Terminal Sliding Mode Control Method Research Articles

Flexible Droop Coefficient-Based Inertia and Voltage Cascade Control for Isolated PV-Battery DC Microgrid

To realize the coordinated distribution of power in the multi-source system, maintain the charging balance among energy storage units, and improve the anti-interference capability of the bus voltage, a cascade control for an isolated PV-battery DC microgrid is proposed in this paper. First, to provide inertia for the microgrid so that it can cope with external disturbance, the parameters of the droop curve were adjusted by correlating the bus voltage variation rate, which improved the conventional droop control. Secondly, a nonsingular terminal sliding mode control was proposed to track voltage and current references and, thus, enhance the robustness of the DC microgrid. Moreover, the high-frequency chattering of the sliding mode control was inhibited with the exponential reaching law, and the Lyapunov function was utilized to verify the stability of the proposed nonsingular terminal sliding mode control method. Both the simulated and experimental results verified the correctness and effectiveness of the proposed method.

Adaptive Neural Network-Based Fixed-Time Tracking Controller for Disabilities Exoskeleton Wheelchair Robotic System

In this paper, an adaptive neural network approach is developed based on the integral nonsingular terminal sliding mode control method, with the aim of fixed-time position tracking control of a wheelchair upper-limb exoskeleton robot system under external disturbance. The dynamical equation of the upper-limb exoskeleton robot system is obtained using a free and typical model of the robotic manipulator. Afterward, the position tracking error between the actual and desired values of the upper-limb exoskeleton robot system is defined. Then, the integral nonsingular terminal sliding surface based on tracking error is proposed for fixed-time convergence of the tracking error. Furthermore, the adaptive neural network procedure is proposed to compensate for the external disturbance which exists in the upper-limb exoskeleton robotic system. Finally, to demonstrate the effectiveness of the proposed method, simulation results using MATLAB/Simulink are provided.

Nonsingular terminal sliding mode control with sliding perturbation observer for a permanent-magnet spherical actuator

In order to deal with the modeling of uncertainty and external environment disturbance in the trajectory tracking system of 3 degrees of freedom permanent-magnet spherical actuator, a nonsingular terminal sliding mode control method with sliding perturbation observer is proposed in this article. First, a sliding perturbation observer, which can estimate compound disturbance only by feedback position signals, is proposed to reduce the uncertainty caused by angular velocity observation. Then, based on the sliding perturbation observer, a nonsingular terminal sliding mode control method is designed to satisfy the requirements of system nonsingularity, robustness, and control accuracy. The stability of the controller is proved by the Lyapunov theory. Finally, simulation and experimental results show that the proposed control method has excellent anti-disturbance performance, which provides an important reference for the future applications of permanent-magnet spherical actuators in aerospace and other industrial fields.

A nonsingular terminal sliding algorithm for swing and stance control of a prosthetic leg robot

The design of swing and stance control for path following of a prosthetic leg robot subject to uncertain dynamics and exterior disturbances is a serious issue, which affects the development of wearable robots. In wearable robots, parametric uncertainties and external disturbances are unavoidable problems. This problem is associated with practical engineering of wearable robots due to the actual swing and stance situations, where the combination of contact and tracking control objectives is highly complex. This paper proposes two novel finite-time controllers for a prosthetic leg robot with three degree-of-freedom. A prosthetic leg robot should emulate hip vertical displacement, thigh and knee angles according to human gaits in the presence of ground friction force and external disturbances. For the swing phase, a nonsingular fast terminal sliding mode control method is designed to track the reference trajectories fast and in the finite time without any non-singularity problem and chattering phenomenon. Moreover, the other designed controller can deal with input saturation by using a hyperbolic tangent function and an auxiliary system. For the stance phase, an impulse momentum sliding mode control scheme is introduced which allows the prosthetic leg robot to emulate the mechanics of human walking. Using the proposed controller, the robot imitates the patient momentum exchange and weight transfer in the stance phase. The proposed techniques cause the transition between contact and off-contact phases and contact phase itself. Finally, the simulation results verify the efficiency of the provided technique. In our future work, we will focus on employing this technique to a practical prosthesis legged robot.

Fuzzy-Based Fixed-Time Nonsingular Tracker of Exoskeleton Robots for Disabilities Using Sliding Mode State Observer

In this article, the position tracking control of the wheelchair upper-limb exoskeleton robotic system is investigated with the aim of rehabilitation of disabled people. Hence, the fuzzy nonsingular terminal sliding mode control method by using the state observer with a fixed-time convergence rate is designed in three main parts. In the first part, the fixed-time state observer is proposed for estimation of the states of the system. Secondly, the fixed-time convergence of position tracking error of the upper-limb exoskeleton robot system is examined by using the nonsingular terminal sliding mode control approach. In the third part, with the target of the improvement of the controller performance for removal of the chattering phenomenon which diminishes the controller performance, the fuzzy control method is used. Finally, the efficiency and proficiency of the proposed control method on the upper limb exoskeleton robotic system are demonstrated via the simulation results which are provided by MATLAB/Simulink software. In this part, simulation results are obtained based on different initial conditions in two examples using various desired values. Thus, it can be demonstrated that the proposed method applied to the upper-limb exoskeleton robot system is robust under various initial conditions and desired values.

An Adaptive Barrier Function Terminal Sliding Mode Controller for Partial Seizure Disease Based on the Pinsky–Rinzel Mathematical Model

This paper proposes an adaptive barrier function terminal sliding mode control method for partial seizure based on the Pinsky–Rinzel model. A terminal sliding mode control technique is designed to achieve the convergence of trajectories to the desired value in a finite time, while an adaptive barrier function is used to ensure that the outputs, which are independent of the disturbance boundary, converge to the predetermined zero location. The performance of the proposed approach is checked for the nonlinear two-compartmental Pinsky–Rinzel pyramidal neuron model. The obtained method of the finite time stability, in the presence of uncertainty and disturbance, is proven by the Lyapunov theory. The simulation results confirm the effectiveness of the proposed control scheme. Finite time convergence, robustness, chattering-free dynamics and near-zero error are the advantages of the proposed technique.

Full-Order Terminal Sliding-Mode Control for Soft Open Point

In this paper, a full-order terminal sliding-mode control method is proposed for the rectifier side and the inverter side of the soft open point (SOP). The rectifier-side DC voltage control system consists of the voltage- and current-loops with controllers which are designed using full-order sliding-mode (FOSM) to enhance the dynamic performances and anti-disturbance. The integral type virtual control signal without chattering is designed to compensate for the unmatched uncertainties including external disturbances and some parameter perturbations. The full-order terminal sliding-mode (FOTSM) controller for the current-loop can force the current response to track its reference in finite time. The inverter side power control system is designed to regulate the power. The FOTSM controller for the power-loop ensures the power-tracking accuracy under a disturbed condition. Finally, the simulations demonstrate the effectiveness of the proposed controllers for the rectifier and inverter sides in the soft open point (SOP).

Control of Time Delay Force Feedback Teleoperation System With Finite Time Convergence.

In order to make the teleoperation system more practical, it is necessary to effectively control the tracking error convergence time of the teleoperation system. By combining the terminal sliding mode control method with the neural network adaptive control method, a bilateral continuous finite time adaptive terminal sliding mode control method is designed for the combined teleoperation system. The Lyapunov theory is used to analyze the stability of the closed-loop system, and the position tracking error is able to effectively converge in time. Finally, the effectiveness of the proposed control scheme is verified by MATLAB Simulink numerical simulation, and the numerical analysis of the results shows that the method has better system performance. Compared with the traditional two-sided control method (TPDC) of PD time-delay teleoperation system, the control method in this paper has good performance, improves stability, and makes steady-state errors smaller and better tracking.

Optimization of Grid-Connected Photovoltaic Power Generation Technology Based on Nonlinear Back-Stepping Controller

To address the issue of energy scarcity and to use solar photovoltaic energy as a renewable source, a three-phase grid-connected photovoltaic inverter system with uncertain system model parameters is investigated, which converts DC power into AC power, feeds it into the grid, and maintains the grid-connected part’s quality. An enhanced back-stepping approach is proposed to explore the control strategy of three-phase solar grid-connected inverter, which includes adaptive control, dissipative theory, sliding mode control, and rapid terminal sliding mode control, respectively. It is verified that the system is subjected to external interference F = 5 during 0.5 s–0.8 s. As per the simulation results, the improved adaptive terminal sliding mode control method can suppress the interference to a certain extent and has strong robustness to the external interference. When compared with the adaptive sliding mode control approach, the anti-interference ability is better, and the system stability is improved. Then, to improve the above approach, a high speed terminal sliding mode control method is proposed, which can swiftly converge in finite time and the estimated value of uncertain parameters is closer to the actual value, thereby boosting the system’s robustness.

Prescribed Performance-Based Adaptive Terminal Sliding Mode Control for Virtual Synchronous Generators

Due to the lack of inertia and damping in the distributed power system with power electronic devices as interface, the stability of the power system will be adversely affected when the distributed power system is connected to the grid. In order to solve the problem of low inertia and improve stability, an adaptive terminal sliding mode control method based on the electromagnetic transient characteristics of virtual synchronous generators is proposed. During the design process, projection operators and parameter adaptive law control methods are introduced to compensate for parameter errors caused by environmental interference. Furthermore, by utilizing a prescribed performance function, the terminal sliding surface of the system will have the desired dynamic response, and variations of the system tracking error can be restricted. Simulation results show that the proposed controller has improved control accuracy and response speed, frequency stability, and power response.

Continuous finite-time sliding mode control for synchronization of perturbed bistable electrostatic and piezoelectric transducers with external disturbances

Despite that the synchronization of chaotic systems has been extensively investigated and demonstrated to contribute to physical, chemical, financial, and biological applications, the synchronization of different perturbed bistable systems appears to be an open issue. This is significant with the fact that the bistability widely exists from the visual perception to the electrical and mechanical systems. Therefore, this paper proposes a continuous finite-time terminal sliding mode control method to synchronize two bistable electromechanical transducers, with the electrostatic one acting as the master system and the piezoelectric one acting as the slave system. The model of two systems as well as the control method considering external disturbances and unmodeled dynamics are presented. Numerical simulation results show that two bistable systems can be synchronized with our proposed control method in intrawell, chaotic, and interwell oscillation modes. Furthermore, the chattering issue in conventional discontinuous controllers is eliminated with our designed continuous finite-time terminal protocols for bistable chaotic systems so as to improve the robustness of the controller and avoid its failure. Interesting findings are discussed for the varying system responses and control inputs in different oscillation modes. This work also is expected to facilitate the development of applications where bistability is found such as power or communication systems to resist the external disturbances.

Non-Singular Finite Time Tracking Control Approach Based on Disturbance Observers for Perturbed Quadrotor Unmanned Aerial Vehicles.

In this paper, a disturbance observer based on the non-singular terminal sliding mode control method was presented for the quadrotor in the presence of wind perturbation. First, the position and attitude dynamical equation of the quadrotor was introduced in the existence of windy perturbation. It was difficult to exactly determine the upper bound of the perturbations in the practical systems such as robot manipulators and quadrotor UAVs. Then, a disturbance observer was designed for the estimation of wind perturbation which was entered to the quadrotor system at any moment. Afterward, a non-singular terminal sliding surface was proposed based on the disturbance observer variable. Furthermore, finite time convergence of the closed-loop position and attitude models of the quadrotor was proved using Lyapunov theory concept. Unlike the existing methods, the new adaptive non-singular terminal sliding mode tracker for quadrotor unmanned aerial vehicles enabled accurate tracking control, robust performance, and parameter tuning. Through the combination of the finite time tracker and disturbance observer, the position and attitude tracking of quadrotor UAVs could be accurately performed not only in the nominal environment but also in the existence of different types of perturbations. Finally, simulation results based on the recommended method were provided to validate the proficiency of the suggested method. Moreover, comparison results with another existing study were presented to prove the success of the proposed method.

ELM-Based Non-Singular Fast Terminal Sliding Mode Control Strategy for Vehicle Platoon

Vehicle platoon is one of the innovations in the automated highway systems, which has the potential to reduce fuel consumption, alleviate traffic congestion and lighten the driver’s burden. How to control the vehicle effectively to ensure the stability of the queue is a challenge. Aiming to overcome the shortcomings of the platoon control method based on traditional sliding mode control, a non-singular terminal sliding mode control method optimized by the extreme learning machine is proposed in this paper. Firstly, the vehicle longitudinal dynamics are derived from the analysis of the forces acting on the vehicle in the longitudinal direction. A constant time headway policy is taken as the spacing policy. The modified non-singular terminal sliding mode control method has outstanding performance, simulation results demonstrate that the following vehicles can rapidly track the trajectory of the leading vehicle in the platoon with less spacing error and guarantee string stability. In this study, several experiments are set up to consider the disturbance and other uncertain practical factors. The performance of the proposed method is superior to the traditional sliding mode control method. Experimental results show that the proposed method can significantly reduce chattering and has good robustness under the circumstances of the disturbance.

Leader-follower formation control of USVs using APF-based adaptive fuzzy logic nonsingular terminal sliding mode control method

Leader-follower formation control of USVs using APF-based adaptive fuzzy logic nonsingular terminal sliding mode control method

SLIDING MODE CONTROL OF UNMANNED AERIAL VEHICLE BASED FINITE-TIME DISTURBANCE OBSERVER

Because of the advantages of high maneuverability, vertical takeoff and landing, free hovering, and easy portability, quadrotor UAVs have become one of the research hotspots in recent years. Aiming at the finite-time trajectory tracking control problem for quadrotor under unknown environmental disturbance and modeling uncertainty, a fast terminal sliding mode control method using a finite-time disturbance observer is proposed. First, the modeling uncertainty and unknown external disturbance of the quadrotor were combined into lumped disturbance, and a finite-time disturbance observer was designed to estimate the lumped disturbance online. Secondly, a fast terminal sliding mode controller was constructed for the realization of a finite-time tracking control of the quadrotor, and the estimated value of the limited-time disturbance observer was compensated to the controller. Thereby, the influence of compound disturbance was eliminated, the quadrotor can achieve a finite-time trajectory, and the disturbance suppression capability of tracking control was improved. Finally, we conducted simulation experiments and confirmed that the control strategy proposed in this paper is effective.

A Novel Robust Super-Twisting Nonsingular Terminal Sliding Mode Controller for Permanent Magnet Linear Synchronous Motors

For accurate position tracking and robust control of permanent magnet linear synchronous motor (PMLSM) servo systems against various uncertainties, such as parameter change, load disturbance, friction force, and so on, this article proposes a novel super-twisting nonsingular terminal sliding mode control method based on a high-order sliding mode observer. First, a dynamic model of PMLSM with uncertainties is established. A novel nonsingular terminal sliding mode function combined with the super-twisting algorithm is then proposed to design a robust super-twisting nonsingular terminal sliding mode controller, which ensures the system convergence to the equilibrium state within a finite time, effectively eliminating the chattering phenomenon and improving the system robustness. To further improve the system tracking performance and anti-interference ability, a high-order sliding mode observer is used to estimate the system uncertainties. The effective tracking performance and robustness of the proposed control method are validated by the experimental results.

Three-dimensional cooperative guidance law to control impact time and angle with fixed-time convergence

This article proposes a new terminal cooperative guidance law to control both impact time and impact angle in three-dimensional engagement. The presented guidance law employs on and normal line-of-sight accelerations to control the impact time and angle together. Two parts are included in this guidance law, that is, the guidance laws with impact time constraint and impact angle constraint. The first is designed based on fixed-time consensus theory to fulfill the salvo attack of the target, and the second is developed based on fixed-time nonsingular fast terminal sliding mode control method to achieve the desired impact angles. The stability analysis of this guidance law based on Lyapunov theory is also presented in detail. Moreover, the maneuvering target can be intercepted successfully with the presented guidance law, and the fixed-time stability and less control energy are well ensured. Additionally, the effectiveness and applicability of the proposed guidance scheme are explicitly verified through simulation tests.

Nonlinear cascade control of an electro‐hydraulic actuator with large payload variation

AbstractElectro‐hydraulic actuators have been widely used in industrial production, but the unknown variable payload seriously affects its position control accuracy. Therefore, a radial basis function neural network disturbance observer is designed to estimate the lumped disturbance force through strong online learning ability in the absence of force sensor. Besides, a nonlinear cascade controller with double loop structure is proposed in this paper. A global fast terminal sliding mode control method is firstly applied in the outer loop position system, which can eliminate chattering and improve convergence speed comparing to traditional sliding mode control. The inner loop force system adopts a backstepping control method to calculate the actual input of the whole system. Theoretical analysis indicates that the proposed controller is stable even if existing time‐variant disturbance. Moreover, three comparative controllers are designed and tested in both simulations and experiments. Comparative results show that the developed method has absolute average errors of 1.14 and 0.49 mm in different position tracking, which means more satisfactory tracking performance compared to the contrast controllers.

A Hybrid Autonomous Recovery Scheme for AUV Based Dubins Path and Non-Singular Terminal Sliding Mode Control Method

In order to improve the persistent operation capacity of autonomous underwater vehicle (AUV), autonomous recovery system draws more and more attention in recent years. A hybrid scheme combined with navigation, guidance and control is proposed to complete the function of autonomous recov-ery of AUV in the paper. Based on the hybrid scheme, the autonomous recovery is firstly transformed into the trajectory tracking problem, and the Dubins path planning method is adopted to build the three-dimensional(3D) motion path of AUV. Secondly, the virtual target guidance strategy is introduced to guide the AUV to track the desired path. Finally, a non-singular terminal sliding mode controller is designed to control the AUV. Due to the existence of model inaccuracy of AUV and external disturbances from the environment, a finite-time disturbance observer is adopted to estimate the disturbance and uncertainty in the system. Numerical simulation is conducted to verify its performance. The simulation results show that a 3D motion path can be planed and the AUV can track the motion path well.

A Parameters Adaptive Non-Singular Terminal Sliding Mode Control Method for Overhead Crane System

In this paper, a non-singular terminal sliding mode control method based on parameter adaptation is proposed for trajectory tracking control of overhead cranes with parameter uncertainties. The method can realize fast tracking of the planned overhead crane trajectory when the payload mass and the length of the suspension rope are unknown. At the same time, the hyperbolic tangent function is used to replace the switching term in the sliding mode control, which improves the robustness of the control method to external disturbances to suppress the charting during the crane operation. Using Lyapunov theorem, it is proved that the displacement trajectory can converge to the target trajectory in a finite time. The effectiveness of the proposed control scheme is verified by platform experiments.