Fixed-time observer-based sliding mode tracking control for magnetic levitation systems

This paper introduces a novel model-free nonsingular fixed-time sliding mode control (MF-NFxTSMC) strategy for precise trajectory tracking in robot arm systems. Unlike conventional sliding mode control (SMC) approaches that require accurate dynamic models, the proposed method leverages the time delay estimation (TDE) approach to effectively estimate system dynamics and external disturbances in real-time, enabling a fully model-free control solution. This significantly enhances its practicality in real-world scenarios where obtaining precise models is challenging or infeasible. A significant innovation of this work lies in designing a novel fixed-time control framework that achieves faster convergence than traditional fixed-time methods. Building on this, a novel MF-NFxTSMC law is developed, featuring a novel singularity-free fixed-time sliding surface (SF-FxTSS) and a novel fixed-time reaching law (FxTRL). The proposed SF-FxTSS incorporates a dynamic proportional term and an adaptive exponent, ensuring rapid convergence and robust tracking. Notably, its smooth transition between nonlinear and linear dynamics eliminates the singularities often encountered in terminal and fixed-time sliding mode surfaces. Additionally, the designed FxTRL effectively suppresses chattering while guaranteeing fixed-time convergence, leading to smoother control actions and reduced mechanical stress on the robotic hardware. The fixed-time stability of the proposed method is rigorously proven using the Lyapunov theory. Numerical simulations on the SAMSUNG FARA AT2 robotic platform demonstrate the superior performance of the proposed method in terms of tracking accuracy, convergence speed, and control smoothness compared to existing strategies, including conventional SMC, finite-time SMC, approximate fixed-time SMC, and global fixed-time nonsingular terminal SMC (NTSMC). Overall, this approach offers compelling advantages, i.e., model-free implementation, fixed-time convergence, singularity avoidance, and reduced chattering, making it a practical and scalable solution for high-performance control in uncertain robotic systems.

A novel adaptive fixed-time controller (AFTC) based on disturbance compensation technology is proposed to achieve high performance position precision control for magnetic levitation system in this paper. Firstly, the dynamic model of the magnetic levitation system is established and a fixed-time controller (FTC) is designed to realize the closed-loop control. However, this approach usually requires a large switching gain to suppress interference, resulting in chattering. In view of this, the generalized proportional integral observer (GPIO) is introduced to estimate and compensate the time-varying interference, which can not only improve the anti-interference ability, but also reduce the chattering by choosing a smaller switching gain. Nevertheless, these two performance improvements come at the cost of the dynamic response rate. In order to improve steady state performance without sacrificing dynamic performance, an adaptive fixed-time controller based on GPIO is proposed, which has a significant advantage because of the adjustable switching gain. Specifically, when the system state is far from the sliding mode surface, a larger switching gain is adjusted to improve the convergence rate. When the system state is close to the sliding mode surface, a smaller switching gain is adjusted to reduce chattering. Simulation and experimental results demonstrate the superiority of the proposed AFTC-GPIO method qualitatively and quantitatively. Note to Practitioners–As a highly nonlinear system easily affected by external disturbances and system uncertainty, high precision position control of magnetic levitation system is a great challenge. In this paper, based on the accurate estimation of lumped time-varying interference by GPIO, an adaptive fixed time sliding mode controller is designed to suppress the disturbance and achieve the high precision control. Traditional sliding mode control inevitably has to choose between improving convergence rate and suppressing chattering, and the dynamic and steady performance of the system cannot be considered simultaneously. In view of this issue, this paper combines sliding mode control with adaptive control, and an adaptive and adjustable switching gain is designed, so that the system has the performance of fast convergence and small chattering. Simulation and experimental results verify the effectiveness of the proposed method. The reported AFTC-GPIO idea can also be extended to control of other types of systems.

This study proposes a novel nonlinear adaptive fuzzy hybrid sliding mode (AFHSM) control strategy for the precise trajectory tracking of autonomous mobile robots (AMRs) equipped with four Mecanum wheels. The control design addresses the inherent complexities of such platforms, which include strong system nonlinearities, significant parametric uncertainties, torque saturation effects, and external disturbances that can adversely affect dynamic performance. Unlike conventional approaches that rely on model linearization or dimension reduction, the proposed AFHSM control retains the full nonlinear characteristics of the system to ensure accurate and robust control. The controller is systematically derived from the trajectory-tracking error dynamics between the AMR and the desired trajectory (DT). It integrates higher-order sliding mode (SM) control, fuzzy logic inference, and adaptive learning mechanisms to enable real-time compensation for model uncertainties and external perturbations. In addition, a saturation handling mechanism is incorporated to ensure that the control signals remain within feasible limits, thereby preserving actuator integrity and improving practical applicability. The stability of the closed-loop nonlinear system is rigorously established through the Lyapunov theory, guaranteeing the asymptotic convergence of tracking errors. Comprehensive simulation studies conducted under severe conditions with up to 60 percent model uncertainty confirm the superior performance of the proposed method compared to classical SM control. The AFHSM control consistently achieves lower trajectory and heading errors while generating smoother control signals with reduced torque demand. This improvement enhances tracking precision, suppresses chattering, and significantly increases energy efficiency. These results validate the effectiveness of the AFHSM control approach as a robust and energy-aware control solution for AMRs operating in highly uncertain and dynamically changing environments.

In this paper, a nonlinear disturbance observer-based backstepping finite-time sliding mode control scheme for trajectory tracking of underwater vehicles subject to unknown system uncertainties and time-varying external disturbances is proposed. To reduce the influence of the uncertainties and external disturbances, a nonlinear disturbance observer is developed without any acceleration measurements to identify the lumped disturbance term. Additionally, the finite-time trajectory tracking controller is designed by combining second-order sliding mode control and backstepping design technique with the nonlinear disturbance observer. The finite-time convergence of motion tracking errors and the stability of the overall closed-loop control system are guaranteed by the Lyapunov approach. Besides, comprehensive simulation studies on trajectory tracking control of underwater vehicles are provided to demonstrate the effectiveness and performance of the proposed control scheme.

This paper presents a model reference adaptive control (MRAC) scheme for trajectory tracking of a nonholonomic wheeled mobile robot (WMR) in presence of parametric uncertainty in its dynamic model. The control scheme consists of kinematic and dynamic controllers. The desired values of the linear and angular velocities are generated by the kinematic controller for the given trajectory. The adaptive controller designed based on the dynamic model provides the torques of the robot actuators for yielding the required velocities. The stability proofs are given for the two stage control system. Simulations also demonstrate the good performance of the proposed control scheme for trajectory tracking under the presence of the dynamic parameter uncertainties.

This paper proposes an event-triggered model predictive-preview control strategy for autonomous vehicle trajectory tracking. First, the dynamic equation is established based on the preview road curvature and the vehicle’s 2 degree-of-freedom relationship. A model predictive tracking controller is designed by predicting the system dynamics in the future. Second, to reduce the computational burden of the controller, the triggering conditions are designed according to the system’s stability and feasibility. The proposed event-triggered model predictive-preview control strategy not only makes the autonomous vehicles maintain tracking accuracy but also reduces the number of online optimization. Then, asymptotically stable of closed-loop systems are proved by using Lyapunov’s theorem. Finally, simulation experiments show that the proposed strategy has some advantages over traditional model predictive control in terms of improving vehicle tracking accuracy and reducing algorithm complexity.

ABSTRACTThis paper introduces a semi‐model‐free adaptive backstepping dynamical sliding mode control scheme for trajectory tracking of robot manipulators subject to uncertain dynamics. The proposed methodology synthesizes backstepping control and dynamical sliding mode control paradigms through Lyapunov stability theory to derive an innovative dynamic control law coupled with an adaptation mechanism. A key advantage of this approach is its dependence solely on the nominal inertia matrix, thereby circumventing the requirement for a comprehensive dynamic model. In contrast to conventional model‐based adaptation laws, which depend on precise knowledge of system dynamics, and model‐free approaches that often rely on the restrictive assumption of zero time‐derivative for uncertain terms, the proposed adaptive law bypasses both limitations. Instead, this adaptive mechanism estimates the aggregate effects of uncertain dynamic components—encompassing centripetal and Coriolis forces, gravitational effects, external disturbances, and unmodelled dynamics—and incorporates these estimates within the dynamic control framework. Through rigorous stability analysis, we demonstrate that the integration of these control techniques ensures global uniform boundedness of both tracking and estimation error trajectories, thereby establishing robust convergence properties. The efficacy of the proposed control architecture is validated through comprehensive numerical simulations conducted on a 6‐degree‐of‐freedom Universal Robots UR5 manipulator platform, implemented within both MATLAB and the Gazebo simulation environment interfaced with the robot operating system framework. Simulation results demonstrate the closed‐loop system's superior performance in tracking predefined trajectories despite significant model uncertainties. An integrated motion planner further optimizes performance by reducing peak torque during goal‐to‐goal positioning tasks.

This research focuses on the modeling and lateral control of an autonomous vehicle, employing a novel robust fixed-time sliding mode control method. Prior to any further analysis, a detailed model of the lateral dynamics of an autonomous vehicle is developed in order to accurately represent its nonlinear behavior and dynamic characteristics. Furthermore, a novel fixed-time sliding mode controller is employed to control the vehicle’s movement, effectively addressing nonlinearities while reducing the impact of uncertainties and external disturbances. This approach is known for its ability to provide a specific time of convergence, which results in achieving high accuracy and fast response. Subsequently, the stability of the overall system must be maintained by applying Lyapunov functions. In order to validate the effectiveness of the proposed control method, it is tested through simulations and compared with classical fixed-time sliding mode control and fixed-time fast terminal sliding mode control techniques. The results confirm the superior robustness and performance of the proposed control method, thereby highlighting its potential for autonomous vehicle applications.

A control algorithm for the position tracking of a magnetic levitation system is presented in this article. The magnetic levitation system is well known for its non-linear dynamic characteristics and open-loop instability. The external disturbances will deteriorate the dynamic performance of the magnetic levitation system, and may give rise to system instability. This problem triggers enormous interests in designing various controllers for the non-linear dynamic system. In this article, a magnetic levitation system is first modelled. Then, a sliding mode controller is proposed, with a simple yet effective disturbance observer to perform disturbance rejection. Both the simulation results and the experimental results verify the validity of the robust controller.

Introduction: This study presents a control strategy for trajectory tracking of Hexacopter UAVs using sliding mode control. The Hexacopter's nonlinear mathematical model is first derived using Newton-Euler's formulation. A nonsingular fast terminal sliding mode controller (NSTSMC) is then developed to enable precise tracking of the flight trajectory, while accommodating variations in orientation angle. To evaluate the controller’s robustness, additional disturbances and chattering reduction techniques are introduced in the tests. The control system's performance, compared with a classical PID controller, is assessed using MATLAB-Simulink simulations. The results demonstrate that the Hexacopter, under the NSTSMC, effectively mitigates disturbances with minimal deviation from the planned trajectory, requiring less effort.

Event-triggered sliding mode tracking control of autonomous surface vehicles

In this paper, nonlinear adaptive particle swarm optimization-based gain optimization of sliding mode control systems is presented under matching model uncertainty and random Gaussian external disturbances for magnetic levitation position control systems. The main problems in magnetic levitation control systems are: lack of nonlinear control system; limited position control, i.e., up to 1mm only; convergence rate; accuracy of control; chattering problems in conventional SMC; and lack of considering the effects of system parameters and loading mass changes into account with external disturbance. In this paper, first, a third-order dynamic nonlinear model was created, which includes mechanical (ball position and velocity) and electrical (the current) subsystems with uncertainty in the system parameter and loading mass of 20% each. Secondly, a sliding mode control system for position control systems under both matched model uncertainty (internal) and external Gaussian disturbances is designed for magnetic levitation position tracking systems. Then, the gain of the sliding mode control system is allocated in such a way that the ITSE fitness function is minimal using the adaptive particle swarm optimization technique. The suggested control method, which is based on the combination of the proposed sliding mode control system and adaptive particle swarm optimization, offers control performance with a significant improvement in terms of chattering reduction using arc tangential function, high precision control accuracy, and fast convergence rate. Moreover, a robust optimal SMC controller designed for magnetic levitation systems under both internal and external disturbances is able to reject all disturbances. Finally, the algorithm’s performance is demonstrated by model simulation and the proposed control, with simulation results indicating good convergence for given constant and constant plus sinusoidal reference positions.

This study proposes an adaptive non‐singular integral terminal sliding mode control (ANITSMC) scheme for trajectory tracking of autonomous underwater vehicles (AUVs) with dynamic uncertainties and time‐varying external disturbances. The ANITSMC is first proposed for a first‐order uncertain non‐linear dynamic system to eliminate the singularity problem in conventional terminal sliding mode control (TSMC) and avoid the requirement of the bound information of the lumped system uncertainty. The time taken to reach the equilibrium point from any initial error is guaranteed to be finite. The proposed ANITSMC is then applied to trajectory tracking control of AUVs. It guarantees that the velocity tracking errors locally converge to zero in finite time and after that the position tracking errors locally converge to zero exponentially. The designed ANITSMC of AUVs avoids the requirement of the prior knowledge of the lumped system uncertainty bounds as opposite to the existing globally finite‐time stable tracking control (GFTSTC), provides higher tracking accuracy than the existing GFTSTC and adaptive non‐singular TSMC (ANTSMC) and offers faster convergence rate and better robustness against dynamic uncertainties and time‐varying external disturbances than the adaptive proportional‐integral sliding mode control (APISMC). Comparative simulation results are presented to validate the superiority of the ANITSMC over the APISMC.

Accurate and robust trajectory tracking is essential for ensuring the safety and efficiency of underactuated ships operating in complex marine environments. However, conventional sliding mode control (SMC) methods often suffer from issues such as chattering and slow convergence, limiting their practical application. To address these challenges, this paper proposes a novel non-singular fast terminal sliding mode control (NFTSMC) strategy for sustainable trajectory tracking of underactuated ships. The proposed approach first designs a virtual control law based on surge and sway position errors, and then develops a non-singular fast terminal sliding mode control law using an exponential reaching strategy, guaranteeing finite-time convergence and eliminating singularities. The Lyapunov-based stability analysis proves the boundedness and convergence of tracking errors under external disturbances. The simulation results demonstrate that the proposed non-singular fast terminal sliding mode control outperforms traditional sliding mode control in terms of convergence speed, tracking accuracy, and control smoothness, especially under wind, wave, and current disturbances.

A control strategy for trajectory tracking of straight line trajectories for autonomous surface vehicles (ASV) is presented in this paper. Our control strategy is based on input-output feedback linearization with the so called hand position point as output. This is motivated by a method previously used for ground autonomous vehicles, without external disturbances. The proposed control strategy may be used also for path following. The control approach proposed in this paper is furthermore able to deal with external disturbances, e.g. unknown irrotational ocean currents, and gives an estimate of the disturbance. Using Lyapunov analysis, almost-global asymptotic stability (almost-GAS) of the closed-loop system is proven. Simulation results are included to validate the theoretical result.