Reinforcement Learning-Based Optimal Nonlinear Control for Magnetic Levitation

Reinforcement learning based online gain scheduling PID control for DC servo motors

Stabilization and Tracking Control of Magnetic Levitation Systems Using Backstepping Technique

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.

Novel nonlinear control algorithms for hexacopters to overcome control challenges with nonlinear systems in the presence of uncertainty

A novel DIO optimized sigmoid-activated 2DOF-PID controller for robust control of magnetic levitation systems

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.

Reinforcement Learning for Real-Time Auto-Tuning of Robot’s Controllers

This research introduces an innovative control technique for Series Elastic Actuators (SEAs) that utilizes Reinforcement Learning (RL) to address the shortcomings of previously fixed-gain adaptive controllers, which are a hybrid of State Feedback Control (SFC) and Model Reference Adaptive Control (MRAC) by using Lyapunov Stability Analysis. This controller is optimized by adjusting the adaptation factor. b. This study presents an intelligent agent based on reinforcement learning to find the value of b with a dynamic auto-tuner. It trains via the Soft Actor-Critic (SAC) algorithm for 100,000 time steps. A comparison between the two methods was presented according to simulation results under different conditions; the RL-based controller shows much better tracking accuracy, how quickly it reaches the target output, and how little control torque it uses, where the agent's policy could automatically adjust in real-time based on system conditions, such as uncertainties and disturbances, where it has a settling time of 1.7 seconds, while the fixed parameter controller has a 1.95-second settling time, resulting in a reduction of 15.3%. It also lowers the control torque caused by disturbances by 19.5% compared to the fixed parameter controller, which has a control torque of 3.99 Nm, while the maximum control torque for the RL-optimized controller is 3.21 Nm.

Hybrid Control Strategies for High-Accuracy Robotic Manipulators

Robotic manipulators are essential in modern fields such as industrial automation, precision manufacturing, medical robotics, and aerospace. While traditional control methods like PID, computed torque, and adaptive control perform well in structured environments, they struggle with nonlinearities, uncertainties, payload variations, and disturbances. To address these limitations, hybrid control strategies combining conventional and intelligent techniques—such as fuzzy logic, neural networks, and sliding mode control—have emerged as effective solutions. This work focuses on hybrid control approaches that enhance accuracy, robustness, and adaptability. It begins with dynamic modeling using the Euler-Lagrange formulation, highlighting the nonlinear and complex nature of robotic systems. The proposed method integrates computed torque control for trajectory tracking, fuzzy logic for handling uncertainties, and neural networks for adaptive tuning and parameter estimation. Literature indicates that hybrid methods like fuzzy-PID and neural-based adaptive control significantly improve tracking performance, reduce steady-state error, and enhance robustness, though challenges like computational complexity remain. Simulation and experimental results demonstrate that the proposed hybrid controller outperforms traditional methods in terms of tracking accuracy, settling time, and disturbance rejection. In conclusion, hybrid control strategies offer a powerful framework for high-precision robotic manipulation by effectively addressing nonlinearities and uncertainties. Future work will focus on real-time implementation, optimization of hybrid designs, and integration with advanced sensing technologies.