Fast Terminal Sliding Mode Surface Research Articles

Finite-time attitude tracking control of stratospheric airship in the presence of multiple disturbances

Abstract This paper proposes a composite non-singular fast terminal sliding mode attitude control scheme based on a reduced-order extended state observer for the stratospheric airship’s attitude system affected by multiple disturbances. First, the feedback linearisation method is applied to address the nonlinearity of the attitude motion model and achieve decoupling of the model in three channels. Second, the overall disturbances, encompassing airship parameter perturbations and external disturbances, are treated as an aggregate. A reduced-order extended state observer is designed for each channel to formulate a composite non-singular fast terminal sliding mode surface. In the control design phase, the hyperbolic sine function is adopted as replacement for the sign function to ensure the continuity of the control signal. The estimated disturbances are incorporated in the control law design to directly offset the effects of multiple disturbances on the attitude motion of the airship. Third, based on Lyapunov theory, it has been proven that the control law can drive the attitude tracking error to converge to zero within a finite time. Simulation results demonstrate that the proposed control scheme exhibits favorable disturbance rejection capability, as well as higher tracking accuracy and faster response speed.

Fixed-time tracking control of manipulators based on non-singular fast terminal sliding surface

As for the problem of trajectory tracking of a multi-joint serial manipulator, a novel fixed-time control scheme is proposed based on non-singular fast terminal sliding mode control. By employing a fast terminal sliding mode surface, we solve the singularity problem existed in traditional terminal sliding mode surface. In the meantime, in order to improve the rapidity of the system, the fixed-time control is incorporated with the fast terminal sliding mode surface control. Theoretical analysis proves that the proposed control scheme guarantees that better tracking performance is obtained, and its convergence time upper limit is not affected by the initial states. In addition, a reaching law with the exponential approach characteristic is added to the control law, which effectively reduces the chattering phenomenon in the controller design. Finally, the effectiveness and feasibility of the designed controller are verified through a numerical simulation.

Adaptive Neural Network Global Fractional Order Fast Terminal Sliding Mode Model-Free Intelligent PID Control for Hypersonic Vehicle’s Ground Thermal Environment

In this paper, an adaptive neural network global fractional order fast terminal sliding mode model-free intelligent PID control strategy (termed as TDE-ANNGFOFTSMC-MFIPIDC) is proposed for the hypersonic vehicle ground thermal environment simulation test device (GTESTD). Firstly, the mathematical model of the GTESTD is transformed into an ultra-local model to ensure that the control strategy design process does not rely on the potentially inaccurate dynamic GTESTD model. Meanwhile, time delay estimation (TDE) is employed to estimate the unknown terms of the ultra-local model. Next, a global fractional-order fast terminal sliding mode surface (GFOFTSMS) is introduced to effectively reduce the estimation error generated by TDE. It also eliminates arrival time, accelerates the convergence speed of the sliding phase, guarantees finite time arrival, avoids the singularity phenomenon, and bolsters robustness. Then, as the upper bound of the disturbance error is unknown, an adaptive neural network (ANN) control is designed to approximate the upper bound of the estimation error closely and mitigate the chattering phenomenon. Furthermore, the stability of the control system and the convergence time are proven by the Lyapunov stability theorem and are calculated, respectively. Finally, simulation results are conducted to validate the efficacy of the proposed control strategy.

Speed Regulation and Optimization of Sensorless System of Permanent Magnet Synchronous Motor

Aiming at the problems of speed overshoot, slow convergence and poor anti-interference in the control of permanent-magnet synchronous motors (PMSMs) without a position sensor, a pulse vibration high-frequency signal injection method for a permanent-magnet synchronous motor with an improved sliding mode control was designed. Firstly, the improved approach rate function is combined with the improved non-singular fast terminal sliding mode surface to design the non-singular fast terminal sliding mode controller (NFTSMC), which is used in the speed loop to improve the speed convergence ability and reduce its overshoot. Secondly, in order to eliminate the influence of the band-pass filter on the system bandwidth in the traditional high-frequency injection method, a pulse vibration high-frequency signal injection method that injects high-frequency voltage signals and synchronous current signals into the d^ axis of the estimated two-phase rotation coordinate system d^q^ and the αβ axis of the two-phase stationary coordinate system αβ was designed to estimate the motor position and speed to achieve sensorless control. Finally, the above control strategy was compared with the speed loop PI and the traditional sliding mode controller (SMC) of the speed loop, respectively. The simulation and experimental results show that whether it is a no-load variable speed or fixed speed loading, the above control strategy can effectively reduce the speed overshoot, accelerate the speed convergence and improve the load capacity of the system.

Multi-motor position synchronization control method based on non-singular fast terminal sliding mode control.

In order to improve the position high-precision synchronization performance of multi-motor synchronous control, a multi-motor position synchronization control method based on non-singular fast terminal sliding mode control (NFTSMC) combined with an improved deviation coupling control structure (Improved Deviation Coupling Control(IDCC), NFTSMC+IDCC). Firstly, this paper designs a sliding mode controller using a non-singular fast terminal sliding mode surface with a Permanent Magnet Synchronous Motor (PMSM) as the control object. Secondly, the deviation coupling is improved to enhance the coupling between multiple motors and achieve position synchronization. Finally, the simulation results show that the total error of multi-motor position synchronization under NFTSMC control is 0.553r in the simulation of multi-motor synchronization control under the same working conditions, which is 2.873r and 1.772r less than that of SMC and FTSMC in terms of speed error, and the anti-disturbance performance is 83.68% and 76.22% higher than that of both of them, respectively. In the subsequent simulation of the improved multi-motor position synchronization structure, the total error of the multi-motor position is in the range of 0.56r-0.58r at three speeds, which is much smaller than the synchronization error under the Ring Coupling Control (RCC) structure and Deviation Coupling Control (DCC) structure, showing a better The synchronization error is much smaller than that of the RCC structure and DCC structure, which shows better position synchronization performance. Therefore, the multi-motor position synchronization control method proposed in this paper has a good position synchronization effect and achieves the control effect of small displacement error and fast convergence of the multi-motor position synchronization control system after being disturbed, the control performance is significantly improved.

Third‐order integral sliding mode control of piezoelectric actuators based on rate‐amplitude‐dependent Prandtl‐Ishlinskii model

AbstractAiming at trajectory tracking control of piezoelectric actuators (PEAs), this article proposes a third‐order integral sliding mode control (3‐ISMC) based on rate‐amplitude‐dependent Prandtl‐Ishlinskii (PI) inverse model feedforward (3‐RAPI) scheme, which can achieve finite time convergence and avoid singular problems, while ensuring the continuity of the control signal. In this control scheme, a rate‐amplitude‐dependent PI (RAPI) model is proposed to describe the hysteresis characteristics of PEA, and the RAPI hysteresis inverse model is used to realize the feedforward control. The simulation results verify the improvement of the modeling accuracy of the RAPI model compared with the traditional PI model. In order to reduce the influence of modeling error and improve the robustness of the system, a 3‐ISMC scheme based on integral non‐singular fast terminal sliding mode surface is proposed. Simulation and experimental results demonstrate that the tracking performance of 3‐ISMC is improved compared with the existing third‐order integral terminal sliding model control (3‐ITSMC). Finally, the composite control algorithm is realized by combining the RAPI hysteresis inverse model feedforward with the 3‐ISMC algorithm. The experimental results further show that the control algorithm can track the input signal in a wide range of rate and amplitude.

Fixed time sliding mode control for disturbed robotic manipulator

In this study, a new fixed-time sliding mode control approach for trajectory tracking control of robotic manipulator systems is devised, which provides fixed-time convergence, robust stabilization, and high precision. A novel fixed-time non-singular fast terminal sliding mode surface (FNFTSMS) with fixed-time convergence is provided, and with settling time independent of the initial condition of the system and can be pre-determined using design parameters. Furthermore, using adaptive disturbance observer and the suggested FNFTSMS, a new composite robust control approach is developed. The adaptive disturbance observer is intended to boost control performance and compensate for unpredictably occurring disturbances. The Lyapunov stability theory is used to establish the fixed-time stability of sliding surface and system states under the suggested composite control strategy. Finally, numerical simulations are carried out using PUMA560 robot in order to demonstrate the effectiveness and efficacy of the proposed control method in terms of accuracy of tracking, fast response, and convergent speed.

Fixed time robust control for tower cranes with unmatched disturbances and input saturation

SummaryTo address the challenging problem of fixed‐time anti‐sway and positioning control for tower cranes with uncertain disturbances and input saturation, a novel fixed‐time anti‐saturation robust algorithm is proposed. First, on the basis of a newly designed fixed‐time convergence system, a fixed‐time disturbance observer (FTDO) is developed to estimate the matched and unmatched disturbances. Then, an anti‐saturation compensator is employed to deal with the input saturation and make the control input leave the saturated region rapidly. Upon which, a novel non‐singular fast terminal sliding mode surface is presented. Furthermore, in order to ensure the stability of each subsystem, a hierarchical sliding mode surface taking into account unmatched disturbances and input saturation is designed. Finally, the FTDO based hierarchical sliding mode control law is introduced to improve the transient control performance and robustness of tower cranes. The fixed‐time convergence of the closed‐loop system is proved by Lyapunov technique. Numerical simulations for four scenarios demonstrate the validity of the presented control scheme and fastest convergence speed in comparison to the recently proposed fixed‐time control methods.

A novel model-free adaptive terminal sliding mode controller for bridge cranes

To achieve stabilisation control of an underactuated bridge crane system, a new robust control strategy for the sliding mode is proposed in this paper. It can realise finite-time-convergent stabilisation control under the conditions of model uncertainty, parameter perturbation and external interference. In contrast to the existing methods, our method does not need prior information of the dynamic characteristics of the bridge crane system, and can make the system converge to the equilibrium state at the preset time. Specifically, the nonlinear model of the bridge crane system is linearised with partial feedback, and adaptive signals are introduced. Then, according to the form of the transformed system, a fast terminal sliding mode surface is constructed, and an adaptive terminal sliding mode controller is designed. According to strict analysis, the proposed control law ensures that the system converges to the equilibrium point in finite time and provides the convergence time. Finally, the effectiveness and robustness of the proposed control method are verified by comparing the simulation and experimental results with existing methods.

Fault-tolerant control of second-order systems based on augmented improved extended state observer and non-singular high-order fast terminal sliding mode

In this article, a fault-tolerant control method based on augmented improved extended state observer and non-singular high-order fast terminal sliding mode is proposed for a class of second-order systems with actuator faults. First, the initial peak of the traditional extended state observer is avoided by improving the structure of the observer. Second, the total disturbance and its change trend are observed simultaneously, so as to better realize the compensation of total disturbance. The convergence of the observer is proved theoretically. In addition, by designing non-singular high-order fast terminal sliding mode surface, the sliding mode variable converges rapidly during the whole process to improve the algorithm’s rapidity. Finally, the chattering of control signal caused by sliding mode control is greatly reduced using high-order sliding mode technology, and the stability of the whole closed-loop system is proved by Lyapunov criterion. The comparative experimental results on the fault-tolerant control platform of the quadrotor unmanned aerial vehicle demonstrate the effectiveness and superiority of the proposed observer and controller.

Adaptive Non-Singular Fast Terminal Sliding Mode Trajectory Tracking Control for Robot Manipulators

In order to improve the efficiency of human–robot interaction (HRI), it is necessary to carry out research on precise control of the manipulator. In this paper, an adaptive non-singular fast terminal sliding mode control scheme is proposed for robot manipulators to solve the trajectory tracking problem with model uncertainty and external disturbances. At first, a novel non-singular fast terminal sliding mode surface is proposed, and by introducing an auxiliary function, the singularity problem caused by the inverse of the error-related matrix could be avoided in the controller design process. Then, the controller is developed by using Lyapunov synthesis. A robust adaptive strategy is used to deal with lumped uncertainty, with an adaptive update law designed to compensate for the upper bound of lumped uncertainty whose upper bound is prior unknown. Finally, a two-link robot manipulators as a simulation example is given to illustrate the effectiveness of the proposed scheme. Compared with other similar algorithms, the proposed adaptive non-singular fast terminal sliding mode control scheme has higher efficiency and smaller computational complexity for the reason that no piecewise continuous function is needed to be constructed during the controller design.

Control and synchronization of chaotic spur gear system using adaptive non-singular fast terminal sliding mode controller

This study reports a novel adaptive non-singular fast terminal sliding mode controller for the tracking control and synchronization of a chaotic spur gear system. The proposed novel control law attenuates the chattering phenomena of the conventional sliding mode controller. In addition, a non-singular fast terminal sliding mode surface is employed to remove the singularity problem, increase the convergence rate, and guarantee finite-time convergence. An extreme learning machine (ELM) neural network is utilized to estimate the unknown dynamics of the spur gear system and the reaching law coefficients; hence, this control scheme is a combination of the direct and indirect adaptive control. The adaptation rules of the ELM are derived based on the Lyapunov stability theorem to ensure closed-looped stability. Finally, some different numerical simulations are considered to check the validity and efficiency of the proposed control strategy compared with other control methods.

Nonsingular fast terminal sliding mode-based robust adaptive structural reliable position-mooring control with uncertainty estimation

This paper addresses a novel robust structural reliable position mooring scheme for a turret-moored floating production storage and offloading (FPSO) vessel subject to system uncertainties, environmental disturbances and unmeasurable velocity. A realistic mooring tension model considering buoys and different cable materials that can improve the capacity of the mooring system is derived. A sigmoid tracking differentiator (STD) is employed as a state observer to estimate the unmeasurable velocity. A structural reliability index is introduced to design a position mooring control law so that an FPSO vessel adequately uses a mooring system on the premise of safety to maintain position in an allowable region. It provides strong robustness and a fast transient response and suppresses chattering by merits of a backstepping method and an integral nonsingular fast terminal sliding mode surface (INFTSMS). An adaptive estimator is proposed to address the required unknown uncertainties and disturbances. Theoretical analysis proves the globally asymptotic stability of the whole system. Finally, comparative simulations on an FPSO vessel are conducted to illustrate the effectiveness and superiority of the proposed position mooring control scheme.

Trajectory Tracking Robust Control Method Based on Finite-Time Convergence of Manipulator with Nonsingular Fast Terminal Sliding Mode Surface

In order to make the manipulator track the desired trajectory in a finite time, a new control method based on fast nonsingular terminal sliding mode has been designed. This method combines the traditional fast terminal sliding mode with the nonsingular terminal sliding mode, has rapidity, nonsingularity, finite-time convergence, and strong robustness, and can effectively suppress the inherent chattering phenomenon of the sliding mode controller. The nonsingular fast terminal sliding mode surface is used to accelerate the convergence speed of manipulator trajectory tracking error, and the singularity problem in terminal sliding mode is solved. The finite-time convergence of the algorithm is proved by the Lyapunov function. The simulation results demonstrate that the proposed method can achieve accurate finite-time trajectory tracking characteristics and has robustness against external disturbances.

Global Nonsingular Fast Terminal Sliding Mode Control of Aerodynamic Heat Simulation Heating System Based on Linear Extended State Observer

In this paper, a novel global nonsingular fast terminal sliding mode control (GNFTSMC) method based on linear extended state observer (LESO) is proposed for Aerodynamic Heat Simulation Heating System (AHSHS). The global nonsingular fast terminal sliding mode surface (GNFTSMS), comprising constant reaching law and LESO, establishes a closed-loop control for the whole control process. Firstly, the designed GNFTSMS eliminates the reaching stage, so that the whole control process is confined on the sliding mode surface. The fast term and nonsingular term ensure convergence speed in the sliding phase, and eliminate the singularity and suppress the chattering phenomenon. Then, the constant reaching law can effectively solve the problem of convergence stagnation in the control process and further accelerate the convergence speed. Then, LESO can feed back the observation of input disturbances and external disturbances to the control system. Furthermore, Lyapunov stability theorem is utilized to prove the stability of the closed-loop system. Finally, the simulation results verify that the proposed GNFTSMC method based on LESO is superior.

Nonsingular fast terminal sliding mode control for manipulator based on combinatorial reaching law

Aiming at the problems of external disturbance, modeling errors, tracking speed and chattering in manipulator trajectory tracking control, a nonsingular fast terminal sliding mode control strategy for manipulator based on combinatorial reaching law was proposed. First, the nonlinear disturbance observer was used to observe the system’s external disturbance and modeling errors. Then, on the basis of the nonsingular fast terminal sliding mode surface, an improved nonsingular fast terminal sliding mode surface was proposed, which improves the convergence speed in the sliding motion process of sliding mode control. At the same time, a combinatorial reaching law combining the power reaching law and the variable speed reaching law was proposed, which improved the approach speed of the system under the premise of weakening the chattering. The simulation results verified the effectiveness of this control strategy.

Fast-Exponential Sliding Mode Control of Robotic Manipulator With Super-Twisting Method

This brief addresses the trajectory tracking problem for robotic manipulators without angular velocity measurements in the presence of parameter perturbation and torque disturbance. A novel fast terminal sliding mode surface is developed to ensure global strong robustness and fast error convergence. Then, a high-order sliding mode observer (HOSMO) is constructed to estimate unknown joints’ angular velocities and the system lumped disturbance in a finite time. Chattering avoidance can be realized via the continuous control strategy based on super-twisting method. The finite-time arrival of sliding mode surface and fast-exponential convergence of the tracking error are strictly proved based on the Lyapunov stability theory. Finally, an example of a two-link robotic manipulator is provided. From the comparison with other control strategies, the advantages of proposed method are fully demonstrated.

Adaptive super‐twisting algorithm‐based fractional‐order sliding mode control of redundantly actuated cable driving parallel robot with uncertainty and disturbance estimation

This paper proposed an adaptive super-twisting (AST)-based fractional-order sliding mode control algorithm under disturbances for redundantly actuated cable driving parallel robots. A novel fractional-order non-singular fast terminal sliding mode surface is constructed, and the fast response convergence and accuracy tracking performance can be obtained in the sliding mode phase; meanwhile, an auxiliary system is designed to overcome the adverse effects of the input saturation. Then, to compensate for the model uncertainty and external disturbances, the uncertainty and disturbance estimation is designed, and a novel AST algorithm is developed to suppress the estimation error without the known bound of the adaptive gains and guarantee the finite-time convergence in the reaching phase. The Lyapunov stability theory is employed to prove the convergence of the proposed controller. Finally, numerical simulations are conducted in the commercial software of MATLAB/SIMULINK to demonstrate the effectiveness of the proposed controller.

Robust finite-time cooperative formation control of UGV-UAV with model uncertainties and actuator faults

This paper investigates the finite-time cooperative formation control problem for a heterogeneous system consisting of an unmanned ground vehicle (UGV) - the leader and an unmanned aerial vehicle (UAV) - the follower. The UAV system under consideration is subject to modeling uncertainties, external disturbance as well as actuator faults simultaneously, which is associated with aerodynamic and gyroscopic effects, payload mass, and other external forces. First, a backstepping controller is developed to stabilize the leader system to track the desired trajectory. Second, a robust nonsingular fast terminal sliding mode surface is designed for UAV and finite-time position control is achieved using terminal sliding mode technique, which ensures the formation error converges to zero in finite time in the presence of actuator faults and other uncertainties. Furthermore, by combining the radial basis function neural networks (NNs) with adaptive virtual parameter technology, a novel NN-based adaptive nonsingular fast terminal sliding formation controller (NN-ANFTSMFC) is developed. By means of the proposed adaptive control strategy, both uncertainties and actuator faults can be compensated without the prior knowledges of the uncertainty bounds and fault information. By using the proposed control schemes, larger actuator faults can be tolerated while eliminating control chattering. In order to realize fast coordinated formation, the expected position trajectory of UAV is composed of the leader position information and the desired relative distance with UGV, based on local distributed theory, in the three-dimensional space. The tracking and formation controllers are proved to be stable by the Lyapunov theory and the simulation results demonstrate the effectiveness of proposed algorithms.

Adaptive Nonsingular Fast Terminal Sliding Mode Tracking Control for an Underwater Vehicle-Manipulator System with Extended State Observer

An adaptive nonsingular fast terminal sliding mode control scheme with extended state observer (ESO) is proposed for the trajectory tracking of an underwater vehicle-manipulator system (UVMS), where the system is subjected to the lumped disturbances associating with both parameter uncertainties and external disturbances. The inverse kinematics for the system is obtained by the quaternion-based closed-loop inverse kinematic algorithm. The proposed controller consists of the modified nonsingular fast terminal sliding mode surface (NFTSMS) and ESO, and the adaptive control law. The utilized NFTSMS can ensure the fast convergence of the tracking errors, together with avoiding the singularity in the derivation. According to the ESO method, the estimation error of the lumped disturbance vector can realize the fixed-time convergence to the origin, along with replacing the sign function with the saturation function to attenuate the chattering. A continuous fractional PI-type robust term with adaptive laws is introduced to handle the unknown bound of the estimation error. The closed-loop system is proved to be asymptotically stable by the Lyapunov theory. Simulations are performed on a ten degree-of-freedom UVMS under four different strategies. Comparative simulation results show that the proposed controller can achieve better tracking performance and stronger robustness of the disturbance rejection.