Terminal Sliding Mode Approach Research Articles

Enhanced tracking control for n-DOF robotic manipulators: A fixed-time terminal sliding mode approach with time delay estimation

This work proposes a fixed-time terminal sliding mode control scheme with time delay estimation (FxTSM-TDE) for unknown nonlinear robotic systems under uncertainties and unknown bounded disturbances. The idea of the fixed-time terminal sliding mode control method (FxTSM) is thoroughly explained and analyzed. The FxTSM approach has been used to achieve nonsingular fixed-time control, non-chatter control inputs, and superior trajectory tracking performance. Then, the proposed approach for estimating the unknown robot dynamics utilizes the TDE approach. The Lyapunov analysis is used to establish the fixed-time stability of the system. The effectiveness of the suggested approach is evaluated, demonstrated, and contrasted with the existing control schemes by illustrating the results of the proposed method's enhanced performance in tracking accuracy, robustness, and convergence speed when implemented in robotic manipulator dynamics. The results indicate that the existing scheme has corresponding root mean square (RMS) error values of 0.0235 and 0.0283, while the proposed scheme has values of 0.0178 and 0.0188, respectively.

Research on Fourier Coefficient-Based Energy Capture for Direct-Drive Wave Energy Generation System Based on Position Sensorless Disturbance Suppression

In order to improve the energy capture efficiency of direct-drive wave power generation (DDWEG) systems and enhance the robustness of the reference power tracking control, a Fourier coefficient-based energy capture (FCBEC) and a position sensorless disturbance suppression (PSDS) control strategy are proposed. For energy capture, FCBEC is proposed to construct the objective function by maximizing the average power over a period of time and expanding the variables in the Fourier basis when the maximum power is captured, which is used as the basis for obtaining the reference trajectory. To address the limitations of the mechanical encoder, the position sensorless technique, based on a sliding mode observer (SMO), is used in the power tracking control, and the position information is obtained through an inverse tangent function. The perturbation caused by the inverse electromotive force error in the system is theoretically analyzed. A full-order terminal sliding mode approach is employed to design a current controller that suppresses the perturbation and ensures accurate tracking of the reference current. Simulation results show that the ocean-wave energy capture strategy proposed in this paper can make the energy captured by the PTO reach the optimal value under the impedance matching condition, and that the response speed and robustness of the full-order terminal sliding mode are better than the traditional PI control.

Disturbance-rejection position tracking control of industrial robots via a discrete-time super-twisting observer–based fast terminal sliding mode approach

Disturbance-rejection position tracking control of industrial robots via a discrete-time super-twisting observer–based fast terminal sliding mode approach

Fixed-Time Aircraft Spin Recovery Control Based on a Nonsingular Integral Terminal Sliding Mode Approach

This paper introduces a control strategy to recover from various spin motions to level trim flight conditions, utilizing a fixed-time nonsingular terminal sliding mode approach to minimize altitude loss. Firstly, an integral terminal sliding mode surface is constructed to guarantee the tracking errors of the spin recovery system converge to the origin within a fixed time and avoid the singularity problem. Next, a fixed-time type reaching law is proposed to weaken the chattering phenomenon and guarantee terminal sliding hyperplanes converge to zero in a fixed time. Furthermore, the stability analysis indicates the fixed-time convergence stability of the spin recovery control system and provides an accurate calculation of the settling time. Finally, comparative simulations are performed to validate the effectiveness and superiority of the developed spin recovery control scheme.

Finite-Time Robust Flight Control of Logistic Unmanned Aerial Vehicles Using a Time-Delay Estimation Technique

This paper proposes a cascaded dual closed-loop control strategy that incorporates time delay estimation and sliding mode control (SMC) to address the issue of uncertain disturbances in logistic unmanned aerial vehicles (UAVs) caused by ground effects, crosswind disturbances, and payloads. The control strategy comprises a position loop and an attitude loop. The position loop, which functions as the outer loop, employs a proportional–integral–derivative (PID) sliding mode surface to eliminate steady-state error through an integral component. Conversely, the attitude loop, serving as the inner loop, utilizes a fast nonsingular terminal sliding mode approach to achieve finite-time convergence and ensure a quick system response. The time-delay estimation technique is employed for the online estimation and real-time compensation of unknown disturbances, while SMC is used to enhance the robustness of the control system. The combination of time-delay estimation and SMC offers complementary advantages. The stability of the system is proven using Lyapunov theory. Hardware-in-the-loop simulation and flight tests demonstrate that the control law can achieve a smooth and continuous output. The proposed control strategy can be effectively applied in complex scenarios, such as hovering, crash recovery, and high maneuverability flying, with significant practicality in engineering applications.

Terminal sliding mode attitude tracking control for unmanned vehicle with predefined-time stability

In this paper, we proposed a predefined-time terminal sliding mode approach for attitude tracking control of unmanned aerial vehicle (UAV). In order to obtain the high convergence speed and steady-state performance controller, the modified non-singular terminal sliding mode control (TSMC) we adopted can switch sliding mode surfaces under different conditions. The system stability is achieved within a predefined time, which can be set by modifying the explicit parameters in advance. Due to the existence of model uncertainties and unknown external disturbances, an adaptive neural network-based approach is applied to compensate the error between the actual and nominal model without requiring any prior knowledge of the disturbances. Several comparative studies are carried out between the proposed approach and other predefined-time techniques in previous work, and simulation results and experimental results are presented to validate the correctness of analysis and superiority of the proposed control scheme.

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.

A Trajectory Tracking Control Based on a Terminal Sliding Mode for a Compliant Robot with Nonlinear Stiffness Joints.

A nonlinear stiffness actuator (NSA) can achieve high torque/force resolution in the low stiffness range and high bandwidth in the high stiffness range. However, for the NSA, due to the imperfect performance of the elastic mechanical component such as friction, hysteresis, and unmeasurable energy consumption caused by former factors, it is more difficult to achieve accurate position control compared to the rigid actuator. Moreover, for a compliant robot with multiple degree of freedoms (DOFs) driven by NSAs, the influence of every NSA on the trajectory of the end effector is different and even coupled. Therefore, it is a challenge to implement precise trajectory control on a robot driven by such NSAs. In this paper, a control algorithm based on the Terminal Sliding Mode (TSM) approach is proposed to control the end effector trajectory of the compliant robot with multiple DOFs driven by NSAs. This control algorithm reduces the coupling of the driving torque, and mitigates the influence of parametric variation. The closed-loop system’s finite time convergence and stability are mathematically established via the Lyapunov stability theory. Moreover, under the same experimental conditions, by the comparison between the Proportion Differentiation (PD) controller and the controller using TSM method, the algorithm’s efficacy is experimentally verified on the developed compliant robot. The results show that the trajectory tracking is more accurate for the controller using the TSM method compared to the PD controller.

Second‐order adaptive integral terminal sliding mode approach to tracking control of robotic manipulators

A second-order adaptive integral terminal sliding mode controller is proposed for the trajectory tracking control of robotic manipulators with uncertainties. A second-order integral terminal sliding mode surface is designed for which an integral sliding mode (ISM) surface and a fast nonsingular integral terminal sliding mode surface are combined. By using the ISM surface, the reaching phase is removed, which enhances system robustness. The steady-state error is reduced because of the presence of an error integral term. A fast second-order nonsingular integral terminal sliding mode surface is employed to ensure that the ISM surface is able to converge to zero rapidly within a finite period of time without leading to a singularity problem. The control input of the proposed controller is continuous. Thus, the chattering phenomenon is removed. An adaptation technique is employed to estimate the upper bound of unknown lumped disturbance. The second-order derivative of position is calculated using a robust differentiator, making it practical. Simulations and experiments show that the proposed scheme improves the tracking performance and eliminates chattering.

Incorporating fast and intelligent control technique into ecology: A Chebyshev neural network-based terminal sliding mode approach for fractional chaotic ecological systems

In the present study, a new neural network-based terminal sliding mode technique is proposed to stabilize and synchronize fractional-order chaotic ecological systems in finite-time. The Chebyshev neural network is implemented to estimate unknown functions of the system. Moreover, through the proposed Chebyshev neural network observer, the effects of external disturbances are fully taken into account. The weights of the Chebyshev neural network observer are adjusted based on adaptive laws. The finite-time convergence of the closed-loop system, which is a new concept for ecological systems, is proven. Then, the dependency of the system on the value of the fractional time derivatives is investigated. Lastly, the proposed control scheme is applied to the fractional-order ecological system. Through numerical simulations, the performance of the developed technique for synchronization and stabilization are assessed and compared with a conventional method. The numerical simulations strongly corroborate the effective performance of the proposed control technique in terms of accuracy, robustness, and convergence time for the unknown nonlinear system in the presence of external disturbances.

Adaptive Integral-Type Terminal Sliding Mode Control for Unmanned Aerial Vehicle Under Model Uncertainties and External Disturbances

This paper proposes an adaptive integral-type terminal sliding mode approach for the attitude and position tracking control of a quadrotor UAV subject to model uncertainties and external disturbances. First, an integral-type terminal sliding tracker is designed to attain the quadrotor UAV tracking performance in finite time when the upper bound of perturbations and uncertainties are known. Next, an adaptation law is proposed and a modified parameter-tuning integral-type terminal sliding mode tracking control scheme is designed to compensate of the model uncertainties and external disturbances. The stability and finite time convergence of the proposed approach is verified using the Lyapunov theory. Its performance is assessed using a simulation study encompassing various scenarios. Low chattering dynamics, fast convergence rate, and absence of singularities are the main features of the proposed approach.

Design of a chattering‐free integral terminal sliding mode approach for DFIG‐based wind energy systems

SummaryThis article proposes a Fuzzy Second Order Integral Terminal Sliding Mode (FSOITSM) control approach for DFIG‐based wind turbines subject to grid faults and parameter variations. Since traditional terminal sliding mode control (SMC) suffers from singularity, a novel integral terminal sliding manifold is proposed to eliminate chattering and improve the wind turbine's performance in the presence of faults and disturbances. A fuzzy system is proposed to auto‐tune the controllers' gains and ensures the invariance of the sliding surfaces even under heavy uncertainties, thus further improving the reliability and performance of the proposed controller. The performance of the proposed approach was assessed under various operating conditions. A comparison analysis with a standard SMC approach as well as the state of the art in voltage sag mitigation was also carried over. Reliability, robustness, and power availability under faulty grid conditions are among the main features of the proposed approach. In addition, the proposed approach exhibited chattering free dynamics and enabled the finite time convergence of the sliding manifold and overcame the singularity problem associated with standard TSMC.

Robust adaptive neuronal controller for exoskeletons with sliding-mode

A robust neural adaptive integral sliding mode control approach is proposed in the present paper for nonlinear exoskeleton systems. The proposed control technique is composed of two parts: an adaptive neural network controller and an adaptive integral terminal sliding mode controller. The adaptive laws are developed to estimate unknown parameters and ensure asymptotic stability of the closed-loop system. Only classical system’s properties are supposed to be known, such as the bounds on some parameters. The unknown dynamics of the system are estimated on line by the neural network control part. The proposed adaptive control strategy is designed to ensure the reaching of the sliding surface with enhanced tracking performance. The singularity problem of the terminal sliding mode approach is overcomed without adding any constraint. The closed-loop stability of the system in the sense of Lyapunov is demonstrated. The effectiveness of the proposed approach is tested in real time application with healthy human subjects by performing passive arm movements using a 2-DOF upper limb exoskeleton.

Nonlinear robot system finite time consensus control using an adaptive terminal sliding mode approach in presence of input saturation and external disturbance

ABSTRACT In this paper, finite-time consensus control method is presented for a robot nonlinear multi-agent system. To achieve the goal of finite-time consensus control in the presence of input saturation as well as external disturbance, a new adaptive-terminal sliding mode control method has been proposed. The adaptive method is used to handle an external disturbance with unknown bound, while the terminal sliding mode makes it possible to achieve finite-time consensus and reduce settling and reaching times. In the proposed method, the resulting control signals are always below the saturation range, and of course the external disturbance is estimated in a limited time. The simulation results on nonlinear multi-agent robot system show the optimal performance of the proposed method.

Robust Performance Improvement of Lateral Motion in Four-Wheel Independent-Drive Electric Vehicles

In this article a robust two-layer control scheme is proposed to improve the performance of Four-Wheel Independent-Drive (4-WID) electric vehicles. The main objective is to enhance the lateral motion performance of electric vehicle under various manoeuvres and in the existence of parameter uncertainties and exterior disturbances. The upper-layer control law is proposed according to a novel terminal sliding mode approach formulated using the longitudinal velocity and yaw rate dynamics of the electric vehicle. It aims at generating the desired driving forces of each tire along with the vehicle's yaw momentum while guaranteeing chattering-free motion and finite-time stability in the existence of parametric uncertainties and disturbances. The lower-layer control law is formulated in the light of a constrained optimization problem to generate the optimal forces and torques for the in-wheel electric motors and achieve the desired longitudinal force and yaw momentum. The efficacy of the suggested approach is confirmed using CARSIM; a high-fidelity simulation package. Its performance analysis considered three standard driving manoeuvres and included a comparative analysis of other designs. The obtained results show that the offered methodology ensures the finite-time stability of the vehicle and improves its manoeuvrability and tracking performance under various driving conditions.

Adaptive fault-tolerant control for active suspension systems based on the terminal sliding mode approach

In this paper, a control system is designed for a vehicle active suspension system. In particular, a novel terminal sliding-mode-based fault-tolerant control strategy is presented for the control problem of a nonlinear quarter-car suspension model in the presence of model uncertainties, unknown external disturbances, and actuator failures. The adaptation algorithms are introduced to obviate the need for prior information of the bounds of faults in actuators and uncertainties in the model of the active suspension system. The finite-time convergence of the closed-loop system trajectories is proved by Lyapunov's stability theorem under the suggested control method. Finally, detailed simulations are presented to demonstrate the efficacy and implementation of the developed control strategy.

Fractional‐order fault‐tolerant pitch control design for a 2.5 MW wind turbine subject to actuator faults

This paper proposes an active fault-tolerant pitch control design for a 2.5 MW wind turbine. The proposed scheme combines the robustness properties of fractional-order terminal sliding mode control with the accurate estimation of virtual actuators. Its main objective is to enable the wind turbine to retain its nominal pitching performance under faulty conditions whereas simultaneously attenuating chattering. The fault detection scheme implements a bank of modified unscented Kalman filters. The proposed approach was implemented to a 2.5-MW wind turbine subject to pitch actuator faults and sensor noise. Its performance was compared with that of an integer-order terminal sliding mode approach. Guaranteeing the finite time stability of the pitching system under faulty conditions whereas alleviating the chattering phenomena are among the positive features of the proposed fractional-order fault-tolerant pitch control design.

Coordinated Attitude Control for Synthetic Aperture Radar Satellites with Quantization and Communication Delay

This paper studies the coordinated attitude control problem of synthetic aperture radar satellites and proposes two types of terminal sliding mode control schemes. The first control law is investigated based on the conventional non-singular terminal sliding mode approach and modified Rodrigues parameters with the consideration of signal quantization and communication delay. Based on the first control scheme, we develop the second control method with an integral-based event triggering condition to reduce the updating frequency of the control command from controllers to actuators. Finally, numerical simulation examples based on a cluster of three satellites are presented to show the effectiveness of the proposed two designed control methods.

A Novel Adaptive Gain Integral Terminal Sliding Mode Control Scheme of a Pneumatic Artificial Muscle System With Time-Delay Estimation

This paper develops a novel adaptive gain integral terminal sliding mode control with time-delay estimation to enhance the control performance of a pneumatic artificial muscle system. The main contribution of the paper is that the proposed control method can enable the benefits of both terminal sliding mode technique and an integral sliding mode approach. Thus, the controlled system not only achieves finite time convergence and robust performance but also attenuates the drawback of the reaching phase in the conventional sliding mode control approach. To develop the control algorithm, the mathematical of the pneumatic artificial muscle system is first design, which includes a nominal system and all uncertainties and disturbances in the system dynamics. Then, a backstepping terminal sliding mode is designed to achieve a finite time convergence of tracking errors in the nominal system. In addition, an integral terminal sliding mode approach is proposed to reject the uncertainties and disturbances. To enhance the control performance, a time-delay estimation is employed to approximate the nonlinearity and disturbance in the system and an adaptive gain scheme is coupled directly to estimate the ideal robust control gain, which can reduce the chattering phenomenon and increase the tracking accuracy. The stability of the controlled system is analyzed using Lyapunov theory. Moreover, the effectiveness of the proposed control algorithm is verified through a series of experimental tests on a developed pneumatic artificial muscle system.

Modular-Controller-Design-Based Fast Terminal Sliding Mode for Articulated Exoskeleton Systems

This brief deals with a modular controller using a fast terminal sliding mode approach for articulated systems represented by exoskeletons to perform flexion/extension movements. The proposed controller supposes that all model functions are unknown except classical properties related to the boundedness of some parameters. On the other hand, the disturbances are assumed to be bounded. It permits finite-time convergence to the desired trajectories in both position and velocity. The system is divided into several subsystems and a particular unit controls each subsystem. A supervisor using the Lyapunov approach ensures the closed-loop stability of the overall system. The proposed robust controller has been applied in a real-time application to drive an upper limb exoskeleton having 3 DOF. The used device worn by a healthy subject performs flexion/extension movements often practiced for rehabilitation purposes. A strict security protocol, which is generally used by therapists, has been respected. The obtained results are satisfactory and prove the effectiveness and the robustness of the proposed controller.