Super-twisting Algorithm Research Articles

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.

Finite-Time Continuous Nonsingular Terminal Modified Adaptive-Gain Super-Twisting Control: Application to a 2-DOF Planar Robot Manipulator System.

This article proposes finite-time continuous nonsingular terminal modified adaptive-gain super-twisting control (FT-CNT-MAG-STC) for the second-order disturbed systems. Compared with existing sliding-mode controllers, the noteworthy improvements of the proposed framework are the fast finite-time convergence, continuous control signal, ease-of-implementation feature, and relaxation of the assumption related to the information on the bounds of the disturbance and its derivative. In the proposed framework, a fast nonsingular terminal sliding surface is first developed such that the singularity problem is avoided and the convergence rate is improved. Then, we design a continuous modified super-twisting algorithm with an adaptive gain, under which the need for the bounds information of the disturbance and its derivative is relaxed and the performance of the closed-loop system is enhanced. Rigorous analysis is provided to prove the finite-time convergence of the system states to small regions containing the origin. We apply the proposed framework to the position control for a 2-DOF planar robot manipulator system. Various experimental results are illustrated to evaluate the effectiveness of the designed position controller.

Seamless Switching Control Strategy for a Power Conversion System in a Microgrid Based on Extended State Observer and Super-Twisting Algorithm

Microgrids can operate stably in both islanded and grid-connected modes, and the transition between these modes enhances system reliability and flexibility, enabling microgrids to adapt to diverse operational requirements and environmental conditions. The switching process, however, may introduce transient voltage and frequency fluctuations, causing voltage and current shocks to the grid and potentially damaging devices and systems connected to the microgrid. To address this issue, this study introduces a novel approach based on the Extended State Observer (ESO) and the Super-Twisting Algorithm (STA). Power conversion systems use Virtual Synchronous Generator (VSG) control and Power-Quality (PQ) control when they are connected to the grid or when the microgrid is not connected to the grid. VSG and PQ share a current loop. Transitioning the reference current generated by the outer loop achieves the switching of control strategies. A real-time observer is designed to estimate and compensate for current fluctuations, disturbances, and variations in id, iq, and system parameters during the switching process to facilitate a smooth transition of control strategies. Furthermore, to enhance the dynamic response and robustness of the system, the Proportional–Integral (PI) controller in the ESO is replaced with a novel super-twisting sliding mode controller based on a boundary layer. The Lyapunov stability principle is applied to ensure asymptotic stability under disturbances. The proposed control strategy is validated through simulation using a seamless switching model of the power conversion system developed on the Matlab/Simulink (R2021b) platform. Simulation results demonstrate that the optimized control strategy enables smooth microgrid transitions, thereby improving the overall reliability of grid operations.

High-performance steering tracking control of open circuit variable-speed pump-controlled steering system for heavy-duty vehicles based on flow nonlinearity compensation

Heavy-duty vehicles with long bodies, a large number of axles and large loads are subject to increasingly high requirements for precise steering technology due to the increasing trend toward energy conservation and intelligent assisted driving as well as variable driving conditions. In this paper, an energy-efficient open circuit variable-speed pump-controlled steering system (OPCEHSSS) adapted for heavy loads is used, but its strong flow output nonlinearity and system nonlinear dynamic behavior greatly impede the steering performance. Therefore, in order to reduce the influence of the flow leakage of the fixed-displacement pump on the system and to ensure that the flow output of the system matches the control model, a mapping model based on the fitting of a two-layer neural network algorithm with a dynamic real-time compensation strategy (FNC) is proposed. In addition, considering the strong robustness of the system even under parameter uncertainty and unknown disturbance, a complex nonlinear mathematical model is established based on OPCEHSSS physical characteristics, and a dual-objective control strategy of steering angle and pressure based on sliding mode control (SMC) is proposed. However, in order to reduce the influence of high-order switching discontinuity on the steering and ensure the fast convergence of the control system, a fast super twisting algorithm (STA) based on double saturation function of the boundary layer is proposed. The experimental results show that the three different controllers can effectively reduce the steering angle error after the introduction of FNC. And in the case of a single axle loaded with 6 tons, the improved new FNC+STA integrated dual-objective control strategy improves the accuracy by 53.16% compared with PID and 40.67% compared with SMC. The steady-state error is maintained within 0.9°, realizing the high-performance steering tracking control of OPCEHSSS for heavy vehicles.

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.

Adaptive continuous barrier function-based super-twisting global sliding mode stabilizer for chaotic supply chain systems

Supply chains face various uncertainties due to the dynamic and unstable nature of today's worldwide market. Introducing these uncertainties to both the upstream and downstream elements of supply chains adds complexity and nonlinearity to them. This paper investigates the dynamic behavior of a chaotic three-echelon supply chain system and designs a finite-time global nonlinear super-twisting sliding mode controller based on an adaptive continuous barrier function technique for stabilizing the defined system under external disturbances and model uncertainties. This method dynamically adapts the controller parameters according to the system's current state using parameter adaptation algorithms. The adaptive barrier function is used to ensure the system's stability, while the super-twisting algorithm is used to speed up the convergence rate and robustness of the system. Moreover, the genetic optimization algorithm has been employed to attain the optimal values of parameters, thereby enhancing the performance of the designed controller. Ultimately, the effectiveness of this research's proposed approach has been evaluated through simulation in the MATLAB-Simulink environment and experimental testing using the Baseline Real-Time Speedgoat test platform. These analyses are paramount and helpful for strategic decision-makers because they allow visualization and control of the states/dynamics of the entire supply chain. The internal parameters of the supply chain are used as control parameters, and different significant states are discovered to achieve synchronization.

Design and real-time implementation of a robust backstepping non-singular integral terminal sliding mode attitude control for a quadrotor aircraft

This paper concerns the problem of robust attitude control of a quadrotor aircraft subjected to modeling inaccuracies and wind disturbances. First, the model dynamics and state space representation of the quadrotor system are designed by considering the impact of disturbances and uncertainties. Then, a novel robust backstepping non-singular integral terminal sliding mode control (BNITSMC) is synthesized for the quadrotor attitude with the aim of enhancing the tracking accuracy. To strengthen the system’s robustness and guarantee the reachability of the sliding surface while reducing chattering, the supertwisting algorithm (ST) is used. Closed-loop stability and state convergence are guaranteed via the Lyapunov theory. Some experimental flight tests have been executed to validate the workability of the developed flight control. The obtained results prove that the recommended technique can provide improved performance in terms of stabilization and tracking precision.

Saturated STA-based sliding-mode tracking control of AUVs: Design, stability analysis, and experiments

In this study, we developed a saturated super-twisting algorithm for autonomous underwater vehicles to address the trajectory tracking problem. On the basis of Lyapunov arguments, we performed a stability analysis of the resulting closed-loop system under the proposed controller, considering the MIMO system dynamics, parametric uncertainties, and external disturbances. Finally, we conducted several real-time experiments to demonstrate the effectiveness and robustness of the proposed control solution as compared to the traditional super-twisting algorithm.

Dynamic performance enhancement of nonlinear AWS wave energy systems based on optimal super-twisting control strategy

This paper presents a Super-Twisting Algorithm (STA) sliding mode control technique as an alternative to the conventional Proportional-Integral (PI) control system. This application is specifically in the context of a nonlinear Archimedes Wave Swing (AWS) device, which functions as a wave energy converter system (WECS) connected to the power grid. The main goal is dynamic performance enhancement of such wave energy systems under network disturbances. Two STA controllers areessential for the rectifier control system in the grid-connected system to capture the most power from waves while limiting losses in the AWS linear generator. In addition, four STA controllers are incorporated into the inverter control loop to preserve the DC link and common coupling voltages at the preset values. The Honey-Badger Algorithm (HBA) is applied for the optimization of gain parameters of the STA controllers, which are compared to the PI gains adjusted using the coot, the hybrid augmented grey wolf optimizer and cuckoo, and PSO search techniques to assess the worthiness of adopting this new control approach. The grid-connected AWS experiences a variety of faults, includingsymmetrical and unsymmetrical faults with successful and unsuccessful breaker reclosures. Finally, the system is experimentally validated using the OP4510 real-time simulator. The experimental results reveal that the HBA-STA controllers outperformPI controllers in omitting fluctuations in the regulated variables, making the STA a strong contender as a control method.

Finite-time model-free robust synchronous control of multi-lift overhead cranes based on iterative learning

A model-free control method based on iterative learning law combined with adaptive super-twisting is proposed to realize the synchronous coordination control of multi-lift overhead crane system for the problems of inaccurate modeling, system parameter variation, and disturbance uncertainty that exist in multi-lift overhead crane system. First, a load-coupling model of the double-container overhead crane considering the deformation tangential force in the interlocking mode is established. Second, a time-varying sliding mode surface (TSMC) designed using nonlinear functions effectively improves the convergence speed of the system state. The method of iterative learning control is introduced to compensate the system dynamics to achieve model-free control, and the dynamic iterative learning control (DILC) is designed to improve the convergence speed of the error of the system and the steady-state performance. To suppress uncertainty disturbances and avoid control gain overestimation, an adaptive gain is added to the generalized super-twisting algorithm, which has the advantages of both finite-time convergence and chattering suppression, and improves the robustness and tracking performance of the multi-lift overhead crane system. The stability of the controlled system is analyzed using Lyapunov stability theory. The simulation experiments illustrate the effectiveness of the proposed synchronization control scheme.

Trajectory tracking control of wheeled mobile robots with skidding and time-varying delay

This paper tackles the problem of trajectory tracking for wheeled mobile robots subject to time-varying input delay and bounded external disturbances. First, we establish a dynamic model for a wheeled mobile robot under sliding and skidding conditions, and determine the maximum allowable input delay that maintains system stability using Razumikhin-type stability analysis without prior knowledge of the variation in delay. The proposed adaptive robust controller combined with super-twisting sliding mode control is resilient to disturbances such as input delay, system uncertainty, and parameter variation. The proposed adaptive law enables real-time modification of switching gain based on tracking error without predefined knowledge of uncertainty bounds. Compared with traditional sliding mode control strategies, the super-twisting algorithm can eliminate chattering phenomenon while combined robust methods further reduce modeling uncertainties’ influence on system performance. Finally, we select an appropriate Lyapunov function to analyze and prove uniformly ultimately bounded of the closed-loop system. MATLAB simulation comparison results demonstrate that this approach achieves high tracking accuracy, faster response speed, and robustness.

An adaptive fault tolerant control method for electromagnetic formation spacecraft with external disturbances

Fault-tolerant control (FTC) is an essential consideration for the reason that the proper functioning of electromagnetic formation spacecraft (EMFS) actuators are challenged by the harsh space environment. An Integral-Type Sliding Mode Control (ISMC) scheme is proposed for actuator faults and external disturbances (AFED) caused by coil failure and external complex environment of EMFS system. Before the system state reaches the sliding mode surface, we use super-twisting algorithm to accelerate the reaching of the sliding mode surface and reduce the chattering. After reaching the sliding surface, a novel nominal proportional passive controller is proposed that integrates a damping term, thereby enhance system robustness and expediting system stabilization. Moreover, the FTC method proposed incorporates adaptive techniques to handle unknown AFED in real-time while ensuring system stability. This paper proposes a new adaptive FTC method that enhances the actuator’s capability without requiring controller reconfiguration. Simulation results illustrate the effectiveness of this method for suppressing AFED in harsh space environment.

Dynamic performance of rotor-side nonlinear control technique for doubly-fed multi-rotor wind energy based on improved super-twisting algorithms under variable wind speed

The paper proposes a nonlinear controller called dual super-twisting sliding mode command (DSTSMC) for controlling and regulating the rotor side converter (RSC) of multi-rotor wind power systems that use doubly-fed induction generators. It was proposed that this controller be developed as an alternative to the direct power control (DPC), which makes use of a pulse width modulation (PWM) strategy to regulate the RSC's functioning. Overcoming the power/current quality issue with the proposed technique (DPC-DSTSMC-PWM) is characterized by great robustness and excellent performance. The designed strategy was contrasted with the standard method of control and other methods already in use. So, the unique proposed control strategy’s robustness, performance, efficiency, and efficacy in enhancing system characteristics were tested and validated in Matlab/Simulink. In both tests, the proposed method resulted in significant improvements, reducing active power ripples by 83.33%, 57.14%, and 48.57% in the proposed tests. When compared with the traditional regulation method, the reduction rates of reactive power ripples are 64.06%, 52.47%, and 68.7% in the tests. However, in contrast to the conventional method, the proposed tests showed a decrease of between 72.46%, 50%, and 76.22% in the value of total harmonic distortion (THD) of the provided currents. These ratios show how effective the proposed plan is in ameliorating and enhancing aspects of the energy system.

Advanced Torque Sharing Function Strategy With Sliding Mode Control for Switched Reluctance Motors

In this paper, an improved torque sharing function control (TSF) using sliding mode control (SMC) is proposed for switched reluctance motor (SRM). First, as for TSF control strategy, due to low increase rate of inductance in the commutation interval, the latter phase is compensated with torque error for torque ripple reduction. Second, SMC is applied in design of speed controller and disturbance observer for better comprehensive performance. Regarding speed controller, the novel sliding mode reaching law is proposed to further suppress the torque ripple and accelerate approaching speed. With respect to the disturbance observer, a modified super-twisting algorithm is employed to enhance the anti-interference ability. Finally, the simulation and experiments are carried out, which verify that the proposed control method behaves better in aspects of the dynamic response and torque ripple suppression, and anti-interference ability.

Multi-Parameter Fuzzy-Based Neural Network Sensorless PMSM Iterative Learning Control Algorithm for Vibration Suppression of Ship Rim-Driven Thruster

Aiming to reduce motor speed estimation and torque vibration present in the permanent magnet synchronous motors (PMSMs) of rim-driven thrusters (RDTs), a position-sensorless control algorithm using an adaptive second-order sliding mode observer (SMO) based on the super-twisting algorithm (STA) is proposed. In which the sliding mode coefficients can be adaptively tuned. Similarly, an iterative learning control (ILC) algorithm is presented to enhance the robustness of the velocity adjustment loop. By continuously learning and adjusting the difference between the actual speed and given speed of RDT motor through ILC algorithm, online compensation for the q-axis given current of RDT motor is achieved, thereby suppressing periodic speed fluctuations during motor running. Fuzzy neural network (FNN) training can be used to optimize the STA-SMO and ILC parameters of RDT control system, while improving speed tracking accuracy. Finally, simulation and experimental verifications have been conducted on the vector control system based on the conventional PI-STA and modified ILC-STA. The results show that the modified algorithm can effectively suppress the estimated speed and torque ripple of RDT motor, which greatly improves the speed tracking accuracy.

Two different controllers-based DPC of the doubly-fed induction generator with real-time implementation on dSPACE 1104 controller board

The direct power command (DPC) of the doubly-fed induction generators (DFIG) has garnered increasing attention due to its simplicity, ease of implementation, and fast dynamic response that distinguished it from other controls. Recently, nonlinear controllers have been suggested to improve the DPC robustness, in particular the minimization of the DFIG power fluctuations. In the present research work, two different controls are used to regulate the DFIG power, where the first is a traditional DPC and the second is the DPC based on neural super-twisting algorithm (NSTA) controllers. The NSTA controllers were used instead of hysteresis comparators in the DPC technique, and the pulse width modulation (PWM) technique was used as a suitable solution instead of the switching table to better manage the state of switches and simplify the control system. The proposed controls were investigated and implemented using Matlab software and Dspace 1104 card with different tests to determine the best control. Experimental and simulation results show the good efficiency of the NSTA controller in improving energy and current quality. Also, the comparison is made between both techniques and the other controls in terms of reducing current harmonic distortions and ratios of the DFIG power fluctuations.

Accuracy Enhancement of Industrial Robots Based on Visual Servoing Using Optimal Adaptive RBFNN Integral Terminal Fractional-Order Super-Twisting Algorithm

This paper proposes a novel adaptive robust control scheme for accuracy enhancement of eye-to-hand photogrammetry-based industrial robots subject to uncertainties. The proposed method uses two control loops: internal and external loops. The former is the dynamic controller designed for controlling the robot’s joints. The external loop is the kinematic controller to minimize the error of the end-effector detected by the photogrammetry sensor. An adaptive integral terminal fractional-order super-twisting algorithm (AITFOSTA) is developed and employed for both control loops. AITFOSTA is an integral sliding-mode controller (ISMC) whose nominal control law is terminal. Its switching part is replaced with a fractional-order super-twisting algorithm (FOSTA), reducing the chattering to a great extent while rejecting the uncertainties. Additionally, an adaptive uncertainty and disturbance estimator based on radial basis function neural networks (RBFNNs) is designed and employed to reduce the uncertainty bounds, contributing to further chattering reduction. The stability analysis of the proposed controller is also presented. Simulation and experimental results show the superiority of the proposed method over other well-known approaches by reaching an unprecedented tracking accuracy, i.e. 0.06 mm and 0.18[Formula: see text] for position and orientation, respectively.

Exponential super-twisting control for nonlinear systems with unknown polynomial perturbations

The study focuses on the control of nonlinear dynamic systems in the presence of parameter uncertainties, unmodeled dynamics, and external disturbances. The lumped perturbation is assumed to be bounded within a polynomial in the system state with the polynomial parameters and degrees unknown a priori such that it accommodates a quite wider range dynamic systems. Based on the studies in recent super-twisting algorithm designs and the idea from adaptive sliding mode control for nonlinear systems with uncertainties, we propose a novel adaptive super-twisting algorithm with exponential reaching law, or exponential super-twisting algorithm (ESTA), for the high-stability and acceptable accuracy control of the aimed nonlinear dynamics. The stability analysis and practical finite-time (PFT) convergence are proven using Lyapunov theory and an intuitive analysis of the control behaviour. Simulations are performed to compare the proposed ESTA with the existing super-twisting method and the traditional proportional integral differential control. The simulation results demonstrate the effectiveness of the proposed ESTA in terms of the fastest settling time and the smallest overshoot.

Finite-Time Robust Path-Following Control of Perturbed Autonomous Ground Vehicles Using a Novel Self-Tuning Nonsingular Fast Terminal Sliding Manifold

This work presents a finite-time robust path-following control scheme for perturbed autonomous ground vehicles. Specifically, a novel self-tuning nonsingular fast-terminal sliding manifold that further enhances the convergence rate and tracking accuracy is proposed. Then, uncertain dynamics and external disturbances are estimated by a high-gain disturbance observer to compensate for the designed control input. Successively, a super-twisting algorithm is incorporated into the final control law, significantly mitigating the chattering phenomenon of both the input control signal and the output trajectory. Furthermore, the global finite-time convergence and stability of the whole proposed control algorithm are proven by the Lyapunov theory. Finally, the efficacy of the proposed method is validated with comparisons in a numerical example. It obtains high control performance, reduced chattering, fast convergence rate, singularity avoidance, and robustness against uncertainties.

A super-twisting algorithm combined zeroing neural network with noise tolerance and finite-time convergence for solving time-variant Sylvester equation

The time-variant Sylvester equation (TVSE) plays a highly crucial role in many areas of scientific research and engineering applications. Recently, zeroing neural network (ZNN) has been prevailed as an effective solution for time-variant problem. However, the majority of the existing ZNN solution schemes for TVSE are either only considered in noiseless environments or are unable to converge in a finite amount of time, and while there is a pressing need for effective and noise-resisting ZNNs to fulfill real-time applications’ requirements in the actual world. For this reason, inspired by the advantages offered by super-twisting algorithm (STA), being a well-accepted second order sliding mode method, this paper introduces STA into ZNN and establishes a novel STZNN model for TVSE solving. Actually, the intrinsic properties of STA, such as finite-time convergence and anti-noise robustness, are perfectly in line with what an efficient and noise-resisting ZNN model desired to be. Hence, the STZNN model can realize a much quick convergence time and a much great resistance against noise. Moreover, rigorous theoretical analyses on the case of zero noise, constant noise and dynamic bounded noise are conducted, and the illustrative verification not only verifies the STZNN’s convergence property, validates its superior ability in convergence time and noise resisting compared to the gradient-based neural network (GNN), the conventional ZNN (CZNN) model and the integration-enhanced ZNN (IEZNN) model, but also shows the STZNN model’s capability in addressing moving localization problems based on angle of arrival (AoA) and time difference of arrival (TDOA).