Terminal Sliding Mode Method Research Articles

Fault-tolerant controller based on artificial intelligence combined with terminal sliding mode and pre-described performance function applied on ship dynamic position stabilization systems

The presented study, develops an intelligent fault-tolerant controller to automatically control and maintain the position of a ship. The controller possesses the capabilities of holding the ship steady at a fixed position, automatically transferring the ship from one point to another, and tracking a target in the presence of various disturbances, uncertainties in the ship model, and thruster faults. A backstepping control approach based on the Terminal Sliding Mode method is employed to improve the accuracy of the controller. The aforesaid method guarantees time-limited convergence without relying on the initial conditions of system. A pre-described performance function (PPF) is utilized to ensure the performance in transient states and the calculations, which leads to the specific equations achievement for the study, which guarantees the system's stability. Environmental disturbances, uncertainties, and thruster faults are estimated using a Radial Basis Neural Network, allowing the controller to adapt to changes in the ship's environment and system uncertainties. The designed controller is proven to ensure the tracking error remains within a predefined range and can stabilize the ship system within a constant time without being influenced by the initial conditions. This stability is achieved in the presence of environmental disturbances, model uncertainties, and thruster faults, and the tracking error converges to a neighborhood near the origin. The controller is verified using a ship mode in the MATLAB environment, and the results show that the designed controller effectively controls the ship's position. The theoretical findings are successfully verified through these simulation tests.

Adaptive Robust Terminal Sliding Mode Control with Integral Backstepping Synthesized Method for Autonomous Ground Vehicle Control

Autonomous ground vehicles (AGVs) operating in complex environments face the challenge of accurately following desired paths while accounting for uncertainties, external disturbances, and initial conditions, necessitating robust and adaptive control strategies. This paper addresses the critical path-tracking task in AGVs through a novel control framework for multilevel speed AGVs, considering both structured and unstructured uncertainties. The control system introduced in this study utilizes a nonlinear adaptive approach by integrating integral backstepping with terminal sliding mode control (IBTSMC). By incorporating integral action, IBTSMC continuously adjusts the control input to minimize tracking errors, improving tracking performance. The hybridization of the terminal sliding mode method enables finite time convergence, robustness, and a chatter-free response with reduced sensitivity to initial conditions. Furthermore, adaptive control compensators are developed to ensure robustness against unknown but bounded external disturbances. The Lyapunov stability theorem is employed to guarantee the global asymptotic stability of the closed-loop system and the convergence of tracking errors to the origin within finite time. To validate the effectiveness of the proposed control scheme, high-fidelity cosimulations are conducted using CarSim and MATLAB. Comparative analysis is performed with other methods reported in the literature. The results confirm that the proposed controller demonstrates competitive effectiveness in path-tracking tasks and exhibits strong efficiency under various road conditions, parametric uncertainties, and unknown disturbances.

Global fast terminal sliding mode control for path following of ultra large underactuated ship based on predictive LOS guidance

This study proposes a new line-of-sight guidance method based on position prediction that constructs the total path deviation by predicting the future time position of ships. This method can solve the problem of overshoot, which is prone to occur in the path following process of ultra large underactuated ships. A global fast terminal sliding mode method is used to design controllers that allow path deviations to converge in a finite time. To solve the problems of unknown velocity, disturbances, and sideslip angle during navigation, a high-order nonlinear observer is designed to estimate the system states and obtain the velocity values and external disturbances. The sideslip angle of the ship during navigation is obtained by estimating its velocity. Therefore, the problem of an unknown sideslip angle is solved, and the effectiveness of the proposed algorithm is verified through simulation experiments.

Path following control for large inland ships in a restricted waterway using the nonlinear terminal sliding mode method

In order to solve the problem of path following for large ships travelling in restricted waterways, an adaptive Line-Of-Sight (LOS) guidance with the Nonlinear Terminal Sliding Mode (NTSM) algorithm is proposed in this paper. Compared to classical Sliding Mode Controller (SMC) and Adaptive Sliding Mode Controller (ASMC), the proposed system enables large ships to track the desired path much faster, meanwhile, the course stability can also be achieved with the controller saturation and environmental disturbance. To solve the problems of high nonlinearity and uncertainty of ship motion in restricted waters, the mathematical model with Extended state observer (ESO) is proposed to linearize problem. A drift angle observer is established to observe the drift angle during the vessel's navigation, and the LOS guidance law is used to achieve accurate tracking of the desired trajectory. The simulation results show that the inland ships under the control of the proposed scheme can accurately track the desired trajectory in a restricted waterway. The proposed algorithm has good robustness under the effect of environmental disturbances.

Quasi-synchronous control of uncertain multiple electrohydraulic systems with prescribed performance constraint and input saturation

This article focuses on the high accuracy quasi-synchronous control issue of multiple electrohydraulic systems (MEHS). In order to overcome the negative effects of parameter uncertainty and external load interference of MEHS, a kind of finite-time disturbance observer (FTDO) via terminal sliding mode method is constructed based on the MEHS model to achieve fast and accuracy estimation and compensation ability. To avoid the differential explosion in backstepping iteration, the dynamic surface control is used in this paper to guarantee the follower electrohydraulic nodes synchronize to the leader motion with a better performance. Furthermore, a time-varying barrier Lyapunov function (tvBLF) is adopted during the controller design process to constraint the output tracking error of MEHS in a prescribed performance with time-varying exponential function. As the initial state condition is relax by tvBLF, the input saturation law is also adopted during the controller design process in this paper to restrain the surges of input signals, which can avoid the circuit and mechanical structure damage caused by the volatile input signal. An MEHS experimental bench is constructed to verify the effectiveness of the theoretical conclusions proposed in this paper and the advantages of the proposed conclusions in this paper are illustrated by a series of contradistinctive experimental results.

Robust adaptive parameter estimator design for a multi-sinusoidal signal with fixed-time stability and guaranteed prescribed performance boundary of estimation error

In online parameter estimation, fast and accurate estimation without dependence on the initial conditions with good transient properties is an essential issue. Hence, in this paper, a robust adaptive parameter estimation method is proposed that not only can estimate online the unknown parameters of a multi sinusoidal signal in a finite-time without dependence on the initial conditions but also can guarantee the transient and steady-state performance of the estimated parameters with a predefined boundary. At first, to estimate the frequency, offset, phase and amplitude, the multi-sinusoidal signal is represented in a linear regression form. Then, by defining an auxiliary regressor matrix and vector derived by the original regressor vector and output signal, the estimation error is computed indirectly. By employing this parameter estimation error and utilizing the fixed-time stability property of the terminal sliding mode method and Prescribed-Performance concept, robust adaptation laws are designed in such a way that the convergence time of the estimation error is finite so that its settling time is independent from the initial guess, and this time can be predefined. Moreover the estimation error boundary can be predefined. Furthermore, in this method, only the output measurement is needed and there is no need for any observer or predictor. Using the Lyapunov stability theorem it is proved that the estimation error converges to zero when the measurement is free of noise and for the noisy case the estimation error is uniformly ultimately bounded and converges to a compact set around the origin. Three illustrative examples are provided to demonstrate the advantages and effectiveness of the designed estimation laws compared to some existing methods. Simulation results show that the proposed method can estimate the unknown parameters in fixed-time with a pre-adjustable estimation error boundary, even in the presence of measurement noise and confirms the superiority of the proposed method compared to the two existing methods.

A new three-dimensional adaptive sliding mode guidance law for maneuvering target with actuator fault and terminal angle constraints

In this paper, an adaptive terminal sliding mode guidance law is designed to intercept the maneuvering target with terminal line of sight angle constraints in three-dimensional space, and the actuator failure is considered. First, the relative kinematics model of three-dimensional space missile target considering fault is established. Then, the guidance law is designed by using the nonsingular fast terminal sliding mode method, which makes the tracking error and rate converge in finite time; Aiming at the problem of uncertain disturbance and fault in the model, the adaptive method is used to evaluate online. Finally, the Lyapunov stability theorem is used to prove that the missile target system is closed-loop stable under the proposed guidance law. Simulation results verify the performance of the proposed guidance law.

Research on Direct Braking Force Estimation and Control Strategy Using Tire Inverse Model

With the rapid development of computer control and vehicle intelligence technology, speed and safety of vehicles have been greatly improved, and the requirements for vehicle control performance are getting higher and higher. For the direct braking force control, in the process of deceleration, a fast braking response can be obtained, which improves the braking performance and vehicle safety. This paper concentrates on direct braking force estimation and control strategy using a tire inverse model based on the antilock braking system, and to solve the problem of the existing ABS system is mainly antilock braking function, no direct braking force control function. Taking magic formula model for reference inverse model, the critical parameters under different road surfaces are obtained according to experience data. Then, the desired slip ratio corresponding to braking force can be obtained via fast tire inverse model look-up table method. The tyre friction self-adjustment decision making is obtained using the tire inverse model method. A direct braking force antilock braking system (DBF-ABS) controller is built using the nonsingular fast terminal sliding mode method. The simulation results indicated that the control strategy has adaptability and stability to the change of road conditions.

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.

Adaptive saturated tracking control for spacecraft proximity operations via integral terminal sliding mode technique

AbstractThis study presents a tracking control strategy for spacecraft proximity operations subjected to kinematic couplings, input saturation, modeling uncertainties, and external disturbances. First, a coupled six degrees of freedom dynamics is modeled to depict the relative motion between the pursuer and target spacecrafts. To address the input saturation problem, a dead‐zone operator‐based model is introduced. Subsequently, a finite‐time controller is proposed by exploiting the non‐singular integral terminal sliding mode method. By employing the adaptive technique, the proposed control strategy enjoys the feature that it can avoid requiring the prior knowledge of the lumped uncertainty's bounds. Using the Lyapunov theory, the designed controller is proved to guarantee that the translational and rotational tracking errors can converge to the origin within finite time. Finally, numerical simulations are performed to illustrate that the developed control scheme possesses a strong robustness, a fast convergence rate, input saturation elimination as well as chattering suppression.

Control of an IPMC Soft Actuator Using Adaptive Full-Order Recursive Terminal Sliding Mode

The ionic polymer metal composite (IPMC) actuator is a kind of soft actuator that can work for underwater applications. However, IPMC actuator control suffers from high nonlinearity due to the existence of inherent creep and hysteresis phenomena. Furthermore, for underwater applications, they are highly exposed to parametric uncertainties and external disturbances due to the inherent characteristics and working environment. Those factors significantly affect the positioning accuracy and reliability of IPMC actuators. Hence, feedback control techniques are vital in the control of IPMC actuators for suppressing the system uncertainty and external disturbance. In this paper, for the first time an adaptive full-order recursive terminal sliding-mode (AFORTSM) controller is proposed for the IPMC actuator to enhance the positioning accuracy and robustness against parametric uncertainties and external disturbances. The proposed controller incorporates an adaptive algorithm with terminal sliding mode method to release the need for any prerequisite bound of the disturbance. In addition, stability analysis proves that it can guarantee the tracking error to converge to zero in finite time in the presence of uncertainty and disturbance. Experiments are carried out on the IPMC actuator to verify the practical effectiveness of the AFORTSM controller in comparison with a conventional nonsingular terminal sliding mode (NTSM) controller in terms of smaller tracking error and faster disturbance rejection.

Fault-Tolerant Finite-Time Controller for Attitude Tracking of Rigid Spacecraft Using Intermediate Quaternion

This article proposes a fault-tolerant finite-time controller for attitude tracking control of rigid spacecraft using intermediate quaternion in the presence of external disturbances, uncertain inertia parameter, and actuator faults. First, a novel nonsingular fast terminal sliding mode control law is derived using intermediate quaternion, free of singularity, ambiguity, and unwinding phenomenon. Second, a proposed controller is developed by combining the continuous nonsingular fast terminal sliding mode method with the finite-time disturbance observer. The key feature of the proposed control strategy is that it globally stabilizes the system in finite time, even in the presence of actuator faults, inertia uncertainty, and external disturbances. Simulation results are presented under actuator constraint to show the desirable properties and the superiority of the proposed controller compared to an asymptotic controller and nonsingular fast terminal sliding mode controller.

Adaptive Terminal Sliding Mode Control of Uncertain Electro-Hydraulic Position Servo Systems

To solve the position tracking control problem of nonlinear and uncertain electrohydraulic servo systems, an adaptive terminal sliding mode control method based on the backstepping method was proposed. This method combines the adaptive control with the terminal sliding mode method. On the one hand, the proposed adaptive control law can effectively estimate and compensate the uncertain parameters of the electro-hydraulic servo system on line, on the other hand, with the variable coefficient reaching law obtained through introduction of the error attractor into the sliding mode reaching law, the designed terminal sliding mode control law can not only eliminate the non-singular term in the ordinary terminal sliding mode control law, but also greatly reduce the chattering of the sliding mode surface. Finally, according to the Lyapunov stability theory, the finite time stability of the position tracking error was proved strictly. The proposed method was compared with the integral backstepping sliding mode control and the linear sliding mode control. The simulation results show that, the proposed method has good robustness and tracking accuracy in position tracking control of electro-hydraulic servo systems.

Chaotic dynamics of the vertical model in vehicles and chaos control of active suspension system via the fuzzy fast terminal sliding mode control

In this paper, the control of chaotic vibrations in vehicle suspension system is studied via a fuzzy fast terminal sliding mode method. Therefore, the nonlinear equations of motion in the vehicle half model are derived initially through the Newton-Euler laws and then these equations are solved by the fourth-order Runge-Kutta method. For analysis of chaos, some techniques including bifurcation diagrams, frequency response, power spectrum, phase plane trajectories, and Poincare section are used to identify the chaotic behaviors. The chaotic zones are depicted with critical values on the uncontrolled model under the road surface force. In order to eliminate chaotic behavior, the control signals in the active suspension system are generated using the novel fuzzy fast terminal sliding mode control algorithm. The simulation results of the feedback system show that the suspension system can be stabilized the vibrations by efficient fuzzy fast terminal SMC while eliminating irregular chaotic behaviors.

Energy-Efficient Speed Profile Optimization and Sliding Mode Speed Tracking for Metros

Nowadays, most metro vehicles are equipped with an automatic train operation (ATO) system, and the speed control method, combining cruise speed planning and proportional-integral-derivative (PID) control, is widely used. The automation is achieved, and the energy-efficient can be improved. This paper presents an improved artificial bee colony algorithm for speed profile optimization with coast mode and an adaptive terminal sliding mode method for speed tracking. Specifically, a multi-objective optimization model is established, which considers energy consumption, comfortableness, and punctuality. Then, a novel artificial bee colony algorithm named regional reinforcement artificial bee colony (RR-ABC) is designed, to search the optimal speed profile with coast mode, in which some improvements are made to speed up convergence and to avoid local optimal solutions. For speed-tracking control, the adaptive terminal sliding mode controller (ATSMC) is used to improve the speed error, robustness, and energy saving. In addition, a disturbance observer (DOB) is designed to improve the anti-interference ability of the system and further improve the robustness and anti-disturbance, which are also conducive to speed error and energy saving. Finally, the line and train data of the Qingdao Metro Line 6 are used for simulation, which proves the effectiveness of the study. Specific to the energy saving rate, and compared with normal algorithms, RR-ABC with coast mode is approximately 9.55%, and ATSMC+DOB is 7.58%.

Parameter Adaptive Terminal Sliding Mode Control of Flexible Coupling Air-Breathing Hypersonic Vehicle

The highly nonlinear and coupling characteristics of a flexible air-breathing hypersonic vehicle create great challenges to its flight control design. A unique parameter adaptive nonsingular terminal sliding mode method is proposed for longitudinal control law design of a flexible coupling air-breathing hypersonic vehicle. This method uses adaptive reaching law gain instead of the additional adaptive compensation term to handle the uncertainty to improve robustness. The stability of the close loop system is proved via a Lyapunov way. The longitudinal tracking control law for velocity and angle of attack is designed based on a rigid dynamic model of a flexible air-breathing hypersonic vehicle. A strong coupling model of the same vehicle, considering aerodynamic-scramjet engine-flight dynamic-elastic couplings, is established as the verification platform of the designed control law. The remarkable differences of flight dynamic characteristics between this strong coupling model and the rigid body model can be seen, which mean the controller needs to endure very great uncertainty, unmodeled dynamics, and other types of internal disturbance. Simulation results based on the coupling model demonstrate that the designed control law has good performance and acceptable robustness.

Partial Finite-Time Stabilization of Perturbed Nonlinear Systems Based on the Novel Concept of Nonsingular Terminal Sliding Mode Method

Abstract In this article, a new technique to design a robust controller to achieve finite-time partial stabilization for a class of nonlinear perturbed systems is proposed. Indeed the system is partially stabilized in a finite time, based on the novel concept of the nonsingular terminal sliding mode (TSM) control method. In the first step, the nonlinear dynamical system is divided into two subsystems based on their required stability properties of the system's states (where finite-time stability is only desired for the first subsystem). Then, using a partial diffeomorphism map to transform the first subsystem into the normal form, the control law is designed. Indeed, by introducing this new concept of the TSM method, robust finite-time stability of only a part of the system's state is guaranteed. Subsequently, simulation results demonstrate the effectiveness of the proposed method, and the results are compared with the existing methods.

A novel finite-time disturbance observer-based partial control design: A guidance application

This paper presents a novel technique to design a robust finite-time partial stabilizer, based on the non-singular terminal sliding mode method and a disturbance observer for the missile guidance problem. In the proposed method, the finite-time stability is desired for only a part of the state variables in the guidance system. Accordingly, the guidance system is divided into two subsystems where the finite-time stability is desired only for the first subsystem. Then, a partial diffeomorphism transformation is used to convert the first subsystem into the normal form. Finally, the components of the input vector appearing in the transformed form of the first subsystem are designed to achieve finite-time stability based on a partial disturbance observer. In the proposed finite-time disturbance observer, the disturbances are estimated in a finite time without any knowledge about their upper bounds. Simulation results demonstrate the effectiveness of the designed guidance law to intercept maneuvering and non-maneuvering targets compared to the existing methods.

Closed-loop powered-coast-powered predictive guidance for spacecraft rendezvous with non-singular terminal sliding mode steering

The present study aims to present a guidance algorithm based on the relative motion prediction for orbital rendezvous, in which a coast phase is allowed between two powered phases. In both powered phases, the solution of the Hill-Clohessy-Wiltshire equations is used to find the required state variables at each time instant. To track the required trajectory and compensate for any orbital perturbations and uncertainties, a non-singular terminal sliding mode method is utilized as the steering law. Then, the finite time convergence of the state variables is mathematically proved. In addition, the starting time of the second powered phase is adapted to perturbations and uncertainties by another closed-loop algorithm during the coast phase. The prediction of the relative state variables along with the inclusion of a coast phase decreases the fuel consumption, while the last powered phase is responsible for the exactness of the terminal rendezvous. Numerical simulations indicate that the proposed guidance and steering laws result in reduced fuel consumption, exactness of the final conditions, and robustness in the presence of disturbances and model uncertainties.

Maximum power extraction from wind energy system using homotopy singular perturbation and fast terminal sliding mode method

In this paper, two strategies are proposed to simplify the dynamics and design of the controller for a variable speed wind turbine (VSWT) with a fractional order doubly fed induction generator (DFIG) in region 2. In the first strategy, the homotopy singular perturbation method (HSPM) is presented using fractional order singular perturbation method (SPM) and modified homotopy perturbation method (HPM). By exerting this method, the fractional order DFIG based VSWT is divided into two lower order subsystems, including nonlinear integer order subsystem and linear fractional order subsystem. In the second strategy, a nonlinear optimal second order fast terminal sliding mode controller (SOFTSMC) using the Lyapunov-based approach with negative definite solution is designed for nonlinear integer order subsystem. Also, a fractional optimal SOFTSMC is proposed by defining the subsystem error dynamics for linear fractional order subsystem. Finally, the control inputs designed for these subsystems are combined and applied to the original system. The main advantage of the HSPM is that both the integer and fractional modelings are used in the design process. The resulting fractional and nonlinear optimal SOFTSMC can be used effectively to achieve the maximum power extraction from the wind, reduce mechanical loads, attenuate the chattering, finite time convergence by applying a small control input, minimize the control input, ensure the better tracking, and tackle the effects of parametric uncertainties, unmodeled dynamics, and external disturbances. Stability of the original system is evaluated by investigating the Lyapunov stability theorem for each subsystem. The proposed controller designed by the HSPM is compared to some existing control laws, and their performance evaluation are reported in Table 1. The results of Table 1 guarantee the effectiveness of the proposed approaches.