Nonsingular Fast Terminal Sliding Mode Research Articles

Finite-Time Convergence ESO-Based Nonsingular Fast Terminal Sliding Mode Control for PMSM with Unknown Parameters and Time-Varying Load

In this paper, an extended state observer (ESO)-based nonsingular fast terminal sliding mode (NFTSM) control method is proposed for the speed tracking system of permanent magnet synchronous motor (PMSM) in the present of unknown parameters and time-varying load. Firstly, three finite time convergence ESO (FTCESO) are employed to estimate the lumped disturbances in one speed loop and two current loops, respectively, and the estimates are fed forward to controllers for compensation. Secondly, a NFTSM controller is designed, which can drive the speed of PMSM track in desired speed in finite time. The stability of resulting closed-loop system is proved by using Lyapunov theory. Finally, the simulation and experimental results are compared with the existing methods, and the results show that the proposed method has better performance in tracking different kind of desired speed curves, and also performs better in reducing the chattering phenomenon.

Disturbance Observer-Based Sliding Mode Controller for Underwater Electro-Hydrostatic Actuator Affected by Seawater Pressure

This paper presents a disturbance-observer-based sliding mode control strategy for an underwater electro-hydrostatic actuator, particularly considering that electro-hydrostatic actuators (EHAs) significantly suffer from sea pressure disturbance, which makes it hard to achieve high-precision position control. Therefore, a nonlinear disturbance observer was designed to aim at the matched and mismatched disturbance caused by sea pressure disturbance. Then, a nonlinearities model for an underwater EHA was established, and a related non-singular fast terminal sliding mode (NFTSM) controller was designed by changing the conventional sliding mode surface to further improve the control accuracy. In addition, the backstepping tool was used to guarantee the robust stability of the entire three-order hydraulic dynamic system. Finally, a comparative simulation was conducted with different load forces in AMESim and Simulink, which effectively verified the high tracking performance of the proposed control strategy.

Global fast non-singular terminal sliding-mode control for high-speed nanopositioning

This paper presents a new Global Fast Non-singular Terminal Sliding Mode Controller (GFNTSMC) that delivers high-precision tracking of high-frequency trajectories when applied to a piezo-driven nanopositioner. The control scheme is realized by combing inverse hysteresis model and global fast non-singular terminal sliding mode compensation. The inverse Bouc–Wen hysteresis model is used to calculate the required hysteresis-compensating feedforward control voltage according to the reference signal. The key uniqueness of the proposed control strategy is it’s red global fast convergence, achieved with high accuracy and high bandwidth. The stability of the reported GFNTSMC controller is proved with the Lyapunov theory. Its performance is verified through experimentally recorded tracking results, and its superiority over three benchmark control approaches, namely the Proportional–Integral–Derivative (PID), the Positive Position Feedback with integral action (PPF+I) and the conventional linear high-order sliding mode controller (LHOSMC) is demonstrated through comparative tracking error analysis. Its wide-band stability as well as its significant robustness to parameter uncertainty is also showcased.

Yaw Stability Research of the Distributed Drive Electric Bus by Adaptive Nonsingular Fast Terminal Sliding Mode Control

Due to the high center of gravity of distributed drive electric buses, it is crucial to enhance their stability and sliding mode control (SMC) is an effective method to enhance vehicle yaw stability. However, the traditional SMC needs to know the upper limits of the interference term in advance and select a better switching gain to obtain a better control effect, which is impossible for vehicle control. To solve the existing problems, an improved adaptive nonsingular fast terminal sliding mode (ANFTSM) control is presented to enhance the stability of distributed drive electric bus. An uncertainty term is introduced as a switching term in the sliding mode variable and the switching gain in the controller is obtained by parameter adaptation without knowing any uncertainty information. In addition, to enhance the stability of the vehicle in real-time, an adaptive neuro fuzzy inference system (ANFIS) for the weighting factor in the sliding surface is adjusted. A co-simulation of Matlab/Simulink–TruckSim is performed to verify the effectiveness of the algorithm under two typical conditions. The results indicate that the proposed control can follow the ideal value better which improves handling stability and chattering is weaker. Furthermore, the proposed control requires fewer control actions, and also reduces the motor torque variation.

Numerical Simulation of Adaptive Radial Basis NN-Based Non-Singular Fast Terminal Sliding Mode Control with Time Delay Estimator for Precise Control of Dual-Axis Manipulator

Robotic manipulators can reduce the cost of production and improve productivity; however, controlling a manipulator to follow a desired trajectory is a thorny problem. In this study, we introduced various forms of interference to facilitate the modeling of a dual-axis manipulator. The interference associated with the payload is handled by an adaptive radial basis neural network (ARBNN) controller, while other interference is estimated by a time delay estimator (TDE). The control signal is output by a non-singular fast terminal sliding mode controller (NFTSMC) to minimize further interference. Since the proposed controller can deal with the payload, system uncertainties, external disturbances, friction, and backlash, compared with conventional control methods, it has better tracking accuracy and stability.

Fault-tolerant trajectory tracking control of an unmanned marine vehicle via an adaptive non-singular fast terminal sliding mode control

In this paper, a novel finite-time fault-tolerant trajectory tracking controller is created to render a marine vehicle to enhance tracking performance in the presence of complex unknown variables, including model uncertainties, environmental disturbances, and actuator faults. An adaptive fault-tolerant finite-time sliding mode controller is designed by introducing adaptive control techniques, the non-singular fast terminal sliding mode (NSFTSM) function, and a radial base function (RBF) neural network. The radial base function neural network (RBFNN) is developed to eliminate the influences of model uncertainties and environmental disturbances. A fault compensation by integrating the adaption technique is designed to reduce the effects of actuator faults and approximation errors. Suffering from uncertainties and actuator faults, the proposed finite-time tracking controller can track the desired trajectory with high precision. Simulation results and compared simulations indicate the efficiency and superiority of the proposed controller.

Event-Triggered Neural Sliding Mode Guaranteed Performance Control

To solve the trajectory tracking control problem for a class of nonlinear systems with time-varying parameter uncertainties and unknown control directions, this paper proposed a neural sliding mode control strategy with prescribed performance against event-triggered disturbance. First, an enhanced finite-time prescribed performance function and a compensation term containing the Hyperbolic Tangent function are introduced to design a non-singular fast terminal sliding mode (NFTSM) surface to eliminate the singularity in the terminal sliding mode control and speed up the convergence in the balanced unit-loop neighborhood. This sliding surface guarantees arbitrarily small overshoot and fast convergence speed even when triggering mistakes. Meanwhile, we utilize the Nussbaum gain function to solve the problem of unknown control directions and unknown time-varying parameters and design a self-recurrent wavelet neural network (SRWNN) to handle the uncertainty terms in the system. In addition, we use a non-periodic relative threshold event-triggered mechanism to design a new trajectory tracking control law so that the conventional time-triggered mechanism has overcome a significant resource consumption problem. Finally, we proved that all the closed-loop signals are eventually uniformly bounded according to the stability analysis theory, and the Zeno phenomenon can be eliminated. The method in this paper has a better tracking effect and faster response and can obtain better control performance with lower control energy than the traditional NFTSM method, which is verified in inverted pendulum and ball and plate system.

Adaptive Finite-Time Fault-Tolerant Control for Uncertain Flexible Flapping Wings Based on Rigid Finite Element Method

The bionic flapping-wing robotic aircraft is inspired by the flight of birds or insects. This article focuses on the flexible wings of the aircraft, which has great advantages, such as being lightweight, having high flexibility, and offering low energy consumption. However, flexible wings might generate the unexpected deformation and vibration during the flying process. The vibration will degrade the flight performance, even shorten the lifespan of the aircraft. Therefore, designing an effective control method for suppressing vibrations of the flexible wings is significant in practice. The main purpose of this article is to develop an adaptive fault-tolerant control scheme for the flexible wings of the aircraft. Dynamic modeling, control design, and stability verification for the aircraft system are conducted. First, the dynamic model of the flexible flapping-wing aircraft is established by an improved rigid finite element (IRFE) method. Second, a novel adaptive fault-tolerant controller based on the fuzzy neural network (FNN) and nonsingular fast terminal sliding-mode (NFTSM) control scheme are proposed for tracking control and vibration suppression of the flexible wings, while successfully addressing the issues of system uncertainties and actuator failures. Third, the stability of the closed-loop system is analyzed through Lyapunov's direct method. Finally, co-simulations through MapleSim and MATLAB/Simulink are carried out to verify the performance of the proposed controller.

Adaptive Neural-Network-Based Nonsingular Fast Terminal Sliding Mode Control for a Quadrotor with Dynamic Uncertainty

This paper proposes an adaptive neural-network-based nonsingular fast terminal sliding mode (NN-NFTSMC) approach to address the trajectory tracking control problem of a quadrotor in the presence of model uncertainties and external disturbances. First, the dynamic model of the quadrotor with uncertainty is derived. Then, a control scheme using nonsingular fast terminal sliding mode control (NFTSMC) is proposed to guarantee the finite-time convergence of the quadrotor to its desired trajectory. NFTSMC is firstly formulated for the case that the upper bound of the lumped uncertainty is known in advance. Under this framework, a disturbance observer by using the hyperbolic tangent nonlinear tracking differentiator (TANH-NTD) is designed to estimate the external interference, and a neural network (NN) approximator is used to develop an online estimate of the model uncertainty. Subsequently, adaptive algorithms are designed to compensate the approximation error and update the NN weight matrix. An NN-NFTSMC algorithm is formulated to provide the system with robustness to the model uncertainty and external disturbance. Moreover, Lyapunov-based approach is employed to prove the global stability of the closed-loop system and the finite-time convergence of the trajectory tracking errors. The results of a comparative simulation study with other recent methods illustrate the proposed control method reduces the chattering effectively and has remarkable performance.

Wavelet neural network sliding mode control of two rigid joint robot manipulator

To solve the problems of low accuracy and poor stability due to uncertainties, external disturbances and unknown load, which exist in the position control of rigid joint robot manipulator, this article is to propose Non-Singular Fast Terminal Sliding Mode Control strategy with Wavelet neural networks observer (NSFTSMCW). The wavelet observer is designed using the online approximation capability of the neural network, which is used to online estimate the modeling error, external disturbances and uncertainties generated by the dynamic surface control of the joint robot online. Combining the above strategies, the robot manipulators position controller is designed. The stability of this control strategy is demonstrated by stability analysis using the Lyapunov criterion. Simulations on the 2-Link Rigid Joint (2LRJ) robot show that the control strategy can overcome the chattering phenomena ensures the accuracy and stability of the joint robot position control.

Continuous Nonsingular Fast Terminal Sliding Mode Control for Speed Tracking of PMSM Based on Finite Time Disturbance Observer

A continuous nonsingular fast terminal sliding mode (CNFTSM) control strategy with an automated double power reaching law is proposed to improve the performance of speed dynamic response and accuracy tracking for the permanent magnet synchronous motor (PMSM) servo system. In pursuit of robustness against system uncertainties, a finite-time convergent extended state observer (ESO) is designed to estimate external disturbances, parameter variation, and unmodeled dynamics as a feedforward compensation to the output feedback control system. The developed controller, based on Lyapunov stability theory analysis, can guarantee finite time stability from any initial state in the presence of internal and external disturbances. The modified sliding mode reaching law can achieve enough convergence rate compared with the exponential reaching law, and the inherent chattering of sliding mode is reduced when system states approach the equilibrium point. Theoretical analysis and simulation results demonstrate that the proposed composite controller can achieve higher performance than the conventional sliding mode method.

Reentry Attitude Fault Tolerant Control for RLV Based on Adaptive Second-Order Nonsingular Fast Terminal Sliding Mode

Reentry Attitude Fault Tolerant Control for RLV Based on Adaptive Second-Order Nonsingular Fast Terminal Sliding Mode

Adaptive super-twisting sliding mode altitude trajectory tracking control for reentry vehicle

This paper addresses the altitude trajectory tracking control problem of reentry vehicle subject to bounded uncertainty. A new continuous adaptive super-twisting sliding mode control (ASTSMC) method is developed based on conventional super-twisting sliding mode control (STSMC) and adaptive gain technique, which can improve tracking accuracy and achieve high control performance. Based on adaptive gain technique, the designed ASTSMC method requires no prior information on uncertainty and avoids the overestimation of control gain, then the unexpected chattering phenomenon is alleviated. By employing fast power rate reaching law and modified fast nonsingular terminal sliding mode (FNTSM) surface, the designed controller achieves faster convergence and stronger robustness than conventional STSMC methods. Furthermore, the finite-time stability of closed-loop system is proved through Lyapunov theory. Simulation results are executed to validate the superiority of the proposed controller.

Nonsingular Fast Terminal Sliding Mode Control for Permanent Magnet Linear Synchronous Motor via High-Order Super-Twisting Observer

In this article, a nonsingular fast terminal sliding mode (NFTSM) control strategy is proposed based on the high-order super-twisting observer (HOSTO) to acquire a fast and precise tracking performance for position regulation of permanent magnet linear synchronous motor. First, the NFTSM control is introduced to achieve fast convergence of the position tracking error. However, the lumped disturbances result in incompleteness of the system state information, and the robustness of the system is guaranteed through a large switching gain for the NFTSM, which causes system chattering. Therefore, the HOSTO is utilized to estimate the state information. Then, the NFTSM controller is designed based on the estimated state variables. The system’s stability under the proposed control is demonstrated using Lyapunov stability theory. Finally, real-time experiments are carried out to illustrate the efficiency and superiority of the proposed control strategy.

Finite time trajectory tracking control of autonomous agricultural tractor integrated nonsingular fast terminal sliding mode and disturbance observer

A novel control strategy is proposed in this paper to improve the trajectory tracking performance of the autonomous agricultural tractor on both straight-line parallel tracks and headland turning curve tracks in the face of slippage, which combines the nonsingular fast terminal sliding mode (NFTSM) control with a kind of finite time disturbance observer (FDO). The designed FDO ensures robustness outside the sliding mode surface, while the constructed NFTSM ensures the fast convergence of tracking errors and chattering suppression. The effectiveness and advantages of the designed control strategy are verified by simulation comparison with the existing results under MATLAB/Simulink and CarSim co-simulation environment.

Nonsingular fast terminal sliding mode control based on neural network with adaptive robust term for robotic manipulators with actuators

For accurate trajectory tracking of robotic manipulators with actuators, a novel nonsingular fast terminal sliding mode control (NFTSMC) strategy based on radial basis function neural network (RBFNN) is put forward and investigated in this paper. Because of the existence of nonsingular fast terminal sliding mode (NFTSM) manifold, the controller possesses high precision and fast convergence. Considering that it is difficult to obtain accurate model parameters owing to modeling errors or external disturbances, RBFNN is used to approximate the nonlinear uncertainties due to its simple structure and great generalization ability. A new adaptive law is designed to adjust RBFNN. In order to compensate the estimation errors and suppress other unstable factors, a robust term is introduced. A new adaptive law is developed to flexibly adjust the robust term. Then, Lyapunov theory is applied to prove the system stability and finite-time convergence. Finally, a small-sized industrial robotic manipulator Epson LS3-401S with its first two joints is taken as the simulation plant, and several simulations between the proposed controller and the other two controllers are performed. External disturbances and other two conditions are considered to simulate the real environment, and the corresponding results verify the effectiveness and superiority of the proposed controller.

Adaptive Neural Network Global Nonsingular Fast Terminal Sliding Mode Control for a Real Time Ground Simulation of Aerodynamic Heating Produced by Hypersonic Vehicles

This paper presents a strategy for a thermal-structural test with quartz lamp heaters (TSTQLH), combined with an ultra-local model, a closed-loop controller, a linear extended state observer (LESO), and an auxiliary controller. The TSTQLH is a real time ground simulation of aerodynamic heating for hypersonic vehicles to optimize their thermal protection systems (TPS). However, lack of a system dynamic model for the TSTQLH results in inaccurate tracking of aerodynamic heating. In addition, during the control process, the TSTQLH has internal uncertainties of resistance and external disturbances. Therefore, it is necessary to establish a mathematical model between controllable α(t) and measurable T1(t). An ultra-local model of model-free control plays a crucial role in simplifying system complexity and reducing high-order terms due to high nonlinearities and strong couplings in the system dynamic model, and a global nonsingular fast terminal sliding mode control (GNFTSMC) is added to an ultra-local model, which is used to guarantee great tracking performance in the sliding phase and fast convergence to the equilibrium state in finite time. Moreover, the LESO is used mainly to estimate all disturbances in real time, and an adaptive neural network (ANN) shows a good approximation property in compensation for estimation errors by using a cubic B-spline function. The fitted curve of the wall temperature in the time sequence represents a reference temperature trajectory from the surface contour of an X-43A’s wing. The comparative results validate that the proposed control strategy possesses strong robustness to track the reference temperature trajectory.

Adaptive Backstepping Nonsingular Terminal Sliding-Mode Attitude Control of Flexible Airships with Actuator Faults

This paper studies the attitude tracking control of a flexible airship subjected to wind disturbances, actuator saturation and control surface faults. Efficient flexible airship models, including elastic deformation, rigid body motions, and their coupling, are established via Lagrange theory. A fast-nonsingular terminal sliding-mode (NTSM) combined with a backstepping control is proposed for the problem. The benefits of this approach are NTSM merits of high robustness, fast transient response, and finite time convergence, as well as the backstepping control in terms of globally asymptotic stability. However, the major limitation of the backstepping NTSM is that its design procedure is dependent on the prior knowledge of the bound values of the disturbance and faults. To overcome this limitation, a wind observer is designed to compensate for the effect of the wind disturbances, an anti-windup compensator is designed to compensate for actuator saturation, and an adaptive fault estimator is designed to estimate the faults of the control surfaces. Globally exponential stability of the closed-loop control system is guaranteed by using the Lyapunov stability theory. Finally, simulation results demonstrate effectiveness and advantages of the proposed control for the Skyship-500 flexible airship, even in the presence of unknown wind disturbances, control surface faults, and different stiffness variants.

Disturbance Observer-based Nonsingular Fast Terminal Sliding Mode Fault Tolerant Control of a Quadrotor UAV with External Disturbances and Actuator Faults

Disturbance Observer-based Nonsingular Fast Terminal Sliding Mode Fault Tolerant Control of a Quadrotor UAV with External Disturbances and Actuator Faults

ELM-Based Non-Singular Fast Terminal Sliding Mode Control Strategy for Vehicle Platoon

Vehicle platoon is one of the innovations in the automated highway systems, which has the potential to reduce fuel consumption, alleviate traffic congestion and lighten the driver’s burden. How to control the vehicle effectively to ensure the stability of the queue is a challenge. Aiming to overcome the shortcomings of the platoon control method based on traditional sliding mode control, a non-singular terminal sliding mode control method optimized by the extreme learning machine is proposed in this paper. Firstly, the vehicle longitudinal dynamics are derived from the analysis of the forces acting on the vehicle in the longitudinal direction. A constant time headway policy is taken as the spacing policy. The modified non-singular terminal sliding mode control method has outstanding performance, simulation results demonstrate that the following vehicles can rapidly track the trajectory of the leading vehicle in the platoon with less spacing error and guarantee string stability. In this study, several experiments are set up to consider the disturbance and other uncertain practical factors. The performance of the proposed method is superior to the traditional sliding mode control method. Experimental results show that the proposed method can significantly reduce chattering and has good robustness under the circumstances of the disturbance.