ELM-Based Non-Singular Fast Terminal Sliding Mode Control Strategy for Vehicle Platoon

To eliminate the effect of the uncertain disturbances and improve the control accuracy of spacecraft Attitude Control System, a nonlinear control algorithm named nonsingular terminal sliding-mode feedback controller is proposed in this work, which is mainly made up of nonsingular terminal sliding-mode controller and sliding-mode feedback controller. In the first place, nonsingular terminal sliding-mode controller is designed, which guarantees global asymptotic convergence of the attitude in the presence of the uncertain perturbations from the space. Despite that, it is the influence of the uncertain disturbances that hinder the control accuracy. Then, in order to promote the control accuracy, the sliding-mode feedback controller based on the principle of minimum sliding-mode error is proposed, which is used to compensate the control errors of the nonsingular terminal sliding-mode controller caused by the uncertainties. Hence, the determination principle of the weighting matrix in sliding-mode feedback controller is discussed, and the algorithm structure of the sliding-mode feedback controller is also analyzed, which provides the theoretical basis for the sliding-mode feedback controller. By contrast, an adaptive fuzzy algorithm is designed and introduced into the nonsingular terminal sliding-mode controller to improve the control accuracy, which named the nonsingular terminal fuzzy sliding-mode controller. Last but not the least, several numerical examples are presented to demonstrate the efficacy of the proposed nonsingular terminal sliding-mode feedback controller. Simulation results confirm that the control accuracy of the nonsingular terminal sliding-mode feedback controller is higher than the nonsingular terminal sliding-mode controller and the same as nonsingular terminal fuzzy sliding-mode controller. Not only is the calculation of the nonsingular terminal fuzzy sliding-mode feedback controller smaller than nonsingular terminal fuzzy sliding-mode controller, the adjusted parameters are also fewer than nonsingular terminal fuzzy sliding-mode controller obviously. The numerical results clearly indicate that the proposed nonsingular terminal sliding-mode feedback controller based on the principle of minimum sliding-mode error can compensate control errors accurately and quickly; therefore, it can reduce the effect of the uncertainties from the space indirectly.

This paper proposes a non-singular fast terminal sliding mode control strategy based on the self-organizing radial basis function neural network (RBFNN) approximation for the train key network system to realize the safe and reliable operation of the train. In order to improve the RBFNN approximation performance and speed, an improved multi-strategy particle swarm optimization (IMPSO) algorithm, which utilizes multi-strategy evolution ways with a nonlinear deceasing inertia weight to improve the global optimizing performance of particle swarm, is proposed to optimize the structure and parameters for better mapping the highly nonlinear characteristics of train traction braking. In addition, the IMPSO is also introduced into a non-singular fast terminal sliding mode (NFTSM) controller to obtain the most appropriate tuning parameters of the controller and suppresses the chattering phenomenon from sliding mode controller. The stability characteristic of the system under the proposed NFTSM controller is studied based on the Lyapunov theory. Further combined with effective delay prediction and delay compensation methods, the NFTSM high-precision control of the train key nonlinear network system is implemented. The simulation results show that the proposed method has more efficient and robust tracking performance and real-time performance compared with other control methods, which can provide effective means for realizing the symmetrical bus control by automatic train operation (ATO) at both ends of the train, with the safe operation of the train under every complex motion condition.

This paper proposes a Disturbance-Compensated Non-Singular Fast Terminal Sliding Mode Control (DC-NFTSMC) method to address the issues of slow convergence speed and poor robustness in traditional turntable control methods. By designing an improved non-singular fast terminal sliding mode surface and reaching law, the convergence speed of the turntable system is significantly enhanced. Additionally, an Extended State Observer (ESO) is incorporated to estimate and compensate for complex disturbances and improving the robustness of the turntable system. Simulation results demonstrate that, compared with traditional methods, this control method not only effectively improves the tracking response speed of the turntable system but also ensures superior robustness in the presence of multiple superimposed disturbances.

This article proposes an adaptive nonsingular fast terminal sliding mode control scheme with piecewise fast multi-power reaching law for tracking control of underactuated autonomous underwater vehicles under model uncertainties, ocean disturbances, and measurement noise. This control approach enhances the robustness and guarantees faster convergence of state error to zero in finite time while reducing the chattering effect. Utilizing the benefit of adaption law prevents overestimating control parameters, and it eliminates the need for the upper bound value of disturbances. The overall stability of the system is analyzed using the Lyapunov criterion. The results of the proposed approach are compared with adaptive nonsingular terminal sliding mode control and adaptive sliding mode control. The performance of the proposed control approach is evaluated by using the performance indices root mean square error and chattering indicator. The simulation results confirm the efficiency of the proposed approach.

Fractional-order nonsingular terminal sliding mode controller for a quadrotor with disturbances

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.

Global fast non-singular terminal sliding-mode control for high-speed nanopositioning

This paper proposes a high-order nonsingular terminal sliding mode control method for induction motor velocity servo systems. Based on the vector control principle, high-order nonsingular terminal sliding mode controllers in velocity loop, current loop and flux loop are designed respectively. The nonsingular terminal sliding mode control is utilized to improve the response speed and robustness of motor control systems. Meanwhile, high-order sliding modes are adopted to eliminate the chattering phenomenon. For the demand of response speed in current loop, an exponential control law is proposed. The simulation results show that the proposed method has advantage over conventional PI control methods in response speed, control precision, and robustness.

In this paper, an adaptive second-order non-singular fast terminal sliding mode (SONFTSM) control scheme is proposed so as to achieve finite-time stability with chattering-free control inputs for a class of nonlinear uncertain systems. Instead of the traditional control input in primitive sliding mode switching control design, the real control input is the time integration of the designed derivation of control input with discontinuous terms such that the chattering phenomenon can be reduced. An integral terminal sliding mode (ITSM) and a non-singular fast terminal sliding mode (NFTSM) are applied into the equivalent control design such that finite-time convergence of system states can be guaranteed when it moves on a sliding surface. Then, an adaptive method is utilised to estimate the unknown upper bound of the lumped uncertainty caused by modelling error and external disturbance. The stability analysis of closed-loop system can be demonstrated by constructing Lyapunov candidate function. Finally, the simulation results verify the effectiveness of proposed control scheme.

For a hybrid mechanism for automobile electro-coating conveying which is self-developed, a dynamic model is established based on screw theory and the principle of virtual work to simplify the process of modeling. Then, to solve the chattering problem and the slow rate of convergence problem of the existing sliding mode control methods for the hybrid mechanism, a super-twisting algorithm based second-order nonsingular fast terminal sliding mode control method is proposed. The stability of the proposed control method is proved by Lyapunov stability theorem. Finally, compared with the reaching law based sliding mode control method and the super-twisting algorithm based second-order sliding mode control method, it is indicated from the simulation and experiment results that the proposed control method not only has high steady-state accuracy, better dynamic performance and strong robustness, but also reduces the chattering and improves the rate of convergence of the system. And it lays foundation for realizing the high performance control of the hybrid mechanism for automobile electro-coating conveying.

This paper proposes full-order terminal sliding-mode control strategies for wind energy conversion systems. Nonsingular terminal sliding-mode manifolds and related second-order sliding-mode control strategies are designed respectively for the d- and q-axis currents respectively. The control signals in the proposed sliding-mode controllers are continuous and have no chattering phenomenon. So the proposed controllers are suitable for practical applications.

Due to the bus characteristics of large quality, high center of gravity and narrow wheelbase, the research of its yaw stability control (YSC) system has become the focus in the field of vehicle system dynamics. However, the tire nonlinear mechanical properties and the effectiveness of the YSC control system are not considered carefully in the current research. In this paper, a novel adaptive nonsingular fast terminal sliding mode (ANFTSM) control scheme for YSC is proposed to improve the bus curve driving stability and safety on slippery roads. Firstly, the STI (Systems Technologies Inc.) tire model, which can effectively reflect the nonlinear coupling relationship between the tire longitudinal force and lateral force, is established based on experimental data and firstly adopted in the bus YSC system design. On this basis, a more accurate bus lateral dynamics model is built and a novel YSC strategy based on ANFTSM, which has the merits of fast transient response, finite time convergence and high robustness against uncertainties and external disturbances, is designed. Thirdly, to solve the optimal allocation problem of the tire forces, whose objective is to achieve the desired direct yaw moment through the effective distribution of the brake force of each tire, the robust least-squares allocation method is adopted. To verify the feasibility, effectiveness and practicality of the proposed bus YSC approach, the TruckSim-Simulink co-simulation results are finally provided. The co-simulation results show that the lateral stability of bus under special driving conditions has been significantly improved. This research proposes a more effective design method for bus YSC system based on a more accurate tire model.

In order to solve the attitude synchronization control problem of an on-orbit servicing spacecraft autonomously docking to a tumbling satellite with the unknown bounded disturbances and system uncertainties, a fast terminal sliding mode control law is presented in this paper. The most important contribution of this paper is to design an attitude synchronization control law, which will be realized by the terminal sliding mode control method, for a servicing spacecraft autonomously docking to a freely tumbling satellite in space. First of all, the model of relative attitude dynamics is derived from the attitude dynamics of servicing spacecraft and tumbling satellite. Then, the relative attitude dynamic model is converted to the normal formation to apply the control method of fast terminal sliding mode. Furthermore, a fast terminal sliding mode control law for attitude synchronization is designed based on the normal formation of relative attitude dynamic model. During the design process of the control law, the measurement errors and parameter variations are also considered. Finally, several numerical simulations are conducted to verify the designed attitude synchronization control law, and the results verified the effectiveness of the designed control law. Moreover, it's robustness to the unknown bounded disturbances, system uncertainties and measurement errors has also been demonstrated.

The tension control of carbon fiber diagonal weaving looms is severely affected by the coupling between structured friction and unstructured disturbances, leading to strong nonlinearities and time-varying uncertainties. To overcome the chattering and model-dependency issues inherent in traditional sliding mode control, a nonlinear dynamic model incorporating the Stribeck friction term was established. An Improved Adaptive Radial Basis Function-based Nonsingular Fast Terminal Sliding Mode Control (I-ARBF-NFTSMC) framework was then proposed. The framework adopts a divide-and-conquer composite compensation mechanism, in which a smooth Hyperbolic Tanh Fixed-Time Disturbance Observer (Tanh-FTDO) estimates external disturbances and suppresses chattering, and an Improved Adaptive Radial Basis Function (I-ARBF) neural network approximates and compensates internal nonlinear friction. Simulation results show that, compared with the conventional Fixed-Time Extended State Observer-based method (FESO-NFTSMC), the proposed controller achieves higher disturbance-estimation accuracy and tracking performance under sinusoidal, triangular, and composite disturbances. In composite-disturbance conditions, the steady-state mean-squared error is reduced by about 60%, the maximum tracking error decreases from 0.08787 N to 0.01965 N, and the settling time shortens by approximately 25.2%, while effectively mitigating high-frequency chattering. The proposed strategy achieves fast finite-time convergence with enhanced smoothness and robustness, providing a real-time executable solution for high-precision tension control in complex nonlinear weaving processes.

This paper investigates the trajectory-tracking problem of an uncertain quadrotor in the presence of complex disturbances. A new fractional-order terminal sliding mode control method (FOTSMC) is designed for a quadrotor attitude, which can increase the control robustness against the external disturbances and modeling uncertainty, and decrease the chattering problem. A new fractional non-integer sliding mode control technique for a quadrotor position is designed to stabilize its state variables and attenuate wind disturbance and the effects of variation in the mass. The stability analysis is studied by the Lyapunov theory. Numerical simulation for complex flight trajectory under disturbances is given to illustrate the validity of the proposed methods.