The backstepping double integral terminal sliding mode control of upper limb rehabilitation robot based on friction compensation

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.

The lower hook mechanism has the characteristics of long motion path, high moving speed and high external disturbance, significantly impacting the weaving efficiency of the fishing net weaving machine. The multi-motor-based lower hook mechanism exhibits higher moving speed and lesser cam wear compared with the traditional lower hook mechanism, but it requires a high-precision and high-robust control system. In this study, we established a dynamic model for the multi-motor lower hook mechanism using the Lagrange equation. Based on this model, we developed a control system using linear extended state observer (LESO) and piecewise integral terminal sliding mode controller (PITSMC). By introducing a piecewise integral sliding surface, PISMC solved the slow convergence issue of linear sliding surfaces and the singularity problem of integral terminal sliding surfaces. Simulation results for the multi-motor-based lower hook mechanism demonstrate that the proposed PISMC outperforms the nonsingular terminal sliding mode controller and the conventional integral sliding mode controller in terms of control precision and disturbance rejection capability.

This paper focuses on the trajectory tracking control of unmanned underwater vehicles (UUVs) in the presence of dynamic uncertainties and time-varying external disturbances. Two adaptive integral terminal sliding mode control schemes, namely, adaptive integral terminal sliding mode control (AITSMC) scheme and adaptive fast integral terminal sliding mode control (AFITSMC) scheme are proposed for UUVs based on integral terminal sliding mode (ITSM) and fast ITSM (FITSM), respectively. Each control scheme is double-looped: composed of a kinematic controller and a dynamic controller. First, a kinematic controller is designed for each of the two control schemes. The two kinematic controllers are based on ITSM and FITSM, respectively. These kinematic controllers yield local finite-time convergence of the position tracking errors to zero meanwhile avoid the singularity problem in the conventional terminal sliding mode control (TSMC). Then, using the output of the kinematic controller as a reference velocity command, a dynamic controller is developed for each of the two control schemes. The two dynamic controllers are also based on ITSM and FITSM, respectively. An adaptive mechanism is introduced to estimate the unknown parameters of the upper bound of the lumped system uncertainty which consists of dynamic uncertainties and time-varying external disturbances so that the prior knowledge of the upper bound of the lumped system uncertainty is not required. The estimated parameters are then used as controller parameters to eliminate the effects of the lumped system uncertainty. The convergence rate of the integral terminal sliding variable vector is investigated and the local finite-time convergence of the velocity tracking errors to zero in the ITSM or FITSM is obtained. Finally, based on the designed kinematic and dynamic controllers, the finite-time stability of the full closed-loop cascaded system is shown. The two proposed control schemes improve the tracking accuracy over the existing globally finite-time stable tracking control (GFTSTC) and adaptive nonsingular TSMC schemes, and enhance the robustness against parameter uncertainties and external disturbances over the GFTSTC scheme. Compared with the conventional adaptive integral sliding mode control (AISMC) scheme, the two proposed control schemes offer faster convergence rate and stronger robustness against dynamic uncertainties and time-varying external disturbances for the trajectory tracking control of UUVs due to involving the fractional integrator. Comparative numerical simulations are performed on the dynamic model of the Omni Directional Intelligent Navigator UUV for two trajectory tracking cases. The convergence rate and robustness to uncertainties and disturbances are quantified as the convergent time and bounds of the steady-state position and velocity tracking errors, respectively. The results show that the two proposed control schemes improve at least 20s in convergence rate and enhance about 2% robustness in position tracking and 20% robustness in velocity tracking over the AISMC scheme.

Synchronization of angular velocities of chaotic leader-follower satellites using a novel integral terminal sliding mode controller

Extended state observer augmented finite-time trajectory tracking control of uncertain mechanical systems

This study aims to develop an advanced integral terminal sliding-mode robust control method using a disturbance observer (DO) to suppress the forced vibration of a large space intelligent truss structure (LSITS). First, the dynamics of the electromechanical coupling of the piezoelectric stack actuator and the LSITS, based on finite element and Lagrangian methods, are established. Subsequently, to constrict the vibration of the structure, a novel integral terminal sliding-mode control (ITSMC) law for the DO is used to estimate the parameter perturbation of the LSITS based on a continuous external disturbance. Simulation results show that, under a forced vibration and compared with the ITSMC system without a DO, the displacement amplitude of the ITSMC system with the DO is effectively reduced. In the case where the model parameters of the LSITS deviate by ±50%, and an unknown continuous external disturbance exists, the control system with the DO can adequately attenuate the structural vibration and realize robust control. Concurrently, the voltage of the employed piezoelectric stack actuator is reduced, and voltage jitter is alleviated.

This paper proposes a control strategy integrating the non‐linear extended state observer (NLESO) and the non‐singular terminal sliding mode control (NTSMC) for the trajectory tracking of wheeled mobile robots subject to bounded disturbances. A new transformation method of chained model in terms of Lie derivative is presented to simplify the controller design. A specific NLESO combining linear term and non‐linear term is designed to estimate the disturbances with a faster convergence performance. A scheme for determining the gain range of NLESO is explicitly given to facilitate the tuning of experimental parameters. Meanwhile, the NTSMC achieves finite time convergence of the tracking error system and the chattering phenomenon in NTSMC is dramatically alleviated with the compensation from NLESO. The experimental results validate the strong robustness and good performance of the proposed control strategy.

Adaptive disturbance observer-based fast nonsingular terminal sliding mode control for quadrotors

This paper develops a novel fault-tolerant control based on an observer for underactuated robot manipulators with unknown external disturbances, uncertainties, and actuator faults. First, unlike the traditional approach of treating the robot system as a parameter time-varying system, the underactuated robot manipulator with different drive modes can be considered as one of the classical Markov jump nonlinear systems (MJNSs). Second, an adaptive disturbance observer is designed to estimate the state and disturbances of the system. Finally, based on the observation results, a nonsingular fast integral terminal sliding mode controller (NFITSMC) is utilized to implement fault-tolerant control of the system. Compared with traditional observer and terminal sliding mode controller, the adoption of the novel controller and observer can improve response time and reduce chattering. Especially, in order to eliminate chattering, the integral term is introduced into the nonsingular fast terminal sliding mode controller. Structuring Lyapunov–Krasovskii functional (LKF) and based on linear matrix inequalities (LMIs) techniques, the convergence of control strategy and tracking errors is proved. The simulation results show that the actuator faults can be observed successfully and the error system is finite-time stable.

Aiming at the tip trajectory tracking against system parameter uncertainty and disturbance during the painting process of the spray painting manipulator, a sliding model active disturbance rejection trajectory tracking controller is designed integrating terminal sliding mode control (SMC) approach and active disturbance rejection control (ADRC) technique. The reference curve trajectory of the tip position/velocity is planned by the kinematics equation. in which the compensation is taken into account for the deflection of the manipulator. The extended state observer (ESO) is used to estimate the total disturbance consisting of the uncertain system parameters and the uncertain interference resulting from deflection and load. Utilizing non-singular terminal sliding mode control, a feedback control law is designed to achieve fast and accurate trajectory tracking. Simultaneously, according to the actual system parameters in the engineering, the simulation validation is given to show that the proposed control strategy can guarantee good tracking performance of the closed-loop system.

In this paper, a control algorithm based on Central Pattern Generator (CPG) network and nonsingular terminal sliding mode control is proposed for trajectory tracking of the bionic fish. Firstly, the CPG network is designed according to the mechanical structure of the bionic fish designed in the laboratory, and the kinematics equation of the robot based on CPG network is established. The conversion functions between the speed and the CPG model are given by data. Secondly, CPG network is used as the lower control algorithm and nonsingular terminal sliding mode control is served as the upper control algorithm to design a controller innovatively. The CPG parameters of bionic fish are controlled and adjusted by the upper algorithm to realize trajectory tracking. Finally, the effectiveness of the controller is verified by simulation. Under the control of CPG-nonsingular terminal sliding mode controller, the bionic fish can stably and fast track up the trajectory.KeywordsThe Bionic FishTrajectory TrackingCPGNonsingular Terminal Sliding Mode Control

ABSTRACTIn this paper, a non‐singular terminal sliding mode controller based on the adaptive technique is proposed to realize high‐precision control of a spatial three‐degree‐of‐freedom robotic arm under strong disturbances. Firstly, to ensure that the trajectory tracking error can converge to zero in finite time and to avoid the singularity problem in the control law, a control law containing an inverse tangent function is chosen. Secondly, the chattering phenomenon is eliminated by introducing the boundary layer technique. In addition, the adaptive technique is introduced to greatly improve the disturbance rejection capability of the controller while retaining the advantages of the original sliding mode surface, and the drift problem of the adaptive law is solved by introducing the dead‐zone correction term. Based on the Lyapunov theory, the finite‐time convergence of the system is proved, and a simulation platform and a physical experimental setup are built to physically verify the controller. Taking the IAE of the tracking process in the first joint as an example, the proposed controller improves tracking accuracy by 73%, 66%, and 34% compared to non‐singular terminal sliding mode controller (NTSMC), inverse tangent‐based non‐singular terminal sliding mode controller (ATNTSMC), and adaptive robust non‐singular fast terminal sliding mode controller (ARNFTSMC), respectively. Additionally, the proposed methodology achieves the fastest convergence rate, with improvements of 55%, 45%, and 29% over NTSMC, ATNTSMC, and ARNFTSMC, respectively. These results demonstrate the significant potential of the proposed methodology in enhancing the robustness, accuracy, and applicability of robotic systems.

In this paper, a novel fast nonsingular integral terminal sliding mode controller based on an adaptive neural network (ANN-FNITSMC) is proposed for the trajectory tracking control of cable-driven continuum robots (CDCRs) in complex underwater environments with uncertainties. First, a novel fast nonsingular integral terminal sliding mode control (FNITSMC) is designed to solve the chattering and singularity problems of the conventional terminal sliding mode control (TSMC). Second, an adaptive neural network (ANN) based on a radial basis function (RBF) is established to derive the uncertainties and compensate for the control input of CDCRs, enabling high-stable accuracy and strong robustness trajectory tracking in complex underwater environments. Simulation results are presented to demonstrate the high accuracy and strong robustness of the ANN-FNITSMC. Finally, the high accuracy, high stability, and strong robustness of the proposed trajectory tracking strategy are verified through an underwater experiment platform.

In response to the trajectory tracking control problem of manipulators under measurement disturbances, a novel multi-input multi-output discrete integral terminal sliding mode control scheme is proposed. Initially, this scheme establishes a dynamic model of a two-joint manipulator based on the Lagrangian dynamics analysis method. Subsequently, a discrete integral terminal sliding mode control law based on the dynamic model of the two joints is designed, incorporating delayed estimation of unknown disturbances and discretization errors in the manipulator system. To enhance the trajectory tracking accuracy of the control scheme and suppress the impact of sliding mode chattering on the manipulator system, an adaptive switching term is introduced into the discrete integral terminal sliding mode control law. The paper derives an adaptive discrete integral terminal sliding mode control scheme and provides stability proof for the proposed approach. Simulation experiments are conducted to compare the proposed adaptive discrete integral terminal sliding mode control scheme with classical discrete sliding mode control schemes and discrete integral terminal sliding mode control schemes. The simulation results demonstrate that the designed adaptive discrete integral terminal sliding mode control scheme maintains trajectory tracking errors within 0.004 radians for each joint of the manipulator, with minimal changes in control torque for each joint. The absolute integral of the control torque variations is calculated at 5.85×103, which is lower than other control schemes, thereby validating the effectiveness and superiority of the proposed approach.

Sliding Mode Control (SMC) has gained significant attention due to its simplicity, robustness, and rapid response in ensuring system stability, particularly with the Lyapunov approach. Despite its advantages, SMC faces challenges such as chattering near equilibrium, sensitivity to parameter variations, and delayed convergence. To address these issues, advanced techniques like Terminal Sliding Mode Control (TSMC) and Integral Terminal Sliding Mode Control (ITSMC) have been proposed. TSMC ensures finite-time convergence while mitigating chattering, while ITSMC further handles singularities and disturbances. Additionally, Adaptive Switching Control (ASC) based on Particle Swarm Optimization (PSO) is applied to achieve faster convergence, suppress chattering, and enhance system robustness. The adaptive control law, utilizing a Lyapunov-based approach, is employed to estimate and compensate for external disturbances, further improving system performance under uncertainties. Gain tuning, essential for optimizing system performance and reducing tracking errors, is achieved using the efficient Teaching–Learning-Based Optimization (TLBO) algorithm. This study applies TSMC, ITSMC, and ASC-based PSO to an Anti-Lock Braking System (ABS), aiming to enhance robustness, stability, and finite-time convergence while reducing chattering. Stability is analyzed through the Lyapunov theory, ensuring rigorous validation. MATLAB simulations demonstrate the effectiveness of the proposed methods in improving ABS performance, offering a valuable contribution to robust control techniques for systems operating under dynamic and uncertain conditions.