Sliding Mode Surface Research Articles

Integral Sliding Mode Output Feedback Control for Unmanned Marine Vehicles Using T–S Fuzzy Model with Unknown Premise Variables and Actuator Faults

This paper addresses integral sliding mode output feedback fault-tolerant control (FTC) of unmanned marine vessels (UMVs) with unknown premise variables and actuator faults. Due to the complexity of the marine environment, the presence of uncertainties in the yaw angle renders the premise variables in the Takagi–Sugeno (T–S) fuzzy model of UMVs unknown. Consequently, traditional integral sliding mode techniques become infeasible. To address this issue, a control strategy combining integral sliding mode based on output feedback with a compensator utilizing switching mechanisms is proposed. First, a radial basis function neural network is used to approximate the nonlinear terms in the UMV T–S fuzzy model. In addition, an integral sliding mode surface is constructed based on fault estimation information and membership function estimation. On this basis, an FTC scheme based on integral sliding mode output feedback is developed to ensure that the UMV system is asymptotically stable and satisfies the prescribed H∞ performance index. Finally, simulation results are provided to demonstrate the effectiveness of the presented control strategy.

3-D Impact Time and Angle Control Guidance Law Based on Sliding Mode without Speed Control

In modern warship, coordinated combat strategies require missiles hit targets simultaneously, sometimes even require angle constraints, which is difficult to replicate in three-dimensional (3-D) models. This paper proposes a novel 3-D sliding mode guidance law with multiple constraints. First, the 3-D no-thrust guidance model is derived in the coordinate system with [Formula: see text]-axis upward. Second, a novel guidance strategy is proposed. In pitch direction, a fast nonsingular sliding mode surface algorithm is proposed to satisfy the desired line-of-sight elevation angle. In yaw direction, based on the guidance conditions, a special sliding mode surface is proposed, which can achieve desired line-of-sight azimuth angle and desired impact time when reaching the sliding surface. Finally, simulations and comparisons verify the good performance.

Sliding mode control for uncertain fractional-order reaction–diffusion memristor neural networks with time delays

This paper investigates a sliding mode control method for a class of uncertain delayed fractional-order reaction–diffusion memristor neural networks. Different from most existing literature on sliding mode control for fractional-order reaction–diffusion systems, this study constructs a linear sliding mode switching function and designs the corresponding sliding mode control law. The sufficient theory for the globally asymptotic stability of the sliding mode dynamics are provided, and it is proven that the sliding mode surface is finite-time reachable under the proposed control law, with an estimate of the maximum reaching time. Finally, a numerical test is presented to validate the effectiveness of the theoretical analysis.

Integral sliding mode control and stability for Markov jump systems with structured perturbations and time-varying delay driven by fractional Brownian motion

The issues of stability and sliding mode control (SMC) for time-varying delay Markov jump systems (MJSs) with structured perturbations constrained by fractional Brownian motion (fBm) are explored. First, constructing a novel Lyapunov–Krasovskii functional (LKF) with exponential terms that contain the double-integral term, the pth moment exponential stability conditions are derived by utilizing the generalized fractional Itoˆ formula and conditional mathematical expectation. Subsequently, by designing the innovative integral sliding mode surface (SMS) associated with time-varying delay and the SMC law, the state trajectories of the dynamic systems can reach the designed SMS within a finite time. Ultimately, the numerical experiment is executed to confirm and ensure the accuracy and reliability of the obtained results.

Asynchronous output feedback quantized sliding mode dissipative control for Markovian jump time-delay systems with generally bounded transition rates

This article figures out the asynchronous output feedback sliding mode dissipative control issue for Markovian jump delay systems (MJDSs) with uncertain parameters and external disturbances. Different from the massive methods of constructing sliding mode surfaces (SMS), a new dynamic output feedback (DOF) integral SMS is developed, where the SMS is composed of a virtual controller with quantized output and the controller is asynchronous with the system mode. Meanwhile, the reachability of the SMS is guaranteed. In addition, the transition rates (TRs) considered in this paper are generally bounded, which means that the designed method applies to the more general case of TRs, such as fully known and partially unknown TRs. The sufficient criteria of stochastic stability and strict dissipation for the MJDSs are deduced. The design scheme of the controller gain matrix is proposed by the linear matrix inequality (LMI) technique. Finally, two examples are shown to demonstrate the effectiveness and feasibility of the designed technique.

Neural network based adaptive robust synchronous control of double-lift overhead crane considering input saturation

This paper proposes a novel model-free controller, considering the double-lift overhead crane system cannot be accurately modeled and affected by external disturbances. Firstly, to improve the convergence speed of the system states, a time-varying sliding mode surface using a sigmoid-like function is proposed. Then, an adjustable weights radial basis function neural network (AWRBFNN) is introduced to estimate and compensate for the unknown dynamics of the system. This AWRBFNN introduces direct and effective model-free properties, but also brings approximation errors. To estimate the uncertain disturbances and the errors of the neural network, an adaptive uncertainty and disturbance estimator (AUDE) is designed. Furthermore, a fast hyperbolic power reaching law is developed to enhance the robustness while suppressing chattering. Considering that the driving capacity of the actual double-lift overhead crane system and the driving motor torque are limited, an innovative continuous auxiliary system is designed to mitigate the effects of the input saturation while reducing overshoot from synchronization errors. Finally, the stability of the control system is analyzed using the Lyapunov stability theory, and the effectiveness and robustness of the control scheme are verified by simulation.

Robust Fixed-Time Fault-Tolerant Control for USV with Prescribed Tracking Performance

The unmanned surface vessel (USV) is an emerging marine tool with its advantages of automation and intelligence in recent years; the good trajectory tracking performance is an important capability. This paper proposes a novel prescribed performance fixed-time fault-tolerant control scheme for an USV with model parameter uncertainties, unknown external disturbances, and actuator faults, based on an improved fixed-time disturbances observer. Firstly, the proposed observer can not only accurately and quickly estimate and compensate the lumped nonlinearity, including actuator faults, but also reduce the chattering phenomenon by introducing the hyperbolic tangent function. Then, under the framework of prescribed performance control, a prescribed performance fault-tolerant controller is designed based on a nonsingular fixed-time sliding mode surface, which guarantees the transient and steady-state performance of an USV under actuator faults and meets the prescribed tracking performance requirements. In addition, it is proved that the closed-loop control system has fixed-time stability according to Lyapunov’s theory. Finally, upon conducting numerical simulations and comparing the proposed control scheme with the SMC and the finite-time NFTSMC scheme, it is evident that the absolute error tracking performance index of the proposed control scheme is significantly lower, thus indicating its superior accuracy.

Backstepping and Novel Sliding Mode Trajectory Tracking Controller for Wheeled Mobile Robots

A novel variable structure controller based on sliding mode is developed for addressing the trajectory tracking challenge encountered by wheeled mobile robots. Firstly, the trajectory tracking error model under the global coordinate system is established according to the kinematic model of the wheeled mobile robot. Secondly, the novel sliding mode algorithm and backstepping method are introduced to design the motion controller of the system, respectively. Different sliding mode surfaces are formulated to guarantee rapid and stable convergence of the system’s trajectory tracking error to zero. Ultimately, comparative simulation trials validate the controller’s ability to swiftly and consistently follow the reference trajectory. In contrast to traditional controllers, this controller shows rapid convergence, minimal error, and robustness.

Adaptive neural network-based practical predefined-time nonsingular terminal sliding mode control for upper limb rehabilitation robots

This article investigates the predefined time trajectory tracking control problem of upper limb rehabilitation robots in the presence of the model uncertainty and external disturbances. An adaptive neural network-based practical predefined-time fast nonsingular terminal sliding-mode control (PPT-FNTSMC) strategy is proposed, in which a novel sliding mode surface is constructed to achieve predefined-time convergence and avoid the singularity problem as well. Additionally, a neural network is employed to approximate the lumped disturbances, and the estimated values are utilized in the controller for compensation, thereby reducing the required switching gain and mitigating chattering phenomenon. A rigorous theoretical analysis is provided to illustrate that the tracking errors can converge to a vicinity of the origin in a predefined time. Finally, simulations on a two-joint single-arm robot and a 5-DOF upper-limb exoskeleton are conducted and compared with an existing control method to demonstrate the effectiveness and superiority of the proposed control strategy.

Ultralocal Model-Free Adaptive Supertwisting Nonsingular Terminal Sliding Mode Control for Magnetic Levitation System

The magnetic levitation technology has attracted blooming attention from all walks of life thanks to its superiorities such as non-contact and active control. While the intrinsic features of open-loop instability and strong nonlinearity, along with the uncertain external disturbance make the levitation control particularly significant and difficult. For speeding up the convergence and obtaining a better stability and disturbance robustness, this paper proposes an ultra-local model-free adaptive super-twisting nonsingular terminal sliding mode control (ULMF-ASTNTSMC) strategy for the magnetic levitation system. Different from the conventional model-based control, ultra-local model-free control breaks the constraint of a precise system model. Therefore, an improved second-order ultra-local model is established for the magnetic levitation system. For the benefit of finite time convergence and non-singularity, the nonsingular terminal sliding mode surface is chosen. As a second-order algorithm, super-twisting (ST) algorithm can fundamentally suppress the chattering effect of the sliding mode control (SMC). An adaptive super-twisting algorithm is designed for the further improvement of the system dynamic response. The stability of the proposed scheme is strictly verified based on the Lyapunov stability theory. Simulation and experimental comparisons with the existing control methods validate the exceeding performance of the proposed strategy under various operating conditions.

A Novel Adaptive Third-Order Continuous Super-Twisting Controller of a Five Phase Permanent Magnet Synchronous Wind Generator

The aim of this research is to enhance the control of a Wind Energy Generating System (WEGS) incorporating a Five-phase Permanent Magnet Synchronous Generator (5 ph-PMSG) and addressing operational challenges in the presence of disturbances. The commonly employed Second-Order Super-Twisting Controller (SOSTC), with constant gains, has limitations, including uncertainties, significant transient state errors, and chattering effects, hindering its practical applicability. To overcome these drawbacks, the study proposes the application of an Adaptive Third-Order Continuous Super-Twisting Control (ATOCSTC). This novel approach integrates a third-order sliding mode surface, a smoothly continuous switching control term, and an adaptation law. Unlike the conventional SOSTC using discontinuous “sign” functions, ATOCSTC dynamically adjusts gains using tangent hyperbolic functions, providing a continuous and effective control mechanism. Comparative analysis with the conventional SOSTC under various disturbances such as wind speed fluctuations, parameter variations, and Grid Voltage Sag (GVS), reveals significant improvements with ATOCSTC. Notably, ATOCSTC leads to a 75% reduction in power ripples for grid active power and a 40.38% reduction for grid reactive power. These findings underscore the superior performances obtained with the proposed ATOCSTC in WEGS.

Distributed prescribed-time cooperative formation tracking control of networked unmanned surface vessels under directed graph

To investigate the formation tracking control problem of networked unmanned surface vessels (USVs) under a directed graph, this article provides a prescribed-time distributed cooperative formation tracking control scheme that specifies tracking error convergence time in advance. Firstly, aiming at the unknown state of the leading USV, a distributed prescribed-time state observer is designed for the following USVs, which can quickly and accurately estimate the position and speed of the leading USV in a prescribed time. Then, based on the state observer, the prescribed-time sliding surface is designed, and the prescribed-time cooperative formation tracking controller is constructed using the prescribed-time sliding mode surface. In addition, a fast adaptive compensation law is developed to mitigate the issue of input saturation. The analysis based on Lyapunov theory displays that the upper bounds of the convergence time of the observer, the sliding mode surface, and the controller proposed in this study explicitly exist in the controller parameters, so they can be easily adjusted in the control design process and are not restricted by the initial state. Finally, the simulation results demonstrate that the proposed approach exhibits high reliability and effectiveness.

Adaptive Super-Twisting Sliding Mode Control for Robot Manipulators with Input Saturation.

The paper investigates a modified adaptive super-twisting sliding mode control (ASTSMC) for robotic manipulators with input saturation. To avoid singular perturbation while increasing the convergence rate, a modified sliding mode surface (SMS) is developed in this method. Using the proposed SMS, an ASTSMC is developed for robot manipulators, which not only achieves strong robustness but also ensures finite-time convergence. The boundary of lumped uncertainties cannot be easily obtained. A modified adaptive law is developed such that the boundaries of time-varying disturbance and its derivative are not required. Considering input saturation in practical cases, an ASTSMC with saturation compensation is proposed to reduce the effect of input saturation on tracking performances of robot manipulators. The finite-time convergence of the proposed scheme is analyzed. Through comparative simulations against two other sliding mode control schemes, the proposed method has been validated to possess strong adaptability, effectively adjusting control gains; simultaneously, it demonstrates robustness against disturbances and uncertainties.

Quadrotor UAV Trajectory Tracking Control Based on Adaptive Non-singular Terminal Sliding Mode

To address the issue of the quadrotor unmanned aerial vehicle (UAV) being susceptible to external disturbances and model uncertainties during flight, an adaptive non-singular terminal sliding mode controller with disturbance compensation is proposed. Firstly, the quadrotor UAV dynamic model considering system disturbances is constructed using the Newton-Euler method. Next, the trajectory tracking problem is transformed into a command tracking control problem for each channel. To enhance the adaptability and robustness of trajectory tracking for the quadrotor UAV, an adaptive law is designed to dynamically adjust the sliding mode surface gain. In addition, a disturbance observer is introduced to estimate and compensate for external disturbances and model uncertainties. Finally, the stability of the designed controller is proven through the Lyapunov function. Simulation results demonstrate that the proposed controller effectively enhances the disturbance resistance and trajectory tracking response speed of the quadrotor UAV.

A novel adaptive super-twisting trajectory tracking control with back propagation algorithm for a quadrotor UAV

This paper presents a new method for controlling a quadrotor unmanned aerial vehicle (UAV) with neural network adaptive adjustment combined with a super-twisting algorithm, which utilizes back-propagation algorithm in neural networks to design an adaptive method that can adjust the coefficients of the sliding mode surface as well as the control gain adjustment adaptive problem in the super-twisting to improve the stability and accuracy of the position and attitude control of the quadrotor UAV under uncertainty and external disturbances. Specifically, the adaptive neural network learns to dynamically adjust the sliding surface parameters and control gain, effectively inhibiting the sensitivity to parameter uncertainty and external disturbances, while the super-twisting sliding mode control ensures that the sliding trajectory converges in finite time and reduces the chattering phenomenon. In addition, the quadrotor UAV system is divided into a fully-actuated subsystem and an under-actuated subsystem, each of which contains two control inputs and the appropriate control algorithms are designed respectively, and the stability of the algorithm is demonstrated by means of a Lyapunov function in finite time. The proposed control method for quadrotor UAVs is validated through numerical simulations conducted in the Matlab/Simulink environment.

Design of Fractional-Order Non-Singular Terminal Sliding Mode Observer Sensorless System for Surface-Mounted Permanent Magnet Synchronous Motor

A new sensorless speed control system for a fractional-order terminal non-singular sliding mode surface-mounted permanent magnet synchronous motor is proposed. The fractional terminal non-singular sliding mode surface, which can converge in finite time, is designed by combining the fractional-order control theory with the terminal attractor concept. Then, a new control rate is proposed to reduce system buffeting. Secondly, an adaptive back electromotive force filter is designed to reduce the harmonics in the sliding mode function estimation and improve the observation accuracy. In addition, the theoretical analysis of the designed system proves that the system can converge in a finite time. Then, a fraction-order phase-locked loop with variable factors is designed to make the system more capable of tracking the rotor. Finally, a simulation and experiment platform is built, and a comparison experiment is carried out, which proves that the designed algorithm has a stronger rotor position tracking ability and a better dynamic performance of the system.

Event-triggered H∞ control for uncertain discrete-time singular systems via sliding mode approach

This article analyzes the event-triggered (ET) scheme for uncertain discrete-time singular systems via [Formula: see text] sliding mode control (SMC). The issue of network delay is taken into account, and a Bernoulli stochastic variable is used to explain its distribution feature. A sliding mode surface (SMS) function is built by using ET scheme, and the corresponding sliding mode dynamics (SMD) is combined. Then, based on Lyapunov-Kravoskii functional (LKF) stability theory and linear matrix inequality (LMI) technology, [Formula: see text]-admissibility criterion for closed-loop SMD is deduced. Additionally, an improved SMC rule based on ET strategy is created so that the system trajectories can be driven onto the prescribed SMS in finite time. Finally, the effectiveness of the approach is demonstrated by three simulated examples.

Sliding mode control for nonlinear semi-Markov jump systems with cyber attacks via fuzzy logic

This paper studies the security control problem of semi-Markov jump systems. First, the parameter uncertainty, the time-varying delay, the nonlinear function and the cyber attack are considered in the system. Second, the nonlinear function is linearized by the fuzzy logic rule. A sliding mode surface is designed to obtain an equivalent controller and get a sliding mode dynamic system. By constructing Lyapunov functions of the mode dependence, a sufficient condition for H∞ asymptotic stability of the system is obtained. Then, an adaptive sliding mode controller is established, and the original system reaches the sliding mode surface in a finite time. Finally, two examples verify the correctness and practicality of the proposed theory.

A fixed-time nonsingular terminal sliding mode control based on radial basis function neural network for vehicle active front steering system

In our work, a novel fixed-time nonsingular terminal sliding mode controller is developed to improve the control performance for the active front steering system of electric vehicles. First, the sliding mode surface and the sliding mode convergence law are constructed so that the sliding variable can be stabilized to zero at a fixed time. Moreover, the radial basis function neural network is introduced to estimate the systematic uncertainties, which can make the system have stronger anti-disturbance ability. The Lyapunov analysis also is given to verify the fixed-time stability of the whole system. The presented control scheme possesses two appealing advantages, including the strong robustness to perturbations and the fixed-time convergence to zero. Notably, the settling time is independent of the initial value while only related to the controller parameters. Through the joint simulation of CarSim and MATLAB, the given controller is compared with the conventional sliding mode controller and nonsingular terminal sliding mode controller to demonstrate the plausibility and validity of the presented control strategy.

Robust Direct Power Control of Three-Phase PWM Rectifier with Mismatched Disturbances

To effectively eliminate the impacts of both matched and mismatched power disturbances in a three-phase PWM rectifier, this paper proposes a robust direct power control (RDPC) method with a single-loop control structure. Firstly, a nonlinear power model of the three-phase PWM rectifier is established. Then, using the exact feedback linearization method, a linearized power model including matched and mismatched power disturbances is derived and achieves the decoupling of active and reactive power. Secondly, to regulate the DC bus voltage, a sliding-mode controller (SMC) combined with a nonlinear disturbance observer (NDO) is proposed. The proposed SMC combined with an NDO (SMC + NDO) method features a single-loop control structure, which enables a faster response and simpler structure compared to the dual-loop DPC method. By incorporating estimated mismatched power disturbance into the sliding-mode surface, it overcomes the SMC’s defect in incompletely suppressing mismatched disturbances and enables the simultaneous regulation of voltage and active power. Additionally, it effectively reduces sliding-mode chattering. To regulate reactive power, a sliding-mode controller based on the exponential convergence law is designed to suppress matched reactive power disturbances. Finally, the simulation and experimental comparative results demonstrate that the proposed controller exhibits stronger robustness against matched and mismatched power disturbances, as well as a better performance under the constant power load (CPL).