Among the classical testbeds in control engineering, magnetic levitation systems occupy a prominent place owing to their strongly nonlinear character and intrinsic open-loop instability. Stabilizing a freely suspended ferromagnetic object requires careful regulation of the electromagnetic force, which makes these systems particularly demanding for controller design. To address this challenge, the present work introduces a sigmoid-activated two-degree-of-freedom PID (SA-2DOF-PID) controller, wherein a sigmoid-based nonlinear term is embedded within a standard 2DOF-PID architecture. This integration yields smoother actuation signals and increases overall closed-loop robustness. Controller parameter selection is carried out via the dholes-inspired optimization (DIO) algorithm, a recently proposed nature-inspired method. A multi-objective fitness function incorporating peak overshoot, settling time, and cumulative tracking error guides the tuning procedure. Simulation experiments performed under both nominal plant conditions and deliberate parametric perturbations serve to assess the proposed scheme. Quantitative comparisons against secant optimization algorithm (SOA)-, honey badger algorithm (HBA)-, and particle swarm optimization (PSO)-based controllers reveal that the DIO-tuned SA-2DOF-PID achieves markedly lower overshoot, quicker settling, and higher steady-state precision. Robustness evaluations involving intentional variations in system parameters further confirm that the closed-loop behavior remains well-damped with only marginal deterioration. Additional benchmarking against whale optimization algorithm combined with simulated annealing (WOA-SA)-based proportional–integral–derivative (PID), opposition-based artificial electric field algorithm (ObAEF)-based fractional-order PID (FOPID), and manta ray foraging optimization (MRFO)-based real PID with second-order derivative (RPIDD²) controllers corroborates the practical advantages of the proposed approach. Taken together, the study demonstrates that the SA-2DOF-PID framework tuned by DIO constitutes an effective, structurally lean, and computationally tractable strategy for managing nonlinear and open-loop unstable plants.
Magnetic levitation (Maglev) systems are a testbed for advanced control strategies because of their nonlinearity, open-loop instability, and high dynamics. Accurate position control of the levitated object is a difficult task, especially under parameter uncertainties and disturbances. Traditional control approaches, like proportional-integral-derivative (PID) control, are based on linearization of the system and hence suffer from poor performance in the presence of nonlinearities. Sliding mode control (SMC) is a robust nonlinear control method that provides good disturbance rejection and parameter uncertainty tolerance. However, its performance is sensitive to the choice of controller gains, which is often a time-consuming and suboptimal manual task. To overcome this challenge, previous research has used metaheuristic algorithms, like genetic algorithms (GA), for gain tuning. These approaches enhance tracking accuracy and transient response, but are offline and non-adaptive to dynamic system changes. In this work, a Deep Deterministic Policy Gradient (DDPG) reinforcement learning approach is developed for online gain tuning of SMC in a non-linear Maglev system. The DDPG agent engages in continuous interaction with the environment to learn an optimal policy for gain adaptation in response to system dynamics. Asymptotic stability of the closed-loop system is analyzed using Lyapunov’s stability theorem for fixed gains, and the adaptive gain case is discussed. The proposed DDPG-tuned SMC is shown to have better tracking performance, shorter settling time, and better disturbance rejection and parameter uncertainty tolerance than the GA-tuned SMC through simulation studies.
Syed Tariq Naqshbandi, Huzaifah Abbas, D. Zaman· International Conference on...· 0 citations
The rapid adoption of electric vehicles, together with increased battery mass and altered load distribution, is placing greater demands on ride comfort and suspension adaptability, while controller optimization may still request forces beyond the instantaneous capability of the physical semi-active actuator if experimentally supported force limits are not explicitly enforced. This study proposes a unified experimentally constrained optimization framework for a magnetorheological damper (MRD)-based semi-active suspension system using a two-degree-of-freedom quarter-car model. The damper is characterized at eleven current levels and represented by a branch-dependent lookup model that provides the zero-current baseline and instantaneous feasible force range. Proportional–integral–derivative (PID) and linear quadratic regulator (LQR) controllers are independently tuned using a genetic algorithm (GA) and particle swarm optimization (PSO) under identical vehicle dynamics, objective functions, tuning excitation, and MRD force constraints. Each candidate force demand is projected onto the experimentally derived feasible range throughout optimization. The controllers are tuned on a composite B–C–D profile and subsequently evaluated over nine road–speed scenarios. PID-PSO reduces the RMS sprung-mass acceleration by 15.91% and achieves the best acceleration performance in six cases, whereas LQR-PSO provides more balanced improvements in body motion, suspension travel, tire response, and force feasibility. The proposed framework therefore provides a more physically constrained basis for the comparative design and evaluation of MRD-based semi-active suspension control.
Minh Hoang Trinh, B. Le, D. Vu et al.· World Electric Vehicle Journ...· 0 citations
Electro-hydraulic actuator systems are widely used in precision motion-control applications; however, their displacement regulation remains challenging because fast response, low overshoot, and high steady-state accuracy must be achieved simultaneously under strongly dynamic operating conditions. In this study, a proportional-integral-derivative (PID) controller augmented with a Gompertz function (PID-G) is proposed for the position control of a four-way valve-controlled linear actuator, and its parameters are tuned by the recently introduced dholes-inspired optimizer (DIO). First, a control-oriented mathematical model of the electro-hydraulic actuator system is established by combining the valve and actuator dynamics. Then, the PID-G structure is formulated by incorporating a nonlinear Gompertz-based term into the conventional PID framework, and the resulting seven-parameter tuning problem is cast as an optimization task using a composite objective function that accounts for overshoot, steady-state error, rise time, and settling time. The effectiveness of DIO is evaluated comparatively against flood algorithm (FLA), covariance matrix adaptation evolution strategy (CMA-ES), and particle swarm optimization (PSO) under identical simulation conditions. The results show that DIO provides the best optimization performance, yielding the lowest best, average, and standard-deviation values of the objective function among the compared algorithms. In the time domain, the DIO-based PID-G controller achieves the most favorable overall response with a rise time of 0.079511 s, a settling time of 0.099326 s, an overshoot of 0.15110%, and a steady-state error of 0.089317%. The superiority of the DIO-based design is further confirmed by lower values of error based performance metrics (IAE, ISE, ITAE, and ITSE), improved convergence characteristics, and statistically significant advantages in the Wilcoxon test. Additional comparisons with different (PI, PID, 2DOF-PID, and FOPID) controllers also demonstrate that the proposed PID-G structure provides markedly better transient and error-based performance when tuned by DIO. Frequency-domain and varying-setpoint results further indicate satisfactory stability margins, robust tracking ability, and bounded control effort. Overall, the study shows that combining DIO with a Gompertz-augmented PID structure constitutes an effective strategy for high-performance electro-hydraulic actuator displacement control.
Muhammet İsmail Güngör, Davut Izci, S. Ekinci· Biomimetics· 0 citations
The Pendubot is a nonlinear underactuated system with two rotational degrees of freedom and a single actuator, making stabilization a challenging problem for intelligent and nonlinear control methods. Reliable balancing control is important for evaluating control strategies under both simulation and practical hardware constraints. However, although fuzzy and intelligent control methods have been investigated for Pendubot systems, the practical implementation and experimental behavior of ANFIS-based PD-Fuzzy control remain insufficiently documented, particularly in comparison with a conventional PD controller under the same laboratory conditions. This study aims to develop and evaluate an ANFIS-based PD-Fuzzy controller for TOP-position stabilization of a Pendubot. The nonlinear dynamics are formulated using the Euler-Lagrange method, while controllability of the linearized model is examined at the TOP and MID equilibrium points. The proposed controller uses ANFIS-based fuzzy blocks to approximate the proportional control actions, while derivative paths remain explicitly implemented. MATLAB/Simulink simulations show that the baseline PD and PD-Fuzzy controllers produce closely matched TOP-balancing responses, with settling times of approximately 2.36 and 2.37 s for link 1, respectively. Experimental evaluation using an STM32F407-based platform demonstrates practical TOP balancing; however, the baseline PD controller provides more favorable behavior than the PD-Fuzzy realization under the reported hardware conditions. These findings indicate that ANFIS-based PD-Fuzzy control is feasible for Pendubot stabilization but does not necessarily provide performance improvement over a conventional PD controller. The study therefore highlights the importance of hardware-aware tuning, sensor quality, and broader ANFIS training data for future improvements.
Van-Long Mach, Dang-Khoa Huynh, Khanh-Hung Le et al.· Scientific Journal of Engine...· 0 citations
Magnetic levitation systems represent a class of inherently unstable and highly nonlinear electromechanical systems, making them a compelling benchmark for advanced control strategies. This paper presents a nonlinear control approach for the stabilization and trajectory tracking of a magnetic levitation system using the backstepping technique. The controller is systematically designed based on the system's nonlinear dynamics, where virtual control inputs are recursively introduced to ensure stability at each design step. A rigorous Lyapunov-based analysis is conducted to guarantee asymptotic stability within the admissible operating region of the closed-loop system and to prove convergence of the tracking error to zero. The effectiveness of the proposed control scheme is validated through comprehensive numerical simulations under various operating conditions, including set-point regulation and dynamic reference tracking. The results demonstrate fast transient response and minimal overshoot. These findings confirm that backstepping control provides a reliable and systematic framework for handling the nonlinearities and instability inherent in magnetic levitation systems, making it a promising candidate for advanced control applications and educational laboratory platforms.
A. Al-Tamimi, M. Salah, A. Al-Jarrah et al.· IEEE Jordan Conference on Ap...· 0 citations
This study examined the control of a single-axis vertical magnetic levitation (MagLev) system under realistic implementation constraints. The system was considered due to its nonlinear dynamics and inherent open-loop instability, which make it suitable for evaluating practical control limitations. Actuator voltage and current saturation, parameter uncertainty, external disturbances, and measurement noise were explicitly incorporated into the analysis. For comparative evaluation, three control strategies were implemented: local linear state feedback control based on an LQR design, fixed-gain sliding mode control, and adaptive sliding mode control. Rather than relying on a single initial condition, controller performance was assessed over ranges of initial positions and velocities using a capture region framework. The effects of parametric uncertainty were systematically investigated through Monte Carlo–based numerical simulations. The results indicated that the linear controller exhibited zero successful captures over the evaluated initial condition grid, while sliding mode controllers achieved restricted but nonzero capture regions under nominal and disturbance conditions. The adaptive mechanism influenced transient behavior but did not substantially expand the feasible operating region due to actuator constraints. Measurement noise was found to degrade controller effectiveness in all cases. These findings emphasize the importance of jointly considering physical constraints and stability properties when evaluating control strategies for magnetic levitation systems.
Ahmet Çakanel, Mine Menekli, Yaren Kurum et al.· Dicle Üniversitesi Mühendisl...· 0 citations
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