Sliding Mode Control Law Research Articles

Event-Triggered Supercavitating Vehicle Terminal Sliding Mode Control Based on Non-Recursive Observation

Supercavitating vehicles present significant issues in controller design due to their multiphase flow-coupling characteristics. This study addresses force analysis and the construction of a 6-degree-of-freedom mathematical model for a supercavitating vehicle. A terminal sliding mode control law is intended to guarantee the quick tracking of the command signal for high-precision attitude control. To drastically lower the frequency of actuation and communication, a mechanism to trigger events is also introduced into the control link. A disturbance observer, which estimates system uncertainty using a non-recursive differentiator, improves the robustness of the system. The Lyapunov approach is used to prove that the system is stable. Numerical simulation results validate that the proposed method enhances control accuracy and robustness. The event-trigger mechanism reduces the execution frequency to 18.59%, effectively reducing the communication burden.

Robust design of a two-stage composite sliding mode controller for enhanced performance in large-scale systems

This paper introduces an innovative composite sliding mode control strategy tailored for large-scale system, specifically tackling the intricate task of formulating a sliding mode control law for singularly perturbed systems. This paper delineates the development of a composite controller by dissecting it into subsystem controllers for both ‘slow’ and ‘fast’ subsystems, exploring its effectiveness in managing matched bounded external disturbances within the context of large-scale system. While sliding mode control proves to be a robust solution for handling uncertainty and disturbances, its inherent complexity and discontinuous characteristics pose significant challenges in crafting designs suitable for singularly perturbed systems.

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.

Development of sliding mode control based on diagonal recurrent neural network for coupled tank system

This study presents the development of sliding mode control (SMC) using the diagonal recurrent neural network (DRNN) for nonlinear systems. Firstly, the SMC for linear systems is developed for nonlinear coupled tank system. Second, the DRNN is used to design the equivalent part of the SMC law, which is performed to approximate the dynamics of a controlled process. Third, the sliding surface for the switching control is developed using the DRNN. The DRNN parameters are tuned using Lyapunov function to achieve the controlled process stability. For the developed scheme, discontinuous signum function is used to compensate the chattering phenomenon. The developed scheme is applied for controlling the uncertain nonlinear coupled tank system. The simulation results indicate that the developed scheme can respond to the effects of system uncertainties compared to other existing schemes.

Improved sliding mode control law for wind power systems

Improved sliding mode control law for wind power systems

Neural network-based practical fixed-time nonsingular sliding mode tracking control of autonomous surface vehicles under actuator saturation

The article considers the fixed-time tracking control of autonomous surface vehicles (ASVs) subject to actuator saturation. A novel sliding variable with state-dependent exponents is first constructed to alleviate chattering and overcome the singularity. By using the proposed fixed-time sliding variable and the neural network (NN), an NN-based fixed-time sliding mode control (SMC) scheme is developed. Besides, an auxiliary system is utilized to solve the input saturation constraint. Unlike some existing results for ASVs with input saturation, the designed fixed-time SMC law does not require assumptions on a priori upper bound of the lumped disturbances. Through Lyapunov analysis, it is proven that the tracking error can converge to a bounded region in a fixed time. Simulation examples are given to show the validity of the proposed control scheme.

Synchronization of delayed stochastic reaction–diffusion Hopfield neural networks via sliding mode control

Synchronization of stochastic reaction–diffusion Hopfield neural networks with s-delays via sliding mode control is investigated in this article. To begin with, we choose suitable functional space for state variables, then the system is transformed into a functional differential equation in an infinite-dimensional Hilbert space by using appropriate functional analysis technique. Based on above preliminary preparation, sliding mode control (SMC) is constructed to drive the error trajectory into the designed switching surface. Specifically, the switching surface is constructed as linear combination of state variables, which is related to control gains. Then novel SMC law is designed which involving delay, reaction diffusion term, and reaching law. Furthermore, the criterion of mean-square exponential synchronization for stochastic delayed reaction–diffusion Hopfield neural networks with s-delays is given in the form of matrix form. This criterion is less restrictive and easy to check in computer. Meanwhile, a different novel Lyapunov–Krasovskii functional (LKF) mixed with Itô’s formula, Young inequality, Hanalay inequality is employed in this proof procedure. At last, a numerical example is presented to validate the availability of theoretical result. The simulation is based on the finite difference method, and numerical result coincides with the theoretical result proposed.

Robust Hybrid Visual Servoing of Omnidirectional Mobile Manipulator With Kinematic Uncertainties Using a Single Camera.

A robust hybrid visual servoing (HVS) method for a single camera-mounted omnidirectional mobile manipulator (OMM) with kinematic uncertainties caused by slipping is proposed herein. Most existing studies pertaining to the visual servoing of mobile manipulators do not consider the kinematic uncertainties and the singularity of the manipulator that can occur during actual operations; furthermore, they required external sensors other than a single camera. In this study, the kinematics of an OMM are modeled considering kinematic uncertainties. Accordingly, an integral sliding-mode observer (ISMO) is designed to estimate the kinematic uncertainties. Subsequently, an integral sliding-mode control (ISMC) law is proposed to achieve robust visual servoing using the estimates of the ISMO. Additionally, an ISMO-ISMC-based HVS method is proposed to address the singularity issue of the manipulator; this method guarantees both robustness and finite-time stability in the presence of kinematic uncertainties. Overall, the entire visual servoing task is performed using only a single camera attached to the end effector without any other external sensors, unlike in previous studies. The stability and performance of the proposed method are verified numerically and experimentally in a slippery environment that generates kinematic uncertainties.

A Novel reaching law sliding mode control method of PMSM considering iron loss

The loss of motor is ignored in the traditional speed control, while the loss minimization control (LMC) takes the high efficiency of the motor and does not consider the speed performance. Therefore, with the iron loss torque as the bond between efficiency and dynamic performance, this paper presents a sliding mode control method under the loss minimization target to achieve the high efficiency and high dynamic performance of permanent magnet synchronous motor (PMSM). Firstly, a d-axis current compensation method based on Taylor series expansion of virtual power loss (VPL) is proposed to minimize the loss of PMSM. Secondly, to eliminate the influence of iron loss on the speed performance, a PMSM speed tracking model including iron loss is established. Then, an adaptive sliding mode reaching law with disturbance estimation (ASMRLDE) is proposed to avoid energy consumption and the sliding mode chattering of the system caused by excessive sliding mode switch gain by adjusting the speed at which the system state reaches the sliding surface. Finally, the superiority of the proposed sliding mode control method under the loss minimization target in terms of loss minimization and speed control of the motor is proved through multi-condition experiments.

Trajectory Tracking Control of Mobile Manipulator Based on Improved Sliding Mode Control Algorithm

Research on trajectory tracking control for climbing welding robots holds significant importance in the field of automated welding. However, existing trajectory tracking methods suffer from issues such as jitter and slow speed. In this paper, an improved sliding mode control strategy is proposed based on the self-designed wall-climbing welding mobile manipulator. Firstly, a new adaptive sliding mode control strategy is proposed for the mobile platform based on the kinematic model. By introducing a new approach law, the controller is designed when the distance between the center of mass is unknown. Secondly, regarding the manipulator, we analyze simplified dynamic equations, extract uncertain components, and utilize a CNN for compensation. This compensation strategy is integrated into the sliding mode control law, achieving precise control over the manipulator and effectively resolving issues like slow tracking speeds, large errors, and chattering. The stability of the robot control system is proved by the Lyapunov function. Through simulation analysis and experimental validation, the proposed control method is confirmed to be feasible and superior.

Active and passive heave compensation system based on feedback linearization sliding mode variable structure control

This study presents a novel electric-hydraulic servo system with an active–passive lift compensation feature designed for a lifting crane used in offshore operations. Additionally, the study explores the control methodology of this system. Firstly, the principle of the combined active–passive lift-compensated system is explained, and the mathematical model of the response is established. To eliminate the strong nonlinearities inherent and mismatched term, the method of exact input-state linearization is employed. For observing the uncertain disturbance terms in the model, a new type of expanded state sliding mode observer(ESSMO) is designed. Subsequently, a control strategy of sliding mode with variable structure is designed using the method of hyperbolic convergence law. The stability of the controller is proved based on Lyapunov’s stability theorem. Finally, the control method is simulated and analyzed under different working conditions and compared with traditional PID control and sliding mode control strategies directly designed by the nonlinear model. The simulation results demonstrate that the feedback linearized hyperbolic convergence law sliding mode control strategy not only reduces dependence on exact parameters of the original system but also exhibits strong robustness and suppression of model nonlinearities and parameter uncertainty.

Observer-based SMC for discrete semi-Markov switching models

This study focuses on the observer-based sliding mode control (SMC) for discrete stochastic switching models, where the semi-Markov kernel information is incomplete. Because the sensors do not always have direct access to the state vector in a complex environment, an observer-based output measurement is considered to estimate the system state. In contrast to previous works, the observer-based strategy is first investigated in studying the SMC for semi-Markov switching systems under the discrete framework. The sufficient condition for achieving mean-square stability is proposed to solve the desired observer and controller gains by utilizing the upper bound of sojourn time, along with the Lyapunov function that pertains to the system mode and the elapsed time. A mode-dependent SMC law is also constructed to ensure that the system state can reach the specified sliding region. Finally, the efficiency of the proposed method is demonstrated through the single-link robot arm model.

Event-triggered sliding mode control for singular discrete-time fuzzy Markov jump networked systems

In this present paper, the event-triggered sliding mode control (SMC) issue for a type of singular networked Markov jump systems with partly unknown transition probabilities (TPs) is mainly investigated, and it is modeled by discrete-time Takagi–Sugeno fuzzy systems. To save network resources, a mode-dependent event-triggered scheme (ETS) is applied to improve transmission efficiency. Subsequently, a common sliding surface is designed, which can effectively reduce the impact of the jumping process. Therein, the stochastic admissibility criterion for the system with [Formula: see text] performance [Formula: see text] is derived in the sense of partly unknown TPs. Moreover, a novel SMC law that guarantees the reachability of the quasi-sliding mode is given in view of the reaching condition. Finally, the validity of the presented theorems is demonstrated by a numerical example.

Sliding Mode Control for Uncertain 2-D FMII Systems Under Stochastic Scheduling.

In this article, the sliding mode control (SMC) problem is addressed for two-dimensional (2-D) systems depicted by the second Fornasini-Marchesini (FMII) model. The communication from the controller to actuators is scheduled via a stochastic protocol modeled as Markov chain, by which only one controller node is permitted to transmit its data at each instant. A compensator for other unavailable controller nodes is introduced by means of previous transmitted signals at two most adjacent points. To characterize the features of 2-D FMII systems state recursion and stochastic scheduling protocol, a sliding function associated with the states at both the present and previous positions is constructed, and a scheduling signal-dependent SMC law is designed. By constructing token- and parameter-dependent Lyapunov functionals, both the reachability of the specified sliding surface and the uniform ultimate boundedness in the mean-square sense of the closed-loop system are analyzed and the corresponding sufficient conditions are derived. Furthermore, an optimization problem is formulated to minimize the convergent bound via searching desirable sliding matrices, meanwhile, a feasible solving procedure is provided by using the differential evolution algorithm. Finally, the proposed control scheme is further demonstrated via simulation results.

A novel preassigned‐time sliding mode control method for synchronization of T‐S fuzzy stochastic complex networks with time‐varying delay

AbstractThis paper investigates the finite‐time synchronization issue of Takagi‐Sugeno (T‐S) fuzzy stochastic complex networks (TSFSCN) with disturbances and time‐varying delays using the preassigned‐time sliding mode control (SMC) strategy. A novel fuzzy SMC law is designed by introducing a time‐varying function, ensuring that the error system reaches the sliding mode surface (SMS) within any preassigned time and converges to zero along the SMS. The arrival time and sliding time are independent of design parameters and initial values, enhancing the stability and controllability of the system. Additionally, the adoption of a continuous function to replace the sign function reduces the chattering phenomenon in the system. Based on Lyapunov theory and finite‐time SMC strategy, a sufficient condition is derived for the system to achieve arbitrary preassigned‐time synchronization. Finally, the effectiveness of the proposed control method is verified through two examples.

Sensor fault detection and compensation with performance prescription for robotic manipulators

This paper focuses on sensor fault detection and compensation for robotic manipulators. The proposed method features a new adaptive observer and a new terminal sliding mode control law established on a second-order integral sliding surface. The method enables sensor fault detection without the need to know the bounds on fault value and/or its derivative. It also enables fast and fixed-time fault-tolerant control whose performance can be prescribed beforehand by defining funnel bounds on the tracking error. The ultimate boundedness of the estimation errors for the proposed observer and the fixed-time stability of the control system are shown using Lyapunov stability analysis. The effectiveness of the proposed method is verified using numerical simulations on two different robotic manipulators, and the results are compared with existing methods. Our results demonstrate performance gains obtained by the proposed method compared to the existing results.

Fixed‐time sliding mode consensus tracking for second‐order nonlinear multi‐agent system with persistent dwell‐time switching topologies

AbstractThis article investigates the problem of fixed‐time sliding mode consensus tracking for nonlinear second‐order multi‐agent system, in the presence of disturbances and actuator attacks. The interaction topology graph of multi‐agent system is directed and switched, and the switching topologies satisfy a more general persistent dwell‐time switching mechanism. To account for the disturbances, actuator attack, and switching topologies, a nonsingular sliding mode control law with distributed switching scheme is constructed to guarantee the fixed‐time reachability to a sliding surface. By using multiple Lyapunov functions, some new sufficient criteria are derived for fixed‐time consensus tracking of the multi‐agent system with persistent dwell‐time switching topologies. To illustrate the proposed approach, we present a numerical example and a physical example of the single pendulum model.

Adaptive integral sliding-mode finite-time control with integrated extended state observer for uncertain nonlinear systems

For the typical uncertain nonlinear systems subjected to controller gain variation and disturbances, an integrated adaptive robust controller, called integral sliding-mode finite-time controller with an integrated extended state observer (ISFC-IESO), is proposed. The designed controller mainly consists of an integrated ESO (IESO) unit and an integral sliding-mode control (ISMC) unit. The IESO unit is composed of improved linear and nonlinear ESOs which are designed to automatically switch each other, with the aim of enhancing disturbance estimation capability. Moreover, the ISMC unit produces an integral sliding-mode control law (SMCL) based on the newly designed integral sliding-mode surface function (SMSF) and sliding-mode reaching law (SMRL). The integral SMSF is developed based on the n-th estimated state and a designed convergence function of tracking error to suppress the influence of the disturbance estimation error. On this basis, SMRL is further presented by combining integral SMSF with a specially designed variable boundary layer thickness saturation function, for the purpose of eliminating chattering and enhancing robustness. Finally, fourteen control methods are compared to illustrate the effectiveness and superiority of the proposed ISFC-IESO.

Adaptive Fuzzy Sliding Mode Control and Dynamic Modeling of Flap Wheel Polishing Force Control System

Polishing force is one of the key process parameters in the polishing process of blisk blades, and its control accuracy will affect the surface quality and processing accuracy of the workpiece. The contact mechanism between the polishing surface and flap wheel was analyzed, and the calculation model of the polishing force and nonlinear dynamic model of the polishing force control system was established. Considering the influence of friction characteristics, parameter perturbation, and nonlinear dead zone on the control accuracy of the polishing force system, an adaptive fuzzy sliding mode controller (AFSMC) was designed. AFSMC uses a fuzzy system to adaptively approximate the nonlinear function terms in the sliding mode control law, adopts an exponential approach law in the switching control part of the sliding mode control (SMC), and designs the adaptive law for adjustable parameters in the fuzzy system based on the Lyapunov Theorem. Simulation and experimental results show that the designed AFSMC has a fast dynamic response, strong anti-interference ability, and high control accuracy, and it can reduce SMC high-frequency chatter. Polishing experiments show that compared with traditional PID, AFSMC can improve the form and position accuracy of the blade by 42% and reduce the surface roughness by 50%.