Nonsingular Fast Terminal Sliding Mode Research Articles

Finite-Time Control of a Linear Motor Positioner Using Adaptive Recursive Terminal Sliding Mode

Payload variations, friction, and external disturbances deteriorate the control performance of linear motor (LM) positioners. To provide high-speed and high-precision performance for the LM, an adaptive recursive terminal sliding-mode (ARTSM) controller is proposed in this article. For the controller, a fast nonsingular terminal sliding function and a recursive integral terminal sliding function are developed in a recursive structure such that the sliding surfaces are arrived successively and ultimately the tracking error can converge to zero in a finite time. Furthermore, by setting an appropriate initial value for the integral element of the ARTSM controller, the control system is enforced to start on the sliding surface at the initial time such that the reaching time is reduced. Stability analysis is presented to prove the finite-time convergence and zero tracking error of the closed-loop system under the proposed ARTSM controller. Experimental results also demonstrate the effectiveness of the controller in terms of significantly reduced tracking errors and faster disturbance rejection in comparison with a recently reported fast nonsingular terminal sliding-mode (FNTSM) controller for the LM positioner.

Accurate Trajectory Tracking of Disturbed Surface Vehicles: A Finite-Time Control Approach

In this paper, accurate trajectory tracking problem of a surface vehicle disturbed by complex marine environments is solved by creating a finite-time control (FTC) scheme whereby the nonsingular fast terminal sliding mode (NFTSM) and finite-time disturbance observer (FDO) techniques are deployed. Salient features are as follows. By devising an FDO, complex disturbances arising from marine environments can be exactly identified within a short time, in conjunction with the defined NFTSM manifold, and thereby contributing to exact trajectory tracking. Finite-time disturbance observation is completely decoupled from the nominal FTC scheme, and achieves stronger disturbance rejection and faster transient response, simultaneously. Both disturbance observation and trajectory tracking errors can exactly reach to zero in a finite time. Simulation results and comparisons are comprehensively conducted on CyberShip II and demonstrate remarkable superiority of the FTC scheme.

ANFTS Mode Control for an Electronically Controlled Hydraulic Power Steering System on a Permanent Magnet Slip Clutch

There are various uncertain factors such as parameter perturbation and external disturbance during the steering process of a permanent magnet slip clutch electronically controlled hydraulic power steering system (P-ECHPS) of medium and heavy duty vehicles, which is an electronically controlled hydraulic power steering system based on a permanent magnetic slip clutch (PMSC). In order to avoid the immutable single assistance characteristic of a hydraulic power steering system, a PMSC speed-controlled model and P-ECHPS of each subsystem model were studied. Combined with non-singular terminal sliding mode and fast terminal sliding mode, an Adaptive Non-singular Fast Terminal Sliding (ANFTS) mode control strategy was proposed to control precisely the rotor speed of the PMSC in P-ECHPS, thus achieving better power control for the entire P-ECHPS system. The simulation results show that adaptive nonsingular fast terminal sliding mode control enables PMSC output speed to track the target speed. Compared with the non-singular terminal sliding mode control and the ordinary sliding mode control, the convergence speed has been improved by 66.7% and 84.2%, respectively. The rapid control prototype test of PMSC based on dSPACE (dSPACE is a development and verification platform based on MATLAB/Simulink software.) was carried out. The validity of the adaptive NFTSM algorithm and the correctness of the offline simulation results are validated. The adaptive NFTSM algorithm have better robustness and can realize variable assist characteristics and save energy.

Design and Implementation of Finite Time Nonsingular Fast Terminal Sliding Mode Control for a Novel High Step-Up DC-DC Converter

In this paper, a new, high step-up quadratic boost converter with high conversion efficiency is discussed. A storage capacitor and resonant inductor are connected in series with a clamp capacitor through a diode. These compose a voltage multiplier cell, which is applied on the switch of the quadratic boost converter. The clamp capacitor can protect the switch from a voltage spike and absorb energy when the switch turns off; then, the storage capacitor and resonant inductor are charged by the energy stored in the clamped capacitor to increase the voltage transfer gain. In addition, the voltage multiplier cell can also reduce the voltage stresses of power devices. Then, a 16 V input, 200 V output prototype with 80 W nominal power is built up and tested. Furthermore, a finite time fast terminal sliding mode (NFTSM) control is proposed, with constant frequency for the voltageFundamental Building B213:tracking control of this converter. The new NFTSM is obtained by introducing an adjustable nonlinear term into fast terminal sliding mode (FTSM) control, and a singularity problem is avoided. The experiment illustrates that the maximum efficiency of the proposed converter achieves 95% at D = 0.25 , V o = 150 V. The voltage stress is reduced to half of the corresponding component of the basic boost converter at the same voltage level. Moreover, the proposed NFTSM controller can track the reference signal, and provide a short settling time of about 48 ms with no overshoot, and the system response exhibits strong robustness against 11.7% input voltage disturbance and 30% load variation.

Output-feedback super-twisting control for line-of-sight angles tracking of non-cooperative target spacecraft

Without the line-of-sight (LOS) angles rate information, this paper investigates the LOS angles tracking problem of non-cooperative target in chaser’s body frame with the external disturbance force and torque via chaser’s control torque. By integrating with the attitude dynamics of the chaser, a novel coupled LOS-based relative motion model is firstly established, which reveals the redundancy relationship between the LOS angles motion with two Degree-of-Freedom (DOF) and three dimensional control torque. More specially, the LOS angles tracking control problem is formulated as an output-feedback control problem of an uncertain nonlinear system with the actuator redundancy. As a stepping-stone, a fourth order high order sliding mode observer (HOSMO) is proposed to estimate the system state and uncertain terms. A combination of modified super twisting algorithm (STA) with nonsingular fast terminal sliding mode (NFTSM) and control allocation is proposed, the main novelty of modified STA is that the NFTSM is introduced to replace the linear sliding mode (LSM), and the original STA cannot be applied directly, a modified STA is proposed, which can guarantee the fast finite-time convergence. Finally, simulations are conducted to show fine performance of the proposed control scheme.

Adaptive Second-Order Fast Nonsingular Terminal Sliding Mode Tracking Control for Fully Actuated Autonomous Underwater Vehicles

This paper focuses on the design of an adaptive second-order fast nonsingular terminal sliding mode control (ASOFNTSMC) scheme for the trajectory tracking of fully actuated autonomous underwater vehicles (AUVs) in the presence of dynamic uncertainties and time-varying external disturbances. First, a second-order fast nonsingular terminal sliding mode (SOFNTSM) manifold is designed to achieve a faster convergence rate than the existing second-order nonsingular terminal sliding mode (SONTSM) manifold. Then, by using this SOFNTSM manifold, an ASOFNTSMC scheme is developed for the fully actuated AUVs to track the desired trajectory. The designed SOFNTSM manifold yields local exponential convergence of the position and attitude tracking errors to zero, and the developed ASOFNTSMC scheme ensures that the error trajectories always move toward the SOFNTSM manifold and once they hit the manifold, remain on it in the presence of dynamic uncertainties and time-varying external disturbances. By deriving the expression of the bounding function of the system uncertainty and using adaptive technique to estimate the unknown parameters of the system uncertainty bounds, the ASOFNTSMC scheme does not require the prior knowledge of the upper bound of the system uncertainty. Meanwhile, through involving the discontinuous sign function into the time derivative of the control input, the ASOFNTSMC scheme eliminates the chattering without reducing the tracking precision. Compared with the existing adaptive SONTSM control (ASONTSMC) scheme, the proposed ASOFNTSMC scheme offers a faster convergence rate for the trajectory tracking control of fully actuated AUVs. Two comparative simulation cases performed respectively on two fully actuated AUVs demonstrate the superiority of the ASOFNTSMC scheme over the ASONTSMC scheme.

Antisaturation Attitude and Orbit-Coupled Control for Spacecraft Final Safe Approach Based on Fast Nonsingular Terminal Sliding Mode

AbstractThe problem of spacecraft final approach subject to input saturation and a safe constraint is studied in this paper. First, an attitude and orbit-coupling model with input saturation was es...

Disturbance Observer-Based Terminal Sliding Mode Control of a 5-DOF Upper-Limb Exoskeleton Robot

In this paper, a finite-time control strategy composed of disturbance observer and sliding mode controller is investigated for five-degree of freedom (5-DOF) upper-limb exoskeleton subject to system uncertainties and external disturbances. First, a new finite-time disturbance observer (FTDO) is constructed to handle unknown disturbances and modeling uncertainties. Second, a nonsingular fast terminal sliding mode (TSM) approach is presented to follow the desired joint angles. By combining the novel FTDO and the nonsingular fast TSM technology, the exoskeleton angle tracking errors can be forced to zero within a finite time. Furthermore, the stability of the exoskeleton system is illustrated via Lyapunov. Finally, the tracking performance of the proposed control scheme is verified by simulations.

Finite Time Fault Tolerant Control Design for UAV Attitude Control Systems with Actuator Fault and Actuator Saturation

This paper presents a novel fault tolerant control (FTC) strategy for an unmanned aerial vehicle (UAV) subject to multiple constraints of actuator fault, actuator saturation and external disturbance. First, a radial basis function neural network (RBFNN)-based fault estimation observer is developed to obtain the accurate value of actuator fault. Second, an attitude stabilization FTC approach is established with combining the non-singular fast terminal sliding mode (NFTSM) technology, which could tolerate the estimated loss of effectiveness fault. Third, it is discussed asymptotically stability and stabilization of UAV attitude systems in finite time by Lyapunov method and the improved FTC scheme. Finally, the simulation is carried out to verify the fault tolerant capability of the designed algorithm.

Adaptive NFTSM-Based Fault Tolerant Control for a Class of Nonlinear System With Actuator Fault and Saturation

In this paper, an adaptive fault-tolerant control (FTC) strategy is proposed for a class of nonlinear systems in the presence of actuator fault, actuator saturation, and unknown external disturbance. The mathematical model of a second-order nonlinear system with actuator fault is first given, and a fault estimation observer is designed to estimate the occurred time-varying actuator fault. On this basis, the adaptive FTC strategy is proposed using both nonsingular fast terminal sliding mode (NFTSM) and radial basis function neural networks (RBFNNs) techniques to compensate for the negative effects caused by time-varying actuator fault and external disturbance. Another adaptive FTC scheme is further presented under actuator saturation case, and the Lyapunov stability analysis demonstrates that the designed FTC approach could guarantee that the trajectory of sliding mode dynamics could converge to a small neighborhood of the origin within a finite time. Compared with some existing results, the FTC approach proposed in this paper has better fault acceptability. Finally, the proposed adaptive FTC approach is applied to the attitude control of rigid spacecraft, and the simulation results illustrate the advantages of the designed control scheme.

Nonsingular Fast Terminal Sliding Mode Control with Extended State Observer and Disturbance Compensation for Position Tracking of Electric Cylinder

The position tracking problem of the electric cylinder, which has internal perturbation, external disturbance, and measurement noise of the output, is studied in this paper. A control method is proposed for achieving high tracking accuracy and tracking velocity for the wheel-legged robot application. Nonsingular fast terminal sliding mode (NFTSM) control is investigated to ensure that the system output can track the reference input in finite time. Besides, extended state observer (ESO) of the active disturbance rejection control (ADRC) is used to estimate the system lumped perturbation and compensated it in the controller based on the terminal sliding mode. This greatly reduces the chattering of the system caused by the gain of the sliding mode switch. Furthermore, tracking differentiator is designed to attenuate the output measurement noise. Simulation and experimental results illustrate that the NFTSM with ESO and TD algorithm, which is presented in this paper, has obvious superiority in the tracking precision and the antijam ability.

Tracking differentiator and extended state observer-based nonsingular fast terminal sliding mode attitude control for a quadrotor

The attitude control problem is addressed for a quadrotor system subject to the modeling uncertainties and unknown disturbances. A novel attitude control scheme is proposed based on nonsingular fast terminal sliding mode (NFTSM) technique. First, the tracking differentiator (TD) is designed to obtain the smooth tracking signal and its derivative. Then, the extended state observer (ESO) is constructed to provide the estimate of the modeling uncertainties and unknown disturbances. With the designed TD and ESO, a novel NFTSM controller is developed such that tracking error converges to zero in finite time. The transient-state and the steady-state performances are both achieved with the new controller. Finally, the simulation and real experiment results verify the effectiveness and superiority of the proposed control method.

An Enhanced Robust Fault Tolerant Control Based on an Adaptive Fuzzy PID-Nonsingular Fast Terminal Sliding Mode Control for Uncertain Nonlinear Systems

This paper develops an enhanced robust fault tolerant control using a novel adaptive fuzzy proportional-integral-derivative-based nonsingular fast terminal sliding mode (AF-PID-NFTSM) control for a class of second-order uncertain nonlinear systems. In this approach, a new type of sliding surface, called proportional-integral-derivative (PID)-nonsingular fast terminal sliding mode (NFTSM) (PID-NFTSM) which combines the benefits of the PID and NFTSM sliding surfaces, is proposed to enhance the robustness and reduce the steady-state error, whilst preserving the great property of the conventional NFTSM controller. A fuzzy approximator is designed to approximate the uncertain system dynamics and an adaptive law is developed to estimate the bound of the approximation error so that the proposed robust controller does not require a need of the prior knowledge of the bound of the uncertainties and faults and the exact system dynamics. The proposed approach is then applied for attitude control of a spacecraft. The simulation results verify the superior performance of the proposed approaches over other existing advanced robust fault tolerant controllers.

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

In this paper, robust and adaptive nonsingular fast terminal sliding-mode (NFTSM) control schemes for the trajectory tracking problem are proposed with known or unknown upper bound of the system uncertainty and external disturbances. The developed controllers take the advantage of the NFTSM theory to ensure fast convergence rate, singularity avoidance, and robustness against uncertainties and external disturbances. First, a robust NFTSM controller is proposed which guarantees that sliding surface and equilibrium point can be reached in a short finite-time from any initial state. Then, in order to cope with the unknown upper bound of the system uncertainty which may be occurring in practical applications, a new adaptive NFTSM algorithm is developed. One feature of the proposed control law is their adaptation techniques where the prior knowledge of parameters uncertainty and disturbances is not needed. However, the adaptive tuning law can estimate the upper bound of these uncertainties using only position and velocity measurements. Moreover, the proposed controller eliminates the chattering effect without losing the robustness property and the precision. Stability analysis is performed using the Lyapunov stability theory, and simulation studies are conducted to verify the effectiveness of the developed control schemes.

Observer-based continuous finite-time attitude control for rigid–flexible coupling satellites

ABSTRACTIn this paper, a novel finite-time attitude control law is proposed for rigid–flexible coupling satellites in large angle manoeuver. First, the rigid–flexible coupling dynamic model is set up to reflect the coupling effect between the deformation of flexible appendages and the spatial movement of the rigid hub. Then an extended state observer (ESO) is designed to estimate and compensate the total perturbation including high-order flexible coupling terms, external disturbances and uncertain inertia. Following this, a continuous finite-time attitude controller is designed based on non-singular fast terminal sliding mode (NFTSM) and fast power reaching law, which is introduced to smooth the control input and eliminate the chattering. Numerical simulation is designed to verify the finite-time stability, high accuracy, disturbance rejectionand vibration damping of the proposed control scheme and then a ground experimental system is set to further test the controller's practicability.

Synchronization and Tracking Control for Dual‐motor Driving Servo Systems with Friction Compensation

AbstractA nonsingular fast terminal sliding mode (NFTSM) controller is designed by incorporating the variable gain neural network (NN) observer, which is utilized to guarantee motor speed synchronization and load position tracking of dual‐motor driving servo systems. By designing the variable gain NN observer, the states and uncertain nonlinearities of servo systems are estimated with fast convergence rate and small steady‐state error, where the effects from external disturbance are suppressed as well. Based on the estimated states, the cross‐coupling synchronization strategy and NFTSM tracking scheme are designed to achieve the rapid speed synchronization and precise load tracking, where the NNs are introduced to approximate and compensate friction nonlinearities. In particular, a novel nonlinear synchronization factor characterizing the degree of speed synchronization is proposed to achieve switching between synchronization control and tracking control, which is proven to deal with the coupling problem of synchronization and tracking. Finally, the comparative simulations and experiments are included to verify the reliability and effectiveness.

Neural network disturbance observer-based distributed finite-time formation tracking control for multiple unmanned helicopters

The distributed finite-time formation tracking control problem for multiple unmanned helicopters is investigated in this paper. The control object is to maintain the positions of follower helicopters in formation with external interferences. The helicopter model is divided into a second order outer-loop subsystem and a second order inner-loop subsystem based on multiple-time scale features. Using radial basis function neural network (RBFNN) technique, we first propose a novel finite-time multivariable neural network disturbance observer (FMNNDO) to estimate the external disturbance and model uncertainty, where the neural network (NN) approximation errors can be dynamically compensated by adaptive law. Next, based on FMNNDO, a distributed finite-time formation tracking controller and a finite-time attitude tracking controller are designed using the nonsingular fast terminal sliding mode (NFTSM) method. In order to estimate the second derivative of the virtual desired attitude signal, a novel finite-time sliding mode integral filter is designed. Finally, Lyapunov analysis and multiple-time scale principle ensure the realization of control goal in finite-time. The effectiveness of the proposed FMNNDO and controllers are then verified by numerical simulations.

A chattering-free adaptive second-order non-singular fast terminal sliding mode control scheme for a class of nonlinear uncertain systems

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.

Continuous Nonsingular Fast Terminal Sliding Mode Control of Cable-Driven Manipulators With Super-Twisting Algorithm

For the high-accuracy tracking control purpose of cable-driven manipulators under complex lumped uncertainties, a novel continuous nonsingular fast terminal sliding mode (CNFTSM) control scheme using a modified super-twisting algorithm (STA) is proposed and investigated in this paper. The proposed method applies the time-delay estimation (TDE) technique to estimate and compensate the unknown lumped system dynamics leading to an attractive model-free nature. Then, the NFTSM manifold and the modified STA scheme are used to ensure finite-time convergence performance in both the reaching and sliding mode phases. Thanks to the TDE technique, the proposed method is model-free and suitable to use in complicated practical applications; meanwhile, fast convergence, high tracking accuracy, and good robustness against lumped uncertainties can be ensured befitting from the CNFTSM control with NFTSM error dynamics and STA schemes. Stability of the closed-loop control system is proved. Finally, 2 degrees of freedom comparative simulations and experiments were performed to demonstrate the effectiveness and superiorities of our proposed method over the existing TDE-based robust control schemes.

Anti-disturbance rapid vibration suppression of the flexible aerial refueling hose

Abstract As an extremely dangerous phenomenon in autonomous aerial refueling (AAR), the flexible refueling hose vibration caused by the receiver aircraft’s excessive closure speed should be suppressed once it appears. This paper proposed a permanent magnet synchronous motor (PMSM) based refueling hose servo take-up system for the vibration suppression of the flexible refueling hose. A rapid back-stepping based anti-disturbance nonsingular fast terminal sliding mode (NFTSM) control scheme with a specially established finite-time convergence NFTSM observer is proposed for the PMSM based hose servo take-up system under uncertainties and disturbances. The unmeasured load torque and other disturbances in the PMSM system are reconstituted by the NFTSM observer and to be compensated during the controller design. Then, with the back-stepping technique, a rapid anti-disturbance NFTSM controller is proposed for the PMSM angular tracking to improve the tracking error convergence speed and tracking precision. The proposed vibration suppression scheme is then applied to PMSM based hose servo take-up system for the refueling hose vibration suppression in AAR. Simulation results show the proposed scheme can suppress the hose vibration rapidly and accurately even the system is exposed to strong uncertainties and probe position disturbances, it is more competitive in tracking accuracy, tracking error convergence speed and robustness.