Second-order Terminal Sliding Mode Control Research Articles

Second-Order Terminal Sliding Mode Control for Trajectory Tracking of a Differential Drive Robot

This paper proposes a second-order terminal sliding mode (2TSM) approach to the trajectory tracking of the differential drive mobile robot (DDMR). Within this cascaded control scheme, the 2TSM dynamic controller, at the innermost loop, tracks the robot’s velocity quantities while a kinematic controller, at the outermost loop, regulates the robot’s positions. In this manner, chattering is greatly attenuated, and finite-time convergence is guaranteed by the second-order TSM manifold, which involves higher-order derivatives of the state variables, resulting in an inherently robust as well as fast and better tracking precision. The simulation results demonstrate the merit of the proposed control methods.

Research on Super-Twisting Sliding Mode Voltage Regulation Control of Electric Spring

The traditional control of electric spring (ES) is too complex and lack of robustness, as well as the chattering phenomenon and control accuracy of traditional sliding mode control, a second-order terminal sliding mode control based on super twisting algorithm is proposed. In this paper, the phase plane method is used to establish the mathematical model of ES, solve the state space equation, and regard the AC power supply as a simplified error analysis. Then a second-order sliding mode controller is proposed. The controller parameters are solved to obtain the second-order sliding mode control rate, and the stability is verified. Finally, three groups of comparative simulation experiments were set up by Matlab/Simulink, and the effectiveness of the model was verified by considering the voltage mutation caused by the change of power supply and circuit parameters. Compared with the traditional control method, the proposed control strategy not only ensures the voltage stability, but also improves the control accuracy and the performance of suppressing sliding mode chattering, and has better dynamic response ability.

Design of nonsingular second-order terminal sliding mode controller for cyber-physical systems with time-delays and cyber-attack on actuators

This paper introduces an innovative adaptive nonsingular Second-Order Terminal Sliding Mode (SOTSM) control strategy specifically designed to stabilise disturbed nonlinear Cyber-Physical Systems (CPSs) within a finite timeframe. Unlike the conventional methods, our approach incorporates a novel nonlinear sliding surface that eliminates the need for a reaching step, significantly enhancing the system's robustness. Novel real-time adaptive control laws are developed to cope with external perturbations, time-varying delays, and cyber-attack on actuators without requiring the identification of their upper bounds. The proposed method ensures robust performance for time-varying delayed and disturbed nonlinear CPSs, even in the face of strong cyber-attacks targeting the actuators. Moreover, the proposed method has distinct advantages: it delivers rapid response times, enhanced flexibility, exceptional accuracy, smooth and robust control devoid of transient fluctuations or chattering, and ensures finite-time convergence. Simulation results comprehensively demonstrate the superior efficiency and success of our proposed technique compared to traditional methods such as integral Sliding Mode Control (SMC) and State-Feedback Control (SFC) schemes.

Predefined-Time and Prescribed-Performance Control Methods Combined with Second-Order Terminal Sliding Mode Control for an Unmanned Planing Hull System with Input Delay and Unknown Disturbance

In this study, we investigate a terminal sliding mode control (TSMC) system combined with predefined-time and prescribed-performance control methods for an unmanned planing hull (UPH) system in the presence of a control input delay at the heading axis and a porpoising motion due to pitching-moment disturbance. A second-order TSMC system is adopted to bypass the unstable heading-angle response of the conventional first-order TSMC system caused by the control input delay of the hydraulic rudder actuator system. Next, predefined-time and prescribed-performance control methods are proposed to enhance the disturbance rejection performance of an uncertain UPH. The results of sequential comparative simulations show that the disturbance rejection performance of the proposed hybrid disturbance rejector using both the predefined-time and prescribed-performance control methods for a porpoising motion is superior to those of conventional controller systems without introducing disturbance observers.

Collision Avoidance Second Order Sliding Mode Control of Satellite Formation with Air-Floated Platform Semi-Physical Simulation

As the number of satellites in orbit increases, the issue of flight safety in spacecraft formation orbit control has become increasingly prominent. With this in mind, this paper designs a second-order terminal sliding mode controller for spacecraft formation obstacle avoidance based on an artificial potential function (APF). To demonstrate the effectiveness of the controller, this paper first constructs a Lyapunov function to prove its stability and then verifies its theoretical validity through numerical simulation. Finally, a satellite simulator is used for semi-physical simulation to verify the practical effectiveness of the controller proposed in this paper.

Second‐order terminal sliding mode control based on perturbation estimation for nanopositioning stage

This study proposes a robust second-order terminal sliding mode control with perturbation estimation (2OTSMCPE) strategy with application to trajectory tracking control of the flexure-based nanopositioning system. The proposed controller advantages not only lie on its finite-time convergence but also can provide a high tracking precision with a chattering alleviation which is attend by employing a second-order sliding surface with the switching function. The model of the piezo-driven nanopositioning system is presented first. Second, the sliding variable is designed such as proportional–integral–derivative form to enhance the dynamic response of the control system. Then, a non-singular terminal sliding function (NTSM) is used to achieve the finite-time convergence of the linear sliding variable. Next, a perturbation estimation technique is integrated with the control structure for online estimation of the system uncertainties, thus the prior knowledge of the bounds of system uncertainties are not needed in the proposed control design. Afterwards, the theoretical analysis of the 2OTSMCPE with stability proof is investigated herein. Finally, the system performance with the proposed controller is experimentally verified. The results reveal that the 2OTSMCPE has stronger robustness and also has smoother control signals in comparison with both conventional sliding mode control and the NTSM controller.

Adaptive high-order sliding mode control based on quasi-time delay estimation for uncertain robot manipulator

This paper presents the design, and validation of a new adaptive control system based on quasi-time delay estimation (QTDE) augmented with new integral second-order terminal sliding mode control (ISOTSMC) for a manipulator robot with unknown dynamic uncertainty and disturbances. Contrary to the conventional TDE, the proposed Q-TDE becomes sufficient to invoke a fixed artificial time delay and utilize the past data only of the control input to approximate the unknown system’s dynamic uncertainties. The incorporating of new adaptive reaching law with ISOTSMC augmented with Q-TDE policy ensures the continuous performance tracking of the robot manipulator’s trajectories using output feedback. This combination may achieve high performance with a significant chattering reducing procedure. By utilizing the Lyapunov function theory, it can be demonstrated that the robot system is stable and all signals in closed-loop are converging in finite time. Consequently, Simulation and comparative studies with two degrees of freedom robot manipulator were carried out to validate the effectiveness of the designed control scheme.

Second-order terminal sliding mode control of five-phase IPMSM with super twisting observer under demagnetisation fault

This paper deals with demagnetisation fault detection and tolerance for five-phase interior permanent magnet synchronous motors through a second-order sliding mode controller/observer. At the beginning, a super twisting flux-linkage observer is proposed to cope with the chattering problem. This observer estimates the flux-linkage through stator estimated currents. Further, a novel second-order terminal sliding mode controller is developed for mechanical speed control in the presence of the detected demagnetisation fault. Finally, various simulations validate the feasibility and effectiveness of the proposed controller/observer for a five-phase interior permanent magnet synchronous motor.

Second-order terminal sliding mode control of five-phase IPMSM with super twisting observer under demagnetisation fault

Second-order terminal sliding mode control of five-phase IPMSM with super twisting observer under demagnetisation fault

Adaptive compound second-order terminal sliding mode control for the longitudinal attitude control of the fully submerged hydrofoil vessel

Due to the ever-existing environmental disturbance of ocean wave and nonlinear of the system, it is difficult to obtain a satisfying control performance for the longitudinal attitude and desired height tracking of the fully submerged hydrofoil vessel. To solve such problems, an adaptive compound second-order terminal sliding mode controller is proposed. First, a combination of the complementary sliding mode surface and second-order terminal sliding mode control is introduced. Therefore, the closed system is uniformly ultimately bounded, and the steady-state errors converge to a small neighborhood of equilibrium point. Second, the chattering problem in an actual controller is solved by eliminating the sign function contained in the controller after integration without influencing the stability of the closed-loop system. Besides, a revised adaptive radial basis function neural network is introduced to estimate the derivative of the unknown environmental disturbances without the prior information of the disturbance. Finally, the stability of the system is proved by the Lyapunov stability theory. Numerical experimental results demonstrate that the proposed method possesses fast tracking ability and can decrease the stabilization error and the tracking error simultaneously.

Adaptive Force and Position Control Based on Quasi-Time Delay Estimation of Exoskeleton Robot for Rehabilitation

Rehabilitation robots have become an influential tool in physical therapy treatment since they are able to provide an intensive rehabilitation treatment for a long period of time. However, this technology still suffers from various problems such as dynamics uncertainties, external disturbances, and human-robot interaction. In this paper, we present a new integral second-order terminal sliding mode control incorporating quasi-time delay estimation (Q-TDE) applied to an exoskeleton robot with dynamics uncertainties and unknown bounded disturbances. Unlike the conventional TDE approach, the proposed Q-TDE uses delayed one step only of the control input of the system to approximate the uncertain dynamics while avoiding the delays on all states of the system. The proposed controller aims to perform passive and active rehabilitation protocols without the need for velocity and acceleration measurements of the robot system. A finite time of both selected sliding surface and estimation error simultaneous is achieved using an appropriate Lyapunov function. Experimental results with healthy subjects found using a virtual reality environment confirm the effectiveness of the proposed control.

Adaptive finite time control for spacecraft attitude maneuver based on second-order terminal sliding mode

An adaptive fuzzy second-order terminal sliding mode control scheme is developed to solve the problem of rigid spacecraft attitude maneuver in which the external disturbances and uncertain inertia parameters as well as actuator faults are explicitly taken into account. The proposed controller incorporates a second-order terminal sliding mode to obtain finite time convergent performance as well as chattering elimination, meanwhile the fuzzy logical system is implemented to estimate the system uncertainties of the rigid spacecraft. Lyapunov stability analysis shows that the designed control algorithm guarantees the practical finite time stability of the attitude maneuver errors with great robustness to system uncertainties and actuator faults. Numerical simulations are also presented that not only highlights closed-loop performance benefits from the proposed control algorithm, but also illustrates its effectiveness in the presence of disturbances and uncertainties when compared with classic finite time sliding mode control schemes for spacecraft attitude maneuver control.

Second-order terminal sliding mode control for networks synchronization

This paper proposes a second-order terminal sliding mode controller for outer synchronization of a class of complex networks with disturbances. This control scheme adopts a hierarchical control structure to reduce the numbers of controllers. The multivariable error systems were decomposed into two subsystems, a controllable nonlinear subsystem and a linear subsystem. The proposed terminal sliding mode controller was only designed for the nonlinear subsystem. The linear subsystem is set to appropriate sliding mode parameters to implement synchronization. This approach possesses the features of less controllers, faster convergence and higher tracking precision. The performance of the control strategy is evaluated through the control of the complex networks consisting of \(N\) identical Rossler systems. Simulation results demonstrate the effectiveness of the proposed control method.

Second-order terminal sliding mode control for hypersonic vehicle in cruising flight with sliding mode disturbance observer

This paper focuses on the design of nonlinear robust controller and disturbance observer for the longitudinal dynamics of a hypersonic vehicle (HSV) in the presence of parameter uncertainties and external disturbances. First, by combining terminal sliding mode control (TSMC) and second-order sliding mode control (SOSMC) approach, the secondorder terminal sliding control (2TSMC) is proposed for the velocity and altitude tracking control of the HSV. The 2TSMC possesses the merits of both TSMC and SOSMC, which can provide fast convergence, continuous control law and high-tracking precision. Then, in order to increase the robustness of the control system and improve the control performance, the sliding mode disturbance observer (SMDO) is presented. The closed-loop stability is analyzed using the Lyapunov technique. Finally, simulation results illustrate the effectiveness of the proposed method, as well as the improved overall performance over the conventional sliding mode control (SMC).

Complement to ‘Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties’ [Commun Nonlinear Sci Numer Simulat 15 (2010) 3241–3247

Owing to the singularity problem having not been considered in control design process, we present some points to improve the results of paper [Wei Xiang, Yugao Huangpu, second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties, Commun Nonlinear Sci Numer Simulat 15 (2010) 3241–3247].

Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties

This paper is concerned with the stabilization problem for a class of nonlinear systems. Using second-order sliding mode control approach, a robust control scheme is established to make the states of system to zero or into predictable bounds for matched and unmatched uncertainties, respectively. Meanwhile, the chattering phenomenon is eliminated. A comparative example is given to emphasize the effectiveness and robustness of the proposed method.

SECOND-ORDER TERMINAL SLIDING MODE CONTROL OF INPUT-DELAY SYSTEMS

This paper proposes a second-order terminal sliding mode control for a class of uncertain input-delay systems. The input-delay systems are firstly converted into the input-delay free systems and further converted into the regular forms. A linear sliding mode manifold is predesigned to represent the ideal dynamics of the system. Another terminal sliding mode manifold surface is presented to drive the linear sliding mode to reach zeros in finite time. In order to eliminate the chattering phenomena, a second-order sliding mode method is utilized to filter the high frequency switching control signal. The uncertainties of the systems are analysed in detail to show the effect to the systems. The simulation results validate the method presented in the paper.

Second-order terminal sliding mode control of uncertain multivariable systems

A second-order terminal sliding mode controller for uncertain multivariable systems is proposed in this paper. The controller adopts the hierarchical control structure. The paper derives the state transform matrices which are used to transform a multivariable linear system to the block controllable form consisting of two subsystems, an input–output subsystem and a stable internal dynamic subsystem. The proposed controller utilizes a non-singular terminal sliding mode manifold for the input–output subsystem to realize fast convergence and better tracking precision. Meanwhile, a chattering-free second-order terminal sliding mode control law is presented. The stability of uncertain multivariable systems can be realized using the proposed controller. A derivative estimator is utilized in the paper to estimate the derivatives of the sliding mode functions for the controller. The simulation results are presented to validate the design method.