Adaptive robust non-singular fast terminal sliding mode control for a two-link robotic manipulator with NN-based ESO

This work proposes a non-singular fast terminal sliding mode control (NFTSMC) strategy based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm and a nonlinear disturbance observer (NDO) to address the issues of modeling errors, motion disturbances, and transmission friction in robotic manipulators. Firstly, a novel modular serial 5-DOF robotic manipulator configuration is designed, and its kinematic and dynamic models are established. Secondly, a nonlinear disturbance observer is employed to estimate the total disturbance of the system and apply feedforward compensation. Based on boundary layer technology, an improved NFTSMC method is proposed to accelerate the convergence of tracking errors, reduce chattering, and avoid singularity issues inherent in traditional terminal sliding mode control. The stability of the designed control system is proved using Lyapunov stability theory. Subsequently, a deep reinforcement learning (DRL) agent based on the TD3 algorithm is trained to adaptively adjust the control gains of the non-singular fast terminal sliding mode controller. The dynamic information of the robotic manipulator is used as the input to the TD3 agent, which searches for optimal controller parameters within a continuous action space. A composite reward function is designed to ensure the stable and efficient learning of the TD3 agent. Finally, the motion characteristics of three joints for the designed 5-DOF robotic manipulator are analyzed. The results show that compared to the non-singular fast terminal sliding mode control algorithm based on a nonlinear disturbance observer (NDONFT), the non-singular fast terminal sliding mode control algorithm integrating a nonlinear disturbance observer and the Twin Delayed Deep Deterministic Policy Gradient algorithm (TD3NDONFT) reduces the mean absolute error of position tracking for the three joints by 7.14%, 19.94%, and 6.14%, respectively, and reduces the mean absolute error of velocity tracking by 1.78%, 9.10%, and 2.11%, respectively. These results verify the effectiveness of the proposed algorithm in enhancing the trajectory tracking accuracy of the robotic manipulator under unknown time-varying disturbances and demonstrate its strong robustness against sudden disturbances.

Adaptive nonsingular fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems

Diseases such as cerebral palsy can lead to lower limb dysfunction in children. Lower limb rehabilitation exoskeletons have been clinically validated as effective interventions for gait rehabilitation of children. This study proposes a novel lower-limb gait rehabilitation exoskeleton design and its corresponding control method for pediatric applications. A dynamic model was established, and a nonsingular fast terminal sliding mode control (NFTSMC) strategy was developed to achieve precise trajectory tracking. The curve fitting was performed on a publicly available children’s gait dataset to generate reference hip and knee joint trajectories. The Lagrange method was subsequently employed to derive the dynamic model of the lower-limb exoskeleton. Control simulations were conducted using the proposed NFTSMC algorithm. Comparative analysis with traditional sliding mode control (SMC) demonstrated that NFTSMC reduced root mean square error (RMSE) by 75% (hip) and 67.4% (knee), while integral of time-weighted absolute error (ITAE) decreased by 77.3% and 92.3%, respectively. These results confirm that NFTSMC significantly enhances joint trajectory tracking accuracy, system response speed, and tracking precision.

A manipulator often cannot converge rapidly within finite time and has low tracking accuracy owing to factors such as manipulator model errors and external disturbances. To address these problems, this paper proposes a time-varying non-singular fast terminal sliding mode control scheme based on an improved variable power–power reaching law. First, three radial basis function neural networks (RBFNNs) are employed to approximate the dynamic parameters of the manipulator model and thus realize model-free control. Second, to achieve faster finite-time convergence of the system state, a time-varying non-singular fast terminal sliding-mode (NFTSM) surface is designed according to the system state change. In addition, an improved variable power–power reaching law is adopted to avoid chatter and eliminate approximation errors. Finally, comparative simulation experiments are conducted using a 2-DOF manipulator as the research object. The results show that the proposed control scheme facilitates fast convergence, high-precision trajectory tracking, and effective suppression of system chatter under complex uncertainties, thereby confirming its utility and superiority.

A Non-singular Fast Terminal Sliding Mode Approach to Improve the Network Stability of Wind Rich Power Grids

This paper proposes a non-singular fast terminal sliding mode control (NFTSMC) method for micro gyroscopes with unknown uncertainty based on gated recurrent fuzzy neural networks (GRFNNs). First, taking advantage of non-singular fast terminal sliding control, a sliding hyperplane is designed with a nonlinear function to ensure that the tracking error of the system converges to zero within a specified finite time. Then, the unknown model parameters of the micro gyroscope are estimated using a GRFNN. Since the GRFNN can adaptively adjust the base width, center vector, gated recurrent unit parameters, and outer gains, it can achieve accurate approximation to unknown models, enhancing the robustness and accuracy. In addition, due to the introduction of gated recurrent units, The GRFNN can effectively utilize the previous data and avoid the problem of gradient disappearance. The comparison of the simulation results with traditional neural sliding mode control shows that the proposed method can achieve better tracking performance and more accurate estimation of unknown models.

The paper presents a method of synthesizing the Variable Structure Controller (VSC) based on the Fast Terminal Sliding Mode (FTSM) control for an optoelectronic observatory to eliminate the effects of the vibration and the change of vehicle’s direction. An improved fast terminal sliding surface and a fuzzy saturation function have been proposed to develop the improved fast terminal sliding mode variable structure controller (IFTSM-VSC). Based on the theory of Lyapunov stability, the article has proved that the IFTSM-VSC controller ensures the Line of Sight (LOS) stabilization of the observation devices and ensures the tracking errors converge to zero in finite time. The simulation uses data about the vibration and navigation of the vehicle recorded on some streets and roads. Simulation results in Matlab/Simulink show the effectiveness of the IFTSM-VSC controller.

A Global Fast Terminal Sliding Mode Controller (GFTSMC) is proposed for n-link robotic manipulators by employing the Fast Terminal Sliding Mode (FTSM) control concept in both the reaching phase and the sliding phase. Under the control, the system states will reach FTSM in desired finite time and then converge to the origin along the FTSM in specified finite time, resulting in a reduced steady tracking error in comparison with the conventional sliding mode controller. The proposed controller is continuous and therefore chattering-free. An example is presented to demonstrate its effectiveness.

This paper reports our study of an adaptive finite‐time neural network control scheme for redundant parallel manipulators. The proposed controller is based on fully tuned radial basis function neural networks (RBFNs), nonsingular fast terminal sliding mode control (NFTSMC), and nonlinearities in output feedback. RBFNs with a fully online update on the output weights and both the centers and variances of Gaussian functions are used to estimate system uncertainties and disturbances. The proposed approach possesses several advantages over other existing approaches like robustness, rapid response, nonsingularity, higher precision, finite‐time convergence, and better tracking control performance. The stability of the parallel manipulators is ensured by the Lyapunov theory. Finally, simulation results validate the effectiveness of the proposed methodology.

In this paper, a finite-time adaptive fuzzy tracking control scheme is proposed for parallel manipulators with unbounded uncertainties. The proposed approach is based on fuzzy logic systems (FLS), nonsingular fast terminal sliding mode control (NFTSMC) and adaptive sliding compensation from nonlinearities in output feedback. FLS are adopted to handle system uncertainties and external disturbances. This learning approach does not require knowledge of parallel manipulator dynamics. The proposed control scheme can possess several advantages over other state-of-the-art approaches such as rapid response, robustness, higher precision, nonsingular, and finite-time converge. Besides, since the proposed approach is a hybrid scheme of NFTSMC and FLS, the proposed controller can have much better tracking control performance. The finite-time convergence and stability of the closed-loop robotic system are ensured by the Lyapunov theory. Finally, from the simulation results, it is clearly evident that the proposed approach can indeed outperform previous existing methods.

Piezoelectric actuators are widely employed in micro-precision applications due to their fast response and high resolution. This paper investigates the trajectory tracking control of a cantilever piezoelectric stack actuator (CPSA) under external perturbations and hysteresis. A control scheme is proposed that effectively compensates for hysteresis by employing an asymmetric Bouc–Wen model, integrated with a non-singular fast terminal sliding mode control (NFTSMC) featuring a variable convergence law. This methodology guarantees finite-time convergence and robustness, thereby enhancing the overall control performance of the CPSA. Experimental results reveal that the proposed control algorithm significantly improves control accuracy and speed, achieving stable closed-loop system performance and maintaining bounded closed-loop signals within a finite time frame. The effectiveness and superiority of the NFTSMC method are validated through comprehensive experimental studies.

To address the issue of reduced speed tracking accuracy in permanent magnet synchronous motors (PMSM) under variable-speed conditions, this paper proposes a non-singular fast terminal sliding mode controller (NFTSMC) that mitigates the chattering problem inherent in sliding mode control (SMC). For handling external disturbances where the controller exhibits poor convergence, a sliding mode disturbance observer (SMDOB) is designed to ensure effective convergence of the proposed control strategy under disturbed conditions. The superiority of the integrated control approach combining the NFTSMC with the SMDOB was ultimately validated through simulations.

An important function of the steer-by-wire (SBW) system is to follow a desired steering angle accurately. However, it is impossible to avoid transmission backlash in the servo system, which will aggravate the mechanical vibration and cause delays and fluctuations in control system responses. A composite controller for permanent magnet synchronous motor (PMSM) servo system is proposed in this paper to solve the adverse effects resulting from backlash of the SBW system. To mitigate the effects of backlash nonlinearity, the dead-zone backlash model is identified utilizing the particle swarm optimization (PSO) algorithm, and its influence is compensated in the controller. Additionally, to address the model declination and unpredictable disturbances, a nonsingular fast terminal sliding mode controller (NFTSMC) combined with a super-twisting extended state observer (STESO) is designed. In simulation experiments, a SBW control system model is built to evaluate the performance of the disturbance observer and the angle following controller. In hardware-in-loop (HIL) experiments, the angle tracking control capability of the novel method is further evaluated under the double lane change condition. Finally, the results of simulation and HIL experiments are offered to validate the excellence of the novel method.

This paper presents a sensorless speed control method of permanent magnet synchronous motor (PMSM) applying sliding-mode control theory, to enhance the observation precision and improve robustness of control system. Firstly, an improved full-order sliding mode observer (FSMO) with sigmoid function is gifted to weaken the high-frequency (HF) chattering caused by conventional sliding mode observer (SMO). The quadrature phase-locked loop (PLL) is used to calculate high-precision rotor location and speed, avoiding the use of filter. Then the nonsingular fast terminal sliding mode controller (NFTSMC) in speed controller is introduced to replace traditional proportional integral (PI) controller to improve the dynamic performance of control system. The outcomes verify that the presented control method enhances the overall observation precision, suppresses HF chattering, and increases dynamic and stable state response of PMSM.

Hexacopter operations in the atmospheric boundary layer (ABL) are affected by gusty winds and turbulence, leading to collision risks or crashes. Stability of the hexacopter UAV in gusty winds is challenging in urban space. In this paper, non‐singular fast terminal sliding mode control (NFTSMC) is optimized using particle swarm optimization for altitude and attitude control of a hexacopter UAV in turbulent wind conditions. The nonlinear disturbance observer is designed to estimate and compensate for the external perturbations in ABL, such as wind gusts, using the Dryden turbulence model. The presented control law demonstrates superior trajectory tracking of the translational axis () and rotational components (, , ) while ensuring singularity‐free convergence, reduced chattering, and smooth actuation in turbulent wind conditions. Lyapunov‐based stability analysis proves global asymptotic convergence, guaranteeing robustness against unmodeled dynamics and urban wind disturbances.