototype of EHA is built in AMESim software. Then Matlab/Simulink and AMESim cosimulation is carried out. The cosimulation indicated the tracking performances of EHA subjected to different desired signals, parameter variations and external disturbances. Compared to using only PID control for both outer and inner loops, the integration of PID, ESO and RBNN based SMC of EHA indicates superior tracking performance and robustness. Chattering of SMC is also significantly reduced.

Fixed-wing unmanned aerial vehicles (UAVs) can be used for numerous civilian purposes such as passenger transport, cargo transport, crop dusting, forest fire fighting, and aerial photography. This research presents the trim, linearization, and proportional integral derivative (PID) controller design of a fixedwing aircraft. Modeling and simulation studies were carried out using MATLAB/Simulink. The created model takes elevator, aileron, rudder, and throttle as input and produces angles, angular rates, and position as output. The analyzed simulation studies confirm the success of the modeling and controller design.

This study takes the PUMA560 manipulator as the research object, selects its first three rotating joints to construct a 3-degree-of-freedom (3-DOF) manipulator system, and aims to improve the control accuracy of the manipulator and environmental adaptability. First, the Denavit-Hartenberg (DH) parameter method is used to establish the manipulator’s kinematic model; the MATLAB Robotics Toolbox is employed to define the link coordinate system, joint angles, link lengths, and other DH parameters, and a velocity ellipsoid is constructed to analyze the motion characteristics of the end effector. In the trajectory planning stage, the Joint Trajectory Planning (JTRAJ) function (for smooth interpolation in joint space) and the Cartesian Trajectory Planning (CTRAJ) function (for linear path interpolation at the end effector) are compared, and finally, the JTRAJ function is selected to plan the target path. To achieve precise control of the manipulator, a PID (Proportional-Integral-Derivative) control simulation model based on Simulink is built. Simulation results show that compared with manual parameter tuning, the PID control optimized by Genetic Algorithm (GA) has a smaller error fluctuation range, and the error tends to be stable at the end of the simulation, significantly improving the manipulator’s control robustness and trajectory accuracy. This study realizes the effective integration of machine learning and traditional control algorithms, providing a feasible solution for the optimization of manipulator adaptive control; future research can further explore the influence of parameter ranges and fitness function definitions on control effects, and improve data horizontal comparison to deepen the research.

The demand for high-precision, energy-efficient control in industrial robotics necessitates a rigorous comparison between conventional and optimal control methods. This paper presents a detailed comparative analysis of the ubiquitous PID (Proportional-Integral-Derivative) controller and the modern LQR (Linear Quadratic Regulator) optimal controller, applied to the highly non-linear dynamics of a 3-DOF spherical articulated manipulator. The study extends beyond ideal tracking to evaluate performance under realistic industrial constraints, including external disturbances, model uncertainty, and the novel scenario of actuator saturation. Through comprehensive MATLAB/Simulink simulations, we quantify performance using Root Mean Square Error (RMSE) and Integrated Control Effort (∫τ2dt). The results demonstrate that while PID is simple, LQR provides superior stability, higher resistance to parameter uncertainty, and optimal energy consumption across dynamic trajectories. This work offers quantitative guidance for selecting the appropriate controller based on specific industrial requirements, highlighting the trade-offs between implementation complexity and optimal system performance

To address the issues of dynamic lag and parameter conservatism in traditional proportional-integral-derivative (PID) control for solar tracking systems, a dual-stage collaborative optimization controller (HHO–FNN–PID) is proposed, integrating Harris hawks optimization (HHO) and fuzzy neural network (FNN) in two sequential phases: HHO–PID and FNN–PID. In the initial phase, HHO–PID rapidly identifies the feasible ranges of PID parameters and accelerates error convergence. But as the error falls below a predefined threshold, it is substituted by FNN–PID for parameter fine-tuning, to realize the dynamic compensation and overshoot suppression. Simulations show that HHO–FNN–PID reduces rise time by 75.5%, limits overshoot to 3.1%, and shortens disturbance recovery by 74.4% compared to traditional PID. Comparison with other controllers, it improves the response speed and stability of PID controller through the phased cooperation mechanism. This provides a valuable reference for designing high-precision control systems in photovoltaic tracking 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%), along with near-zero steady-state error (4.0776 × 10⁻4%), outperforming all compared methods in both transient response and steady-state accuracy. Robustness analyses further confirm superior disturbance rejection and reliable reference tracking under dynamic uncertainties. These results demonstrate that the proposed methodology offers an efficient, low-complexity, and high-performance control solution suitable for real-time deployment in industrial steam condenser systems.

This paper intends to address the challenges of insufficient robustness and model uncertainty compensation in unmanned aerial vehicle dynamic systems under complex disturbances. The paper proposes a hybrid control architecture that combines deep fusion model predictive control with adaptive Proportional–Integral–Derivative (PID) based on Transformer attention mechanism. The core innovation of this architecture lies in introducing attention neural networks to dynamically tune PID gains online, and forming a deep collaborative control framework of "prediction-learning-compensation" with Model Predictive Control (MPC) and sliding mode disturbance observer with H∞ (H-infinity) robust optimization. This thereby improvs the adaptability and control accuracy of the system under unstructured disturbances and model mismatches. The control architecture employs a robustly optimized upper-layer MPC controller, which, based on the receding horizon principle, utilizes real-time system state updates to predict future state evolution. An H∞ performance criterion is incorporated into the control sequence optimization to strengthen robustness against model parameter perturbations and external disturbances. The lower-layer controller adopts an adaptive PID structure that responds quickly to the reference signals generated by the MPC. To address the degradation of PID tuning performance under dynamic mismatches and unmodeled disturbances, an attention mechanism neural network based on the Transformer architecture is introduced to adjust the PID gains online and capture nonlinear dynamic variations. Additionally, in order to further enhance system stability under severe disturbances, this control framework integrates sliding mode control technology into the disturbance observer design, and constructs a sliding mode disturbance observer module for explicit estimation of external disturbances and model uncertainties. The estimated values are injected into the lower-level adaptive PID controller through a feedforward compensation mechanism to achieve active disturbance rejection. Simulation experiments conducted in a nonlinear disturbance environment built on the AirSim platform, as well as tests using the EuRoc dataset, demonstrate that the proposed method maintains a steady-state tracking error within 5% during path-following tasks. Compared with the traditional MPC combined with fixed gain PID control, this method improves the steady-state robustness by about 17%, and shortens the system adjustment time from 3.15 s to 2.47 s, significantly improving by 21.6%, demonstrating excellent convergence and anti-interference ability. The results indicate that the MPC-PID hybrid control approach offers significant advantages in enhancing the robustness, adaptability, and control accuracy of UAV systems, making it well-suited for intelligent control demands in complex flight missions.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-32436-6.

ABSTRACT This paper presents decentralised and centralised fixed‐structure H∞ robust control methods optimised by the Particle Swarm Optimisation and Gravitational Search Algorithm (PSOGSA) for a coupled multi‐input multi‐output (MIMO) microsurgical manipulator. The design framework explicitly considers uncertainties and disturbance constraints. Conventional H∞ loop‐shaping controllers are typically of high order, complex, and difficult to implement in practice. To address this limitation, Proportional‐Integral‐Derivative (PID)‐structured decentralised and centralised H∞ controllers are proposed, providing compact structures while retaining robustness. The novelty of this work lies in embedding H∞ robustness criteria into practical PID‐based frameworks, bridging the gap between theoretical robust design and experimental implementation in microsurgical applications. The proposed controllers are evaluated against a reduced‐order H∞ controller derived from Hankel norm approximation and a Ziegler–Nichols tuned PID controller, using both simulation and experimental studies. Results demonstrate that the proposed controllers achieve improved stability margins (0.449–0.521 compared with 0.436 for the reduced‐order design), maintain low root‐mean‐square errors (≈0.067–0.089) and remain robust under voltage disturbances where conventional PID control fails. These findings confirm the contribution of a practical and efficient robust control strategy for enhancing the precision and reliability of microsurgical manipulators.

This study addresses the trajectory tracking problem of wheeled mobile robots and proposes two different control strategies, which are comparatively evaluated through simulations. Initially, the mathematical model of the mobile robot is derived, followed by the design of two controllers: a conventional Proportional-Integral-Derivative (PID) controller and a Type-II Fuzzy Logic Controller (Type-II FLC) optimized utilizing the Grey Wolf Optimizer (GWO) algorithm. The suggested control methods are assessed under three different reference trajectory scenarios—circle, square, and star-shaped paths. Simulation results indicate that the PID controller exhibits significant deviations, particularly during sharp turns and sudden maneuvers in square and star trajectories, leading to increased tracking errors. In contrast, the GWO-based Type-II FLC demonstrates smoother and more stable maneuvers, resulting in lower tracking errors and higher trajectory-following accuracy. These findings suggest that the GWO-optimized Type-II FLC enables more reliable and precise navigation of mobile robots in dynamic environments contrasted to the classical PID controller. Furthermore, the Type-II FLC method achieved considerable percentage improvements in tracking performance for circular, square, and star trajectories when contrasted with the PID controller. Specifically, in a square orbit, the X and Y position errors have been improved by 98% and 97%, respectively, according to the Type II FLC, PID control method. Overall, the results highlight the effectiveness of the suggested control method in enhancing position control accuracy.

Pipeline robots play a crucial role in ensuring public safety by routine inspection and cleaning operations. However, their performance is frequently hindered by complex working environments and unexpected collisions. To overcome these challenges, we propose a control algorithm that integrates an enhanced particle swarm optimization (PSO) method with sine chaotic mapping and a radial basis function (RBF)-based fuzzy Proportional–Integral–Derivative (PID) control (IP-PID). Specifically, sine chaotic mapping is utilized within the PSO framework to increase population diversity. Furthermore, adaptive inertia weights and compression factors are introduced to strengthen the PSO’s global search capability and convergence stability. The optimized PSO is then employed to tune the proportional and quantization parameters of the fuzzy PID controller, thereby enhancing its adaptability and control accuracy. To validate the effectiveness of the proposed approach, we conduct comprehensive comparisons with the Back Propagation—Proportional-Integral-Differential (BP-PID) controller, Model Predictive Control (MPC) controller, cascade feed-forward neuro-fuzzy PID controller (CFF-NFPID), and optimal hybrid interval type-2 fuzzy PID + I logic controller (OH-IT2FPID + I) using Simulink simulations and physical experiments. The simulation results demonstrate that, compared to MPC, IP-PID reduces settling time by 83.9% and decreases overshoot by 85%. In both velocity regulation and trajectory tracking tasks, the proposed approach achieves substantially improved reference-tracking accuracy. Experimental results further corroborate the superiority of IP-PID, demonstrating higher control precision, enhanced tracking performance, and greater robustness against external disturbances.

This paper presents a closed-loop fast charging system for lithium-ion batteries based on the Constant-CurrentConstant-Voltage (CCCV) method enhanced with a ProportionalIntegralDerivative (PID) controller. The proposed system dynamically regulates the charging parameters by using real-time feedback from voltage and current sensors, with the aim of improving the efficiency of the charging and ensuring battery safety. Experimental results demonstrate that the PID-controlled method maintains a higher current during the initial bulk charging phase, significantly reduces total charging time, and avoids harmful voltage overshoot. Compared to conventional CCCV charging, the system achieves more stable voltage regulation and gradual current tapering, effectively minimizing thermal stress and preventing overcharging. A comparative analysis shows that the PID approach outperforms traditional methods in terms of energy efficiency, thermal management, and operational safety. The system architecture is suitable for integration into Battery Management Systems (BMS) of electric vehicles, portable electronics, and renewable energy storage. This research not only validates the practicality of using PID in fast charging applications but also lays the foundation for future enhancements using intelligent control strategies and adaptive learning algorithms. The findings suggest that PID-controlled charging systems offer a promising solution to the challenges of rapid, reliable, and safe energy replenishment in modern battery-powered technologies.

Abstract Laser power stability is essential for quantum precision measurements, yet environmental temperature variations can induce significant instabilities in acousto-optic modulator (AOM) based systems. This paper investigates the mechanisms by which temperature affects AOM polarization states, leading to power fluctuations. Our analysis reveals that thermal variations modify crystal birefringence, causing polarization angle shifts that alter beam splitter ratios and ultimately result in power drift. We establish a comprehensive coupling model linking temperature, polarization, splitting ratio, and output power. Based on this model, we have developed a temperature compensation algorithm to augment the performance of a standard proportional-integral-derivative (PID) feedback controller. The algorithm predicts real-time power deviations from thermal drift and dynamically adjusts the PID setpoint, eliminating the need for physical temperature control hardware. Experimental validation over a 15 ∘ C–45 ∘ C temperature range shows that our method reduces the root-mean-square power fluctuation from ±0.095%, achieved with PID control alone, to ±0.076%. This 20% stability enhancement over the conventional feedback-only method significantly improves reliability, a crucial advantage for resource-constrained applications like quantum sensing where additional hardware is impractical.

This study presents a comparative analysis of Proportional-Integral-Derivative (PID) and Sliding Mode Control (SMC) methods applied to a custom-designed and 3D-printed 3-Degree-of-Freedom (3-DoF) Revolute-Revolute-Revolute (RRR) robotic manipulator. A central contribution of this work is the development of a dual-environment validation framework that integrates ROS Noetic with the Gazebo simulation platform, enabling seamless testing of controllers in both virtual and physical settings. This framework provides a practical pathway for bridging the gap between simulation-based evaluations and real-world experimentation, an aspect that remains underexplored in existing studies. The performance of both controllers is assessed through joint position errors, trajectory tracking accuracy, and torque demands for a cubic trajectory application. Experimental results show that while both controllers achieve satisfactory performance, SMC demonstrates superior trajectory tracking, with consistently lower Root Mean Square (RMS) errors across all joints. This improvement, however, is accompanied by slightly higher torque requirements compared to PID, highlighting the trade-off between enhanced accuracy and increased actuator effort. By combining a low-cost robotic platform with a reproducible dual-environment methodology, this study not only offers insights into the practical strengths and limitations of model-free PID and SMC but also establishes a framework that can inform future research and industrial applications.

Purpose This paper aims to realize the high-precision guidance and control for an axisymmetric gliding aircraft based on the improved active disturbance rejection control (IADRC). Design/methodology/approach An integral chain state-space model with attitude angle as the control objective is established, and the three-channel state-space models are simplified to the second order systems with similar expressions. The comprehensive design method of IADRC is proposed based on the second order system, which uses same control parameters for three channels to reduce workload of parameter tuning. The proposed IADRC combines active disturbance rejection control (ADRC) and proportional integral derivative control to suppress the disturbance. Findings The control parameters are selected according to the comprehensive design method, and they are taken into the transfer function and six-degree-of-freedom nonlinear dynamic model for simulation verification. Furthermore, IADRC is checked by the Monte Carlo simulation. The simulation results show that the proposed IADRC has strong adaptability with biased parameters of the axisymmetric gliding aircraft. The guidance and control effect of IADRC is compared with that of other modern control methods, such as standard ADRC, optimal control and pole placement control. The simulation results show that the guidance and control effect of IADRC is better than that of other methods. Originality/value Theoretical analysis and simulation results show that the proposed IADRC is feasible for engineering application. The comprehensive design method of IADRC has excellent guidance and control performance.

The performance of traditional building temperature control systems is often suboptimal due to the inherent complexity of the control objects and the challenges associated with establishing accurate mathematical models. These traditional systems frequently result in energy inefficiency and compromised comfort levels for occupants. Addressing these shortcomings requires an innovative approach to temperature regulation. After a thorough review of existing indoor temperature regulation systems both domestically and internationally, it is evident that there is significant room for improvement. Combining insights from control theory with advanced algorithms, this study proposes the use of a fuzzy PID (Proportional-Integral-Derivative) algorithm to establish a more effective temperature control system. The fuzzy PID algorithm integrates the robustness of PID control with the adaptability of fuzzy logic, providing a more responsive and precise method for temperature regulation. This hybrid approach leverages fuzzy logic to handle the uncertainties and nonlinearities in the control process, adjusting the PID parameters in real-time to optimize performance. As a result, the new system can dynamically respond to changing environmental conditions and occupant needs, maintaining a comfortable indoor climate while minimizing energy consumption.