Adaptive fixed‐time sliding‐mode trajectory following control of nonholonomic AMRs with adaptive sliding‐mode observers

This paper discusses the attitude cooperative control of multiple unmanned aerial vehicle systems (MUAVs) with unknown dynamics and external disturbances. Distributed fast nonsingular terminal sliding mode control (FNTSMC) is used with quaternion-description dynamical systems. The dynamics and external disturbances are changed into lumped disturbances by formula transformation. A robust nonlinear disturbance observer is proposed to estimate the lumped disturbances in finite time. Then, combining the fast terminal sliding mode control, distributed FNTSMC controllers are designed under the directed topology. Based on the Lyapunov stability theory and graph theory, convergence stability of the nonlinear systems is strictly proved, and the tracking errors between the leader and the followers approach to a small residual set. Finally, the simulation example is presented to illustrate the effectiveness and advantage of the proposed controllers.

ABSTRACTPiezoelectric actuators (PEAs) are the key devices in micro/nano positioning system. However, the PEA performance is significantly degraded by the inherent non-linear behaviour. This behaviour is a consequence of the hysteresis properties contained within PEAs. Therefore, in micro/nano positioning applications, a robust control system has to be adopted for such actuators. This paper proposes a systematic control method that utilises a fast non-singular terminal sliding mode (FNTSM) based on online perturbation estimation technique for PEAs. Unlike other sliding mode methods, the FNTSM control method is characterised by chatter free. Besides, a zero error convergence can be guaranteed in finite time in the presence of disturbance and system uncertainties (i.e., hysteresis and gain changes). The design of the FNTSM control based on perturbation estimation (FNTSMPE) is presented. A model-free robust exact differentiator is used to estimate the states of the feedback system from merely measurable position signal. Theoretical analysis and the experimental results of FNTSMPE control reveal that high-precision and robust performance is achieved in comparison with ordinary FNTSM control.

In this paper, for the position control problem of permanent magnet linear motors, a fast nonsingular terminal sliding mode control (FNTSMC) method based on the finite-time disturbance observer (FTDO) is proposed. By employing a fast nonsingular terminal sliding surface, the FNTSMC is designed. Besides, a FTDO is applied to estimate the disturbance and the estimation is served as compensation for the controller. A rigorous analysis based on the Lyapunov stability theory is provided to prove that the proposed control method can achieve faster dynamic response characteristic and higher steady accuracy than the linear sliding mode control method and the PID control method. Numerical simulation results are explored to illustrate the superiority of the proposed approach.

Servomechanisms and motion stages often encounter many mechanical transmission problems such as friction, backlash, and structural resonance, as well as other factors such as system nonlinearity, servo lags, and unknown disturbances. In contour following applications, these problems are the main causes of deterioration in contour following accuracy. As a result, the issue of dealing with the above problems so as to reduce tracking error and contour error is crucial. The Dynamic Fast Nonsingular Terminal Sliding Mode Control (DFNTSMC) scheme proposed in this paper combines the advantages of Fast Nonsingular Terminal Sliding Mode Control (FNTSMC) and Dynamic PID Sliding Mode Control (DSMC) while avoiding their drawbacks. The proposed DFNTSMC has attractive features such as improvement of contour following accuracy, chattering effect suppression, enhancement of robustness, and finite time convergence. The convergence of the proposed DFNTSMC is proved based on Barbalat’s lemma. Several contour following experiments are performed to assess the performance of the proposed DFNTSMC. Experimental results suggest that the proposed DFNTSMC outperforms both FNTSMC and DSMC, two control schemes also tested in the contour following experiment.

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 new control method for the omnidirectional mobile robot (OMR) system with unknown dynamics and disturbances. An unknown system dynamics estimator (USDE) is developed by introducing low-pass filter operations to estimate the unknown dynamics and external disturbances, and only one parameter of the USDE needs to be tuned. Moreover, a new fast nonsingular terminal sliding mode control (FNTSMC) scheme is developed to overcome the singularity and slow convergence rate of the terminal sliding mode control (TSMC) method. Finally, we combine the proposed USDE and FNTSMC schemes to design a feedback controller to guarantee tracking control accuracy of the omnidirectional mobile robot system. In addition, stability analysis of the proposed USED and FNTSMC methods is presented via the Lyapunov theory, and the performance of the proposed control scheme is verified by the simulation.

This paper designs an improved fast nonsingular terminal sliding mode control (FNTSMC) method for permanent magnet linear motors to track the periodic control tasks, which uses an iterative learning controller to learn periodic information and improve the performance. By designing a non-singular terminal sliding surface and using Lyapunov stability theory, the FNTSMC is designed. Afterwards, with the help of the operator stability theory, the asymptotic convergence of the paper algorithm and the improvement of the tracking ability were strictly proved. Lastly, experiments on an actual linear motor setup illustrated the effectiveness and superior performance of the paper method.

Extensive research has focused on enhancing the efficiency and stability of robotic arms. Sliding mode control (SMC) is commonly used in industrial robots due to its robustness and simplicity. However, SMC approaches have challenges such as chattering and slow convergence rates which can compromise tracking accuracy. To address these issues, this paper proposes a novel Super-Twisting Fast Non-singular Terminal Sliding Mode Control (ST-FNTSMC) strategy for a 3-DOF arm robot. The proposed approach significantly improves trajectory tracking accuracy, robustness, and convergence time and eliminates chattering. The proposed controller was tested in the presence of model mismatches and external disturbances. The super-twisting methodology avoided chattering effects and increased robustness against perturbations. Two Lyapunov functions ensure closed system stability and finite-time convergence. The designed ST-FNTSMC controller is implemented in real-time using a Smart Man Robot manipulator. Its performance is compared to other sliding mode controllers, such as conventional PID Sliding Mode Control (PID-SMC), Non-singular Terminal Sliding Mode Control (NTSMC), and Fast Non-singular Terminal Sliding Mode Control (FNTSMC). Experimental results demonstrate the superior performance of the proposed controller, highlighting its effectiveness in improving the efficiency and stability of industrial robots.

This paper presents novel Takagi-Sugeno (T-S) fuzzy model-based robust finite time control methods for a class of uncertain nonlinear systems. First, the nonlinear system is approximated by a suitable T-S fuzzy model in which most of the parameters can be computed offline. Then, a T-S fuzzy model-based nonsingular terminal sliding mode control (TS-NTSMC) method is designed based on a proposed nonsingular terminal sliding mode (NTSM) surface. This method not only alleviates the online computational burden, but also preserves the advantages of fast and finite time convergence, high tracking precision, and robustness to uncertainties and disturbances. However, the discontinuous function [Formula: see text] causes the chattering phenomenon, which is unavoidable. In order to attenuate the chattering, maintain the key properties of the TS-NTSMC method and achieve higher control performance, a novel T-S fuzzy model-based super-twisting higher order nonsingular terminal sliding mode control (TS-STHONTSMC) method is proposed. The global finite time stability of the resulting closed-loop systems is analytically proven herein. Two numerical simulations are presented to illustrate the effectiveness and applicability of the proposed control methods and to validate the theoretical results.

For the four degrees of freedom (4‐DOF) trajectory tracking control problem of underwater vehicles in the presence of parametric uncertainties and external disturbances, a novel multivariable output feedback adaptive nonsingular terminal sliding mode control (ANTSMC) approach is proposed based on the equivalent output injection adaptive sliding mode observer (ASMO) and ANTSMC method. The ASMO is applied to reconstruct the full states in finite time and the ANTSMC method is designed to stabilize the trajectory tracking error to a small field in finite time. The proposed output feedback ANTSMC approach, using the adaptive technology, does not require the bound information of parametric uncertainties or external disturbances which successfully achieves the decrease of undesired chattering effectively. Corresponding stability analysis is presented. Comparative numerical simulation results are presented to validate the effectiveness of the proposed approach.

A robust motion control system is essential for the linear motor (LM)-based direct drive to provide high speed and high-precision performance. This paper studies a systematic control design method using fast nonsingular terminal sliding mode (FNTSM) for an LM positioner. Compared with the conventional nonsingular terminal sliding mode control, the FNTSM control can guarantee a faster convergence rate of the tracking error in the presence of system uncertainties including payload variations, friction, external disturbances, and measurement noises. Moreover, its control input is inherently continuous, which accordingly avoids the undesired control chattering problem. We further discuss the selection criteria of the controller parameters for the LM to deal with the system dynamic constraints and performance tradeoffs. Finally, we present a robust model-free velocity estimator based on the only available position measurements with quantization noises such that the estimated velocity can be used for feedback signal to the FNTSM controller. Experimental results demonstrate the practical implementation of the FNTSM controller and verify its robustness of more accurate tracking and faster disturbance rejection compared with a conventional NTSM controller and a linear H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller.

This paper presents an adaptive fast nonsingular terminal sliding mode control base on a neural network based approximation technique to control the position of a piezo positioning stage (PSS). The proposed terminal sliding mode control can provide faster convergence and higher precision control while maintain its robustness to uncertainties. In the proposed control scheme, the combination of the fast-nonsingular terminal sliding mode control and neural network, which can precisely estimate the uncertainties in dynamic of the PSS system by employing an online tuning scheme, is a promising control approach for actuator systems. In addition, the robust control term is adopted to compensate the modeling error and ensure the robustness corresponding to a bounded disturbance. Stability of the closed loop system is analyzed and proved by using special Lyapunov functions. Experiment results strongly confirm the effectiveness of the proposed control method.

Oftentimes, due to mechanical wear and ambient environment variations, friction-related parameters may vary with respect to the position of the iron-core linear servomotor. In addition, cogging force is also a function of the iron-core linear servomotor's position. In order to cope with the adverse effects caused by friction and cogging force, this article proposes a disturbance compensation approach based on nonuniform rational B-spline (NURBS), in which the parameters of the proposed NURBS-based disturbance compensation approach are represented as a function of the linear servomotor's position. The parameters of the proposed NURBS-based friction model are updated using online adaptive laws designed based on the Lyapunov stability theory. Moreover, in order to attain excellent tracking performance for a motion stage actuated by iron-core linear servomotors, this article combines the proposed NURBS-based friction model and cogging force model with fast nonsingular terminal sliding mode control (FNTSMC) to develop adaptive nonlinear sliding mode control (ADNSMC). The proposed ADNSMC inherits the advantages of both FNTSMC and the proposed NURBS-based disturbance compensation approach. Experimental results indicate that the proposed ADNSMC exhibits satisfactory performance on tracking control and disturbance compensation.

As computer computing capabilities increase, optimization algorithms are becoming more useful for solving engineering problems. Up to now, several metaheuristic algorithms have been exploited in control engineering. However, this effort remains weak in addressing the autonomous ground vehicles (AGVs) trajectory tracking problem. This research presents a novel optimal approach merging the robust non-singular fast terminal sliding-mode control method (NFTSMC) and the neural network optimization algorithm (NNA) for automatic lane changing. First, a reference double lane-change path (DLC) is designed, and the robust non-singular fast terminal sliding-mode steering controller is developed, according to Lyapunov stability theory, to suppress the lateral deviation and ensure the yaw stability. Then, the control strategy is optimized by the NNA algorithm to adjust the steering controller optimally while avoiding local optimums. A comparison, under the same conditions, with the particle swarm optimization algorithm (PSO) revealed the superiority of the control law resulting from the NNA-based optimization. Furthermore, the proposed approach shows its excellent tracking performance versus the integrated backstepping sliding-mode controller (IBSMC) and the adaptive sliding-mode control (ASMC) under severe conditions typical of real-world lane changes.

Active adaptive continuous nonsingular terminal sliding mode controller for hypersonic vehicle