Nonsingular Terminal Sliding Mode Surface Research Articles

Fault‐tolerant attitude tracking control with practical finite time convergence for unmanned aerial vehicles under actuation faults

AbstractThis paper presents an adaptive attitude finite time tracking control algorithm for quadrotor unmanned aerial vehicle (UAV) in presence of actuator faults, input saturation and external disturbance. The dynamic model of the quadrotor UAV is characterized with quaternion representation. Subsequently, using nonsingular terminal sliding mode surface, an adaptive fault‐tolerant finite‐time attitude control scheme is proposed. Using Lyapunov stability analysis, it is shown that the proposed method is able to achieve practical finite time attitude tracking convergence in that the attitude tracking error converges to a small residual set within finite time and all signals of the closed‐loop system remain bounded. The effectiveness of the proposed method is confirmed via numerical simulation.

Speed sensorless control of a BL-IM based on an adaptive nonsingular terminal sliding mode observer

ABSTRACT Aiming at the speed detection accuracy of the optical encoder in a bearingless induction motor (BL-IM) affected by external environment and other factors, a speed sensorless control strategy based on an adaptive nonsingular terminal sliding mode observer (ANTSMO) is proposed. Firstly, a second-order nonsingular terminal sliding mode surface is constructed based on the stator current error. According to the designed sliding mode control law, the stator current and its common coupling term with the rotor flux are observed. Secondly, in order to avoid the bias effect caused by the pure integrator, the model reference adaptive system (MRAS) identification structure is used to realise the speed closed-loop observation . The adaptive sliding mode gain is designed by the identified speed. The stability and convergence of the observation system are proved through the Lyapunov theorem and Popov superstability theory. Finally, simulation analysis and experimental verification of the proposed strategy are carried out on MATLAB/Simulink and the test prototype. The results show that the proposed strategy not only can effectively reduce the observation chattering, and the speed can be accurately estimated under no-load, sudden load and variable speed conditions, but also the BL-IM can achieve good suspension characteristic of the motor rotor.

Refined Disturbance Rejection-Based Composite Control of Flexible Spacecrafts for Tracking a Tumbling Non-Cooperative Target

When tracking a tumbling non-cooperative target, the position and attitude maneuver control with high-precision as well as fast-response performances is required for flexible spacecrafts. However, the unknown rigid-flexible coupling and model uncertainties will degrade the control performances significantly. Therefore, this paper proposes a refined disturbance rejection-based composite control method for spacecraft position and attitude tracking. First of all, the disturbances including the rigid-flexible coupling and model uncertainties are described by an exogenous model by fully using the partially known disturbance information (e.g., modal frequency and damping). Then, a novel exogenous model-based sliding mode disturbance observer (SMDO) is proposed to achieve the refined disturbance estimation. Next, by combining the SMDO in the feedforward loop and an adaptive terminal sliding mode control (ATSMC) in the feedback loop, a finite-time composite control law is proposed to ensure the fast disturbance rejection and position/attitude tracking simultaneously. In the composite controller, a novel nonsingular terminal sliding mode surface with arctangent function is proposed. Moreover, a time-varying boundary Lyapunov function (BLF) is designed to preassign the transient and steady-state performances of sliding mode surface. Finally, the effectiveness of proposed method is verified via numerical simulation.

A Novel Guidance Law for Intercepting a Highly Maneuvering Target

Given the resolution of the guidance for intercepting highly maneuvering targets, a novel finite-time convergent guidance law is proposed, which takes the following conditions into consideration, including the impact angle constraint, the guidance command input saturation constraint, and the autopilot second-order dynamic characteristics. Firstly, based on the nonsingular terminal sliding mode control theory, a finite-time convergent nonsingular terminal sliding mode surface is designed. On the back of the backstepping control method, the virtual control law appears. A nonlinear first-order filter is constructed so as to address the “differential expansion” problem in traditional backstepping control. By designing an adaptive auxiliary system, the guidance command input saturation problem is dealt with. The RBF neural network disturbance observer is used for estimating the unknown boundary external disturbances of the guidance system caused by the target acceleration. The parameters of the RBF neural network are adjusted online in real time, for the purpose of improving the estimation accuracy of the RBF neural network disturbance observer and accelerating its convergence characteristics. At the same time, an adaptive law is designed to compensate the estimation error of the RBF neural network disturbance observer. Then, the Lyapunov stability theory is used to prove the finite-time stability of the guidance law. Finally, numerical simulations verify the effectiveness and superiority of the proposed guidance law.

Fixed-time sliding mode output tracking control for second-order switched systems with power integrators

The issue of fixed-time sliding mode output tracking control is addressed for second-order switched systems, where the tracking reference signal is defined by a power-integrator exogenous system. A novel non-singular terminal sliding mode surface is constructed, in which a reference is introduced into the sliding mode surface. Subsequently, an explicit novel fixed-time output tracking control scheme is constructively developed to drive the tracking error into a small neighborhood of the origin in fixed-time. Some sufficient criteria are developed to guarantee that the switched systems track the reference signal in fixed-time. Finally, a numerical example and an application example of an electro-hydraulic system are provided to demonstrate the validity of the proposed method.

Adaptive finite time attitude tracking control of a rigid spacecraft considering input magnitude and rate saturations

This article investigates the attitude tracking control problem of a rigid spacecraft under the modeling inaccuracy, environmental disturbance, and input magnitude and rate saturations. A robust controller is proposed based on several nonlinear control methods, including the integral terminal sliding mode control, adaptive control, backstepping control, auxiliary system, and nonlinear observer methods. Within the control framework, a new integral terminal sliding mode surface (ITSMS) is first designed which integrates the fast nonsingular terminal sliding mode surface (FNTSMS) with a first-order filter to achieve the finite time stability without the input singularity problem. And adaptive laws are employed to compensate for the modeling inaccuracy and environmental disturbance with no prior knowledge. To satisfy the input magnitude and rate saturation constraints, a dynamic model in the form of a first-order filter is built up to restrict the dynamics of the actuators, which is then associated with the auxiliary system. Meanwhile, a nonlinear observer is used to avoid calculating the derivative of the expected virtual control signal. Semi-globally uniformly ultimate bounded stability is proved for the closed-loop system, and the tracking errors can converge to small regions around the expected equilibrium in finite time. Finally, numerical simulation results are presented to demonstrate the effectiveness of the proposed controller.

Nonsingular Terminal Sliding Mode Control of PMSM Based on Improved Exponential Reaching Law

When a permanent magnet synchronous motor runs at low speed, the inverter will output discontinuous current and generate torque ripple; when the motor is runs at high speed, a large amount of stator harmonic current generates, which affects its speed following ability and torque stability. To ensure the fast and smooth switching of a permanent magnet synchronous motor in the full speed domain, this paper proposes the nonsingular terminal sliding mode control of PMSM speed control based on the improved exponential reaching law. Firstly, the improved exponential reaching law is composed of the state variables and power terms of the sliding mode surface functions. The reaching law function is designed in sections to balance the fast dynamic response of the system and chattering control. Secondly, an improved exponential reaching law based on the sliding mode control strategy of the PMSM speed loop is proposed. By designing the initial value of the integral term in the nonsingular terminal sliding mode surface function, the initial state of the system is located on the sliding mode surface. The integral sliding mode surface is used to reduce the system steady-state error, while the proposed sliding mode reaching law is used to increase the arrival speed and suppress system chattering, ultimately affecting modeling error problems, complex working conditions, and uncertainty factors. This paper proposes a sliding mode observer based on an improved exponential reaching law to compensate for the disturbances. Lyapunov stability theory can prove that this system can make the speed tracking error converge to zero in finite time. Hardware-in-the-loop experiments were used to validate the effectiveness of the proposed method.

Terminal sliding mode‐based tracking control with error transformation for underwater vehicles

AbstractOcean currents and waves can cause the initial position of an underwater vehicle to deviate from the initial state of the desired trajectory. For such cases, this paper investigates the finite‐time tracking control problem for a vehicle in the presence of large initial tracking errors and external disturbances. A continuous finite‐time tracking control scheme is developed for this scenario based on an improved nonsingular terminal sliding mode surface modified by a piecewise function. Compared to the alternative approaches, a method based on error transformation is added to the sliding mode surface, resulting in improved tracking accuracy in the steady state. Then, to reduce the effect of large initial tracking error on the control input signals, an exponential decay function about the initial location of the vehicle is developed to obtain the control law by combining it with a strictly generalized saturation function. In contrast to alternative approaches, a nonlinear structure is used to counteract the approximation error of the neural network used in the modeling of the dynamics. Moreover, it is shown that the tracking error converges to a small neighborhood of zero in a fixed time. Finally, the new control scheme's effectiveness is verified by simulation studies on an underwater vehicle model and the results compared to other existing control designs.

Dynamic modeling and faster finite-time attitude stabilization of receiver aircraft for aerial refueling

This paper studies the faster attitude stabilization problem of receiver aircraft during the refueling phase. Dynamic models of receiver aircraft subject to practical uncertainties and disturbances are established, where the uncertain inertia, the wind disturbance, the time-varying inertia, and the shift of the center of mass are explicitly considered. A faster finite-time stable system is preliminarily proposed and proved rigorously in comparison with the conventional fast finite-time stable system. Then, a nonsingular terminal sliding mode surface is synthesized to ensure a fast convergence rate. An adaptive faster finite-time controller is finally developed with the aircraft attitude stabilized into a small neighborhood of the origin with a faster convergence rate. Simulations are conducted to validate that the proposed solution can accomplish attitude stabilization maneuvers in a faster way.

Fixed-time position coordinated tracking control for spacecraft formation flying with collision avoidance

In this paper, the fixed-time stability of spacecraft formation reconfiguration (position tracking) is studied. Firstly, a novel nonsingular terminal sliding mode surface is designed and based on which a fixed-time coordinated controller is designed to keep the closed-loop system states have a finite settling time bounded by some predefined constants. Secondly, another nonsingular terminal sliding mode surface is designed by combining the artificial potential function and the aforementioned sliding surface, which meets the mutual distance constraint during transition process among spacecraft when it is bounded. Then another coordinated controller with fixed-time observer considering mutual distance constraint is presented, which guarantees the closed-loop system states stable also in bounded settling time. Finally, simulation results are shown to validate the correctness of the proposed theorems. It is worth mentioning that the control schemes also work even though there is a properly limit on the control input.

Asymmetrical Barrier Function-Based Adaptive Vibration Control for Nonlinear Flexible Cantilever Beam With Obstacle Restriction

In this paper, a novel adaptive asymmetrical barrier function-based vibration control law is proposed for the nonlinear flexible cantilever beam system with obstacle restriction, model uncertainties, and distributed disturbances. Firstly, by employing the Hamilton’s principle and the Galerkin projection method, the dynamic of the nonlinear flexible cantilever beam with the piezoelectric actuator is constructed in partial differential equations and simplified to nonlinear ordinary differential equations for the control law design. Then, by introducing the fast nonsingular terminal sliding mode surface, a novel asymmetrical barrier function based sliding mode control law is proposed, in which by means of a novel asymmetrical barrier Lyapunov function is used to guarantee the finite time stability with the obstacle restriction. Further, to deal with the model uncertainties, an adaptive updating law is incorporated with the fast nonsingular terminal sliding mode control law based on asymmetrical barrier function, stability proof shows that the proposed control law can ensure the distributed disturbance rejection and the model uncertainties compensation simultaneously. Finally, the effectiveness of the proposed control laws is demonstrated by the numerical simulations.

Fixed-time attitude coordination control for spacecraft with external disturbance

This paper studies the fixed-time stability of attitude coordination control for spacecraft formation flying (SFF) in the presence of some external disturbance. Firstly, to ensure that the states converge to the origin within a fixed time, a novel nonsingular terminal sliding mode surface (NTSMS) is designed. The convergence time is bounded by some predefined constants. Secondly, an attitude synchronization controller is proposed based on the designed NTSMS, which guarantees the fixed-time stability of SFF under an undirected communication topology. Finally, a fixed-time adaptive control law is designed for cases in which the boundary of the external disturbance is unknown. The fixed-time stability is guaranteed by a revised form of the proposed NTSMS. Simulation results show that the proposed controllers provide fixed-time stability and outperform existing finite-time controllers.

Adaptive funnel fast nonsingular terminal sliding mode control for robotic manipulators with dynamic uncertainties

In this paper, a novel adaptive funnel fast nonsingular terminal sliding mode control for robotic manipulators with dynamic uncertainties is proposed. A modified funnel variable is utilized to transform the tracking error fall within funnel boundary, which improves the transient and steady-state tracking performance of robotic manipulators. Based on the transformed error, a novel funnel fast nonsingular terminal sliding mode surface is developed and a sliding mode control law is designed to stabilize the closed-loop system and achieve high tracking precision. An adaptive update law combined with the sliding mode surface is designed to deal with uncertainties and external disturbances where their upper bounds are unknown in practical cases. The stability and finite time convergence of the closed-loop system are proved by Lyapunov stability theorem. Simulation results and discussions are presented to demonstrate the effectiveness and high-precision tracking control for robotic manipulators.

Trajectory tracking with quaternion-based attitude representation for autonomous underwater vehicle based on terminal sliding mode control

This paper addresses trajectory tracking control problem for autonomous underwater vehicles (AUVs) using quaternion-based attitude representation. A quaternion based adaptive non-singular terminal sliding mode control scheme is proposed for an AUV subject to ocean current and modelling uncertainty. At first, kinematic equations of the translational and rotational motions are described by unit quaternions. And then, a class of modified non-singular terminal sliding mode surface is developed by smoothly switching into a non-singular sliding mode surface formed by sinusoidal functions when the tracking error reaches a small range of the origin. The finite-time convergences of both the position tracking error and quaternion error are proved based on Lyapunov theory. Finally, the proposed control scheme is applied on a typical fully-actuated AUV to perform simulations. And the simulation results illustrate the effectiveness of the proposed control scheme in comparison with another terminal sliding mode control algorithm.

A Novel Non-Singular Terminal Sliding Mode Trajectory Tracking Control for Robotic Manipulators

This brief investigates the trajectory tracking problem of $n$ -link robotic manipulators with internal uncertainties and external disturbances. At first, a novel non-singular terminal sliding mode surface is proposed which contains arctan function (ATNTSM). Then, a robust ATNTSM control law is designed to ensure that the system states globally converges to origin in finite time. Moreover, the sign function is replaced by saturation function in the control law, thus the actual control law becomes continuous and the chattering phenomenon can be completely eliminated. In the end, a two-link robotic manipulators as an example is provided to illustrate the effectiveness of the proposed scheme.

Adaptive wave neural network nonsingular terminal sliding mode control for an underwater manipulator with force estimation

This paper proposes an adaptive wave neural network nonsingular terminal sliding mode control (AWNN-NTSMC) strategy with force estimation, which is exploited to address the path tracking control problem of the underwater manipulator under lumped disturbances. The proposed control scheme contains three parts: a nonsingular terminal sliding mode surface (NTSMS) part, an AWNN part, and a force estimation part. The NTSMS is designed to make the system states achieve fast convergence in the sliding mode phase. The AWNN theory is utilized to approximate the lumped disturbances via online adjustment of the network parameters. The force estimation method is applied in compensating the effect of external force on the control system. Besides, a saturated function instead of the signum function is used aiming to the chattering suppression. Asymptotic stability of the closed-loop system is guaranteed by the Lyapunov stability. Finally, by using a six degree of freedom (DOF) underwater manipulator, comparative simulation results validate the better tracking performance and stronger robustness against disturbances of our proposed scheme.

Prescribed performance adaptive finite-time control for uncertain horizontal platform systems

This paper presents a new approach to the design of prescribed performance adaptive control for uncertain horizontal platform systems with the finite-time convergence. Following an appropriate performance function and error transformation, a new adaptive control law is proposed by using a novel integral non-singular terminal sliding mode surface. The proposed approach simultaneously guarantees that (i) the transient responses of the closed-loop system possess some advanced properties such as the existence of the prespecified lower bound of the convergence rate and of the pre-established upper bound of the maximum overshoot; and (ii) the finite-time convergence of the state trajectories/tracking errors to zero. The global stability and finite-time convergence are strictly analyzed. The proposed method is clarified and verified through two numerical simulation examples.

Non-singular terminal sliding mode control for redundantly actuated parallel mechanism

In this article, the trajectory tracking control is developed by implementing a non-singular terminal sliding mode control for the redundantly actuated parallel mechanism system. The proposed control scheme could guarantee that the tracking errors converge to zero asymptotically. The problem of singularity with regard to conventional terminal sliding mode control scheme can be eliminated with the presented novel non-singular terminal sliding mode surface as well. The corresponding stability of the proposed control scheme has also been proved theoretically in terms of Lyapunov method. In addition, simulations and experiments are conducted for trajectory tracking to validate the effectiveness of the proposed scheme. The illustrative results demonstrate that the proposed scheme is available to solve the uncertainties and external disturbances with self-tuning in real time. Furthermore, the prominent characteristics of the presented control scheme are quick convergence, high accuracy, and high robustness, which can achieve excellent tracking performance as compared with computed torque control scheme and conventional sliding mode control scheme.

Time-Varying Second-Order Sliding Mode Control for Systems Subject to External Disturbance

In this article, the design problem of a class of novel second-order sliding mode controller for systems subject to external disturbance is investigated, where the sliding variable is affected by a time-varying regulation. On the one hand, for the unmatched disturbance bounded by positive functions, a second-order sliding mode controller is proposed to prove the finite-time stability of aforementioned system through the backstepping-like method and virtual control strategy. On the other hand, for the non-vanishing bounded disturbance, a non-singular terminal sliding mode surface containing disturbance observations is designed via a finite-time disturbance observation method and the finite-time stability of the system controlled output is realized. The claimed performances of the proposed methods are validated by two simulation examples.

Fractional-order adaptive controller for chaotic synchronization and application to a dual-channel secure communication system

A novel fractional-order adaptive non-singular terminal sliding mode control (FONTSMC) method is investigated for the synchronization of two nonlinear fractional-order chaotic systems in the presence of external disturbance. The proposed controller consists of a fractional-order non-singular terminal sliding mode surface and an adaptive gain adjusted with sliding surface. Based on Lyapunov stability theory and stability theorem for fractional-order dynamic systems, the controlled system’s stable synchronization is guaranteed. A dual-channel secure communication system is presented to transmit useful signals based on the proposed synchronization controller. Finally, numerical simulations and comparison with fractional-order PID controller, fractional-order PD sliding mode controller and adaptive terminal sliding mode controller are given to demonstrate the effectiveness and the robustness of the proposed FONTSMC control. The application of the proposed synchronization method is studied in the dual-channel secure communication.