Nonsingular Fast Terminal Sliding Mode Control Research Articles

Vehicle stability control strategy for high-speed curves based on mode switching

This study aims to design a mode-switching control system based on a non-singular fast terminal sliding mode (NFTSM) algorithm for the lateral stability problem of vehicles driving in high-speed curves. First, a three-degrees-of-freedom model of the vehicle was established, and a predicted lateral load transfer ratio (PLTR) was proposed as a threshold for dividing the lateral stability index based on the conventional PLTR. Second, for the vehicle driving state in which the vehicle does not satisfy the PLTR threshold, the vehicle lateral deflection angle is adjusted based on the NFTSM controller to improve the bending path-tracking accuracy of the vehicle. For the vehicle critical rollover state that satisfies the PLTR threshold, an NFTSM-based additional yaw moment control algorithm is proposed to estimate various unknown disturbance and parameter ingestion terms in the vehicle modeling process using an adaptive radial basis function neural network and adaptively adjust the key parameters of the NFTSM controller. Finally, a joint Carsim-Simulink simulation model was built to verify the control algorithm proposed herein. The simulation results show that the mode-switching control system can improve the vehicle’s yaw and rollover stability in high-speed curves and prevent the occurrence of rollover.

Extended state observer–based improved non-singular fast terminal sliding mode for mobile manipulators

The robust non-singular fast terminal sliding mode (NFTSM) controller is adopted in this work to solve the problem of tracking trajectory of a mobile manipulator (MM) suffering from uncertainties. The NFTSM method has the capability to ensure convergence rate and to provide good tracking accuracy and robustness against external perturbations and parameter uncertainties (total disturbances). However, the NFTSM controller needs high discontinuous gain to reject the effect of strong disturbances, which results in vibrations in the steady-state and chattering in the control law. To solve these issues, an extended state observer–based NFTSM technique is proposed for [Formula: see text]-degree of freedom (DoF) coupling MM. The proposed method is designed to approximate and compensate in real-time the uncertainties. It also ensures robustness against total disturbances, good convergence rate, and good tracking accuracy. The stability of the proposed control is also verified based on the Lyapunov theory. Experimental works are conducted on a 5-degree-of-freedom (5-DoF) MM where the results obtained demonstrate the effectiveness of the developed technique and prove the stability of the closed-loop system.

Adaptive Finite-Time Trajectory Tracking Control for Coaxial HAUVs Facing Uncertainties and Unknown Environmental Disturbances

In this paper, the problems of system design, dynamic modeling, and trajectory tracking control of coaxial hybrid aerial underwater vehicles (HAUVs) with time-varying model parameters and composite marine environment disturbances are investigated. It is clear that a stable transition between different media remains a challenge in the practical implementation of amphibious tasks. For HAUVs, accurate dynamic modeling to describe complex dynamic variations during vehicle takeoff from underwater to air is a huge challenge. Meanwhile, due to the rapid changes in model parameters and the external environment, vehicles are likely to fall into the sea during the cross-domain process. An integrated continuous dynamic model considering hydrodynamic changes is established by introducing a linear switching coefficient during the process of trans-medium motion. A nonsingular fast terminal sliding-mode control (NFTSMC) algorithm combined with adaptive technology is used to design the position and attitude of the controller. With no previous knowledge of external interferences and lumped uncertainties of the HAUV, the adaptive NFTSMC (ANFTSMC) algorithm achieves the control objectives; at the same time, the inherent chattering problems of sliding mode control (SMC) are weakened. The finite-time stability of the global system is proven strictly using a series of mathematical derivations based on Lyapunov theory. The effect of the controller applied is analyzed through a series of simulations with representative working conditions. The results show that the proposed ANFTSMC can realize a “seamless” air–water trans-medium process, which proves the superiority and robustness of the proposed control algorithm.

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.

Optimal Coordinated Control of Active Front Steering and Direct Yaw Moment for Distributed Drive Electric Bus

This paper suggests a hierarchical coordination control strategy to enhance the stability of distributed drive electric bus. First, an observer based on sliding mode observer (SMO) and adaptive neural fuzzy inference system (ANFIS) was designed to estimate the vehicle state parameters. Then the upper layer of the strategy primarily focuses on coordinating active front steering (AFS) and direct yaw moment control (DYC). The phase plane method is utilized in this layer to provide an assessment basis for the switching control safety of AFS and DYC. The lower layer of the strategy designs an integral terminal sliding mode controller (ITSMC) and a non-singular fast terminal sliding mode controller (NFTSMC) to obtain the optimal additional front wheel steering angle to improve handling performance. A fuzzy sliding mode controller (FSMC) is also proposed to obtain additional yaw moment to ameliorate yaw stability. Finally, the strategy proposed in this paper is subjected to simulation testing and compared with the performance of AFS and DYC systems. The proposed strategy is also evaluated for tracking errors in sideslip angle and yaw rate under two conditions. The results demonstrate that the proposed strategy can effectively adapt to various extreme environments and improve the maneuvering and yaw stability of the bus.

PMSM non-singular fast terminal sliding mode control with disturbance compensation

A non-singular fast terminal sliding mode control (NFTSMC) strategy is proposed for a permanent magnet synchronous motor control system susceptible to load disturbance. First, an NFTSM surface with fast convergence during the finite time is designed to circumvent the singular point in the TSM surface. Then, a novel reaching law (NRL) is presented to resolve the inconsistency between the system chattering and convergence rate in the traditional reaching law (TRL). Meanwhile, a non-singular fast terminal sliding mode disturbance observer (NFTSMDO) is developed to estimate the disturbance value and compensate the speed controller, further enhancing the system's anti-disturbance performance. Finally, the experiments are conducted jointly with MATLAB/Simulink and the dSPACE platform; accordingly, the experimental results indicate that when the system adds load disturbances, the PI overshoot is 38.7 rpm and the adjustment time is the longest. In addition, when the NFTSMC-TRL and NFTSMC-NRL-NFTSMDO overshoots are 37.4 and 22.1 rpm, respectively, the adjustment time is the shortest and the overall anti-disturbance is the best. Compared to SMDO, NFTSMDO improves the observer's response speed and estimation accuracy while suppressing sliding-mode chattering. It can be inferred that the control strategy proposed in this study can effectively suppress the chattering of the sliding mode control system and improve the anti-disturbance ability of the control system.

Disturbance observer based nonsingular fast terminal sliding mode control of underactuated AUV

In this paper, a disturbance observer based nonsingular fast terminal sliding mode control (NFTSMC) scheme is proposed for the trajectory tracking control of an underactuated autonomous underwater vehicle (AUV). A nonlinear disturbance observer (DO) is designed to estimate complex external disturbances and incorporated into a NFTSMC. In constructing sliding surfaces, the parameter selection in the exponential terms in NFTSMC is expanded. Lyapunov's second method proves the uniformly ultimately bounded stability of the proposed DO based NFTSMC. Simulation is performed to demonstrate the effectiveness of the proposed controller. Compared with the existing NTSMC methods, the convergence rate is improved by the proposed NFTSMC. Moreover, the proposed controller has good robustness to smooth external disturbances. For random disturbances along with an impulse at some time, the proposed controller can also track the disturbance well and achieve good robustness.

Neural network optimization algorithm based non-singular fast terminal sliding-mode control for an uncertain autonomous ground vehicle subjected to disturbances

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

Vector Control of PMSM Based on Improved Sliding Mode Observer and Controller

This paper presents a sensorless speed control method of permanent magnet synchronous motor (PMSM) applying sliding-mode control theory, to enhance the observation precision and improve robustness of control system. Firstly, an improved full-order sliding mode observer (FSMO) with sigmoid function is gifted to weaken the high-frequency (HF) chattering caused by conventional sliding mode observer (SMO). The quadrature phase-locked loop (PLL) is used to calculate high-precision rotor location and speed, avoiding the use of filter. Then the nonsingular fast terminal sliding mode controller (NFTSMC) in speed controller is introduced to replace traditional proportional integral (PI) controller to improve the dynamic performance of control system. The outcomes verify that the presented control method enhances the overall observation precision, suppresses HF chattering, and increases dynamic and stable state response of PMSM.

A stochastic configuration networks-based nonsingular fast terminal sliding mode control approach for indirect matrix converter-driven permanent magnet linear synchronous motors

To further improve the fast and stability of the control system of an indirect matrix converter (IMC) driven permanent magnet linear synchronous motor (PMLSM), a nonsingular fast terminal sliding mode control (NFTSMC) algorithm based on the disturbance observer of stochastic configuration networks (SCNs) is proposed. The NFTSMC algorithm is used to design the outer loop controller, which can reduce the influence of the IMC by the power supply voltage and high-frequency harmonics generated by switching. To further reduce the disturbance of IMC-PMLSM during operation, in this paper, a nonlinear disturbance observer based on SCNs is constructed, which solves the drawback that the traditional disturbance observer needs to adjust the parameters frequently under different working conditions. Finally, a simulation model is established on the MATLAB/Simulink platform to verify the effectiveness and advantages of the proposed control method.

Gated Recurrent Fuzzy Neural Network Sliding Mode Control of a Micro Gyroscope

This paper proposes a non-singular fast terminal sliding mode control (NFTSMC) method for micro gyroscopes with unknown uncertainty based on gated recurrent fuzzy neural networks (GRFNNs). First, taking advantage of non-singular fast terminal sliding control, a sliding hyperplane is designed with a nonlinear function to ensure that the tracking error of the system converges to zero within a specified finite time. Then, the unknown model parameters of the micro gyroscope are estimated using a GRFNN. Since the GRFNN can adaptively adjust the base width, center vector, gated recurrent unit parameters, and outer gains, it can achieve accurate approximation to unknown models, enhancing the robustness and accuracy. In addition, due to the introduction of gated recurrent units, The GRFNN can effectively utilize the previous data and avoid the problem of gradient disappearance. The comparison of the simulation results with traditional neural sliding mode control shows that the proposed method can achieve better tracking performance and more accurate estimation of unknown models.

A Non-singular Fast Terminal Sliding Mode Approach to Improve the Network Stability of Wind Rich Power Grids

The increased penetration of wind energy conversion systems (WECS) into the grid creates many challenges for maintaining grid stability, reliability and efficiency. This paper proposes an approach that integrates the robustness and fast convergence capability of non-singular fast terminal sliding mode control (NFTSMC) with the fast current support of static synchronous compensators (STATCOM) to improve the dynamic stability of wind energy systems during network disturbances. The NFTSMC control approach is designed for the inner current control loop of a STATCOM with voltage source inverter topology. Its main objective is to support both the active and reactive currents and thereby effectively regulate the system's frequency and bus voltage. The proposed approach was implemented to a WECS-based test microgrid subject to sudden load variations and mismatched disturbances. The obtained results confirmed its effectiveness in properly mitigating dynamic instabilities stemming from grid disturbances and maintaining the voltage and frequency within their rated values. Further comparison between the performance of the proposed NFTSMC and that of a standard SMC approach showed better performance and reduced chattering compared to the standard SMC.

Robust Path Tracking Control of Distributed Driving Six-Wheel Steering Commercial Vehicle Based on Coupled Active Disturbance Rejection

With the advancement of chassis technology, a distributed driving six-wheel steering commercial vehicle chassis (DD-6WS CVC) became useful for enhancing traffic efficiency and facilitating rapid emergency rescue. In the face of harsh, complex working conditions and multiple unknown disturbances, the difficulty of research is determining how to comprehensively integrate the benefits of various subsystems to improve the stability of dynamics. Based on the dynamic model of the DD-6WS CVC, a coupled active disturbance rejection controller (ADRC) is designed to improve the robustness of path tracking in emergency obstacle avoidance. First, the preview path information is optimized by the tracking differentiator (TD), and then the six-wheel steering control quantity is computed using model predictive control (MPC). Using the extended state observer (ESO), the total lateral disturbance is estimated and compensated. Second, the heading state quantity and disturbance estimation value are incorporated into the nonsingular fast terminal sliding mode control (NFT-SMC) so that the direct yaw moment control (DYC) can achieve yaw stability in real time. Finally, the optimal distribution of six-wheel drive torque is completed. Experiments validate the algorithm's effectiveness and high robustness under multiple coupling disturbance. The results demonstrate that, in comparison to MPC and the linear quadratic regulator (LQR), the proposed algorithm has superior control characteristics and effectively enhances the robustness of the DD-6WS CVC in-phase steering path tracking.

Non-Negative Adaptive Mechanism-Based Sliding Mode Control for Parallel Manipulators with Uncertainties

In this paper, a non-negative adaptive mechanism based on an adaptive nonsingular fast terminal sliding mode control strategy is proposed to have finite time and high-speed trajectory tracking for parallel manipulators with the existence of unknown bounded complex uncertainties and external disturbances. The proposed approach is a hybrid scheme of the online non-negative adaptive mechanism, tracking differentiator, and nonsingular fast terminal sliding mode control (NFTSMC). Based on the online non-negative adaptive mechanism, the proposed control can remove the assumption that the uncertainties and disturbances must be bounded for the NFTSMC controllers. The proposed controller has several advantages such as simple structure, easy implementation, rapid response, chattering-free, high precision, robustness, singularity avoidance, and finite-time convergence. Since all control parameters are online updated via tracking differentiator and non-negative adaptive law, the tracking control performance at high-speed motions can be better in real-time requirement and disturbance rejection ability. Finally, simulation results validate the effectiveness of the proposed method.

Chatter-Free Non-Singular Fast Terminal Sliding Mode Control of Interleaved Boost Converter

In this brief, a global non-singular fast terminal sliding mode controller (NSFTSMC) is proposed to stabilize the output voltage of an interleaved boost converter which is affected by disturbances such as variations in supply voltage, load resistance, and system parameter uncertainties. First, the converter model is transformed into a simplified form to make the controller design process simple. Second, the two-time scale disturbance estimation technique is adopted to estimate the matched, unmatched disturbances, and un-modeled system dynamics. Then, a nonlinear controller based on the sliding mode algorithm is developed to achieve guaranteed large-signal stability. Unlike other controllers, the proposed one ensures global stability and features a fast dynamic response with accurate output voltage tracking ability over wide variations in operating range. Both simulations and experimentations verify the robustness and feasibility of the proposed controller.

An adaptive backstepping nonsingular fast terminal sliding-mode control for the electromechanical brake system with backlash nonlinearity compensation

With the operation of low-floor trams, unavoidable nonlinear factors such as backlash and parameter perturbation are present in electromechanical brake (EMB) systems. This results in poor clamping force tracking performance and challenges the operational safety of trams. Thus, an adaptive nonsingular fast terminal sliding-mode control algorithm is proposed to address this thorny problem. Firstly, a differentiable function approximates the backlash nonlinearity. Then, a dynamic mathematical model for an EMB system with backlash nonlinearity and parameter perturbation is established. Based on the backstepping control principle, this paper divides the system into three subsystems, and the nonsingular fast terminal sliding-mode control (NFTSMC) algorithm is adopted to design the controller of each subsystem. Notably, the NFTSMC algorithm can solve the parameters perturbation problem by the large switching gains, which may cause the chattering phenomenon. This paper utilizes the adaptive law to establish an adaptive NFTSMC algorithm to improve this phenomenon. Furthermore, the global asymptotic stability of the system is analyzed using Lyapunov theory. Finally, experimental results clearly validate the effectiveness and superiorities of the proposed control algorithm.

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.

Adaptive Second-Order Fast Terminal Sliding-Mode Formation Control for Unmanned Surface Vehicles

The formation control of unmanned surface vehicles (USVs) while considering communication topology, dynamic model uncertainties, environmental disturbances, and a fast convergence rate is addressed in this paper. First, graph theory is introduced to describe the connective relationships and establish generalized formation errors among USVs. Then, a second-order fast nonsingular terminal sliding-mode control (SOFNTSMC) is designed to guarantee that the system converges quickly and without chatter. An adaptive update law is designed in order to estimate the model uncertainties and external disturbances without the requirement of the boundary information of the system uncertainties. With the application of the adaptive SOFNTSMC (ASOFNTSMC) and graph theory, a distributed control is developed for every USV to perform the desired formation pattern. Finally, the results of simulations and comparisons demonstrate the effectiveness of the proposed method.

Trajectory Tracking of UAVs Using Sigmoid Tracking Differentiator and Variable Gain Finite-Time Extended State Observer

The problem of quadrotor attitude and position control is considered in the presence of generally lumped disturbances: external disturbances and model uncertainty. The improved active disturbance rejection controller (ADRC) for quadrotor trajectory tracking is proposed for compensating the lumped disturbances. Firstly, the improved sigmoid tracking differentiator (ISTD), combining improved Sigmoid function and sliding mode terminal attractor is proposed, which can accelerate the global convergence rate and effectively reduce the chattering. Secondly, a novel variable gain finite-time extended state observer (VGFESO) approach is proposed to effectively estimate the lumped disturbances, while the observation errors are convergent to zero in finite time. Then, a super-twisting sliding model controller (STWSMC) is utilized for tracking control of the desired position and attitude. Finally, the convergence of VGFESO and the closed-loop stability of the control system are proved. The results show that the convergence time of the proposed control scheme is the shortest, and the integral absolute error of improved ADRC is reduced from 2.64 to 0.91. The anti-disturbance capability of the proposed controller is fully illustrated when compared with ADRC and robust adaptive nonsingular fast terminal sliding-mode controller (RANFTSMC).