Nonsingular Terminal Sliding Mode Research Articles

Adaptive Disturbance Observer-Based Novel Fixed-Time Nonsingular Terminal Sliding-Mode Control for a Class of DoF Nonlinear Systems

In this article,we study a novel fixed-time tracking controller for a class of degree-of-freedom nonlinear systems with mismatched and matched perturbations. A modified fixed-time stable system (FTSS) is first proposed, which has an advantage in convergence rate over the existing results. Moreover, an adaptive version of fixed-time disturbance observer (DO) is established to eliminate the requirement for prior knowledge of the perturbation bounds. Based on the aforementioned FTSS and DO, a new fixed-time terminal sliding-mode surface with singularity circumvention is constructed. Then, a novel composite tracking controller is designed, which can guarantee the tracking errors to converge to zero within the fixed time. The stabilities of both the DO and the resulting closed-loop systems are rigorously proved by the Lyapunov theorem. Simulation results of two representative examples demonstrate the efficiency of the proposed approach.

Integral Non-Singular Terminal Sliding Mode Consensus Control for Multi-Agent Systems with Disturbance and Actuator Faults Based on Finite-Time Observer.

This paper studies the consensus fault-tolerant control problem of a class of second-order leader–follower multi-agent systems with unknown disturbance and actuator faults, and proposes an integral non-singular terminal sliding mode control algorithm based on a finite-time observer. First, a finite-time disturbance observer was designed based on a combination of high-order sliding mode and dual layers adaptive rules to realize fast estimation and compensation of disturbance and faults. Then, a sliding surface with additional integral links was designed based on the conventional sliding surface, and an integral non-singular terminal sliding mode controller is proposed to realize the robust consensus in finite time and accurately diminish the chattering phenomena. Finally, a numerical example and simulation verify the effectiveness.

BLF-Based Neuroadaptive Fault-Tolerant Control for Nonlinear Vehicular Platoon With Time-Varying Fault Directions and Distance Restrictions

This paper investigates the neuroadaptive fault-tolerant control of nonlinear vehicular platoon with unmodeled dynamics, external disturbances, time-varying actuator fault directions, and distance restrictions. For the cases of known and unknown fault directions, by combining adaptive terminal sliding mode (TSM) control technique with barrier Lyapunov function (BLF), two neuroadaptive fault-tolerant controllers are designed based on symmetric and asymmetric BLF to ensure reliability and safety of vehicular platoon. BLF approaches are adopted to avoid collisions and to maintain communication connections simultaneously. In addition, it is worth mentioning that the unfavorable symmetry assumptions in the symmetric BLF and prescribed performance methods can be removed by adopting asymmetric BLF. In the proposed scheme, we also combine the Nussbaum function to solve the influence of unknown time-varying fault directions effectively. Furthermore, the nonsingular TSM control technique and the minimum parameter approximation method in radial basis function neural network (RBFNN) are adopted to ensure that the spacing error can converge to an arbitrarily small region in finite-time. Through the Lyapunov stability theory, we prove that all signals in the closed-loop system are bounded in finite time. The proposed control schemes are validated by means of simulation examples.

Safe operation for teleoperated robotic manipulators with restricted synchronization error via non-singular terminal sliding-mode control

This study presents the design of a robust controller based on the sliding mode theory to ensure the safe operative synchronization of a teleoperated robotic system (TRS). The TRS is integrated by two fully actuated robotic manipulators (RMs) with n degrees of freedom (DoF). The proposed controller implements a decentralized adaptive super-twisting algorithm to obtain the force applied by the human operator and the environment over the TRS. Then, a decentralized non-singular terminal sliding mode (NTSM) controller solves the synchronization problem for the proposed RMs. The novel control approach ensures synchronization, considering that both manipulators have restricted working spaces. The suggested controller enforces the convergence to the origin for the tracking error in a finite time, at least theoretically. The stability analysis of the proposed controller is developed using the second stability method of Lyapunov, considering a class of barrier Lyapunov controlled function. Finally, simulation results are presented to evidence the effectiveness of both proposed algorithms, the adaptive force estimator and the NTSM.

Terminal sliding-mode control for input-constrained free-float space manipulator via learning-based adaptive uncertainty rejection

The free-float space manipulator (FFSM) control problem subject to coupling dynamics, uncertainties, and input saturation constraints is investigated in this paper. The screw-based dynamical model is established through the Lagrangian equation and Hamilton’s variational principle such that the posture of the rigid body can be described uniquely and globally. The derived dynamics is then reduced to a decoupled one in the light of the conservation of the momentum. On this basis, a novel anti-windup finite-time sliding-mode control strategy is investigated to guarantee the tracking performance in the joint space of FFSM, where a learning-based adaptive neural network is designed to estimate the uncertainties. The approximation error is inhibited by a tanh-type slow-varying adaptive law which is integrated into an auxiliary system to compensate for input saturation nonlinearities. With the contributions above, the stability of the proposed nonsingular terminal sliding-mode (NTSM) controller is comprehensively proved. Comparative simulations based on a 6-DOF FFSM confirm the validity of the proposed control scheme.

Time‐varying nonsingular terminal sliding mode control for uncertain second‐order nonlinear systems with prespecified time

AbstractThis article proposes a time‐varying nonsingular terminal sliding mode (TSM) control for a class of uncertain second‐order nonlinear system and its application to n‐links rigid robotic manipulators. First, a time‐varying nonsingular terminal sliding manifold is developed by incorporating a piecewise‐defined function of time into a nonsingular TSM manifold. As a result, the singularity problem is avoided and the reaching phase existing in conventional TSM control is totally suppressed which ensures the global robustness of the system against uncertainties and disturbances. Moreover, adaptive tuning laws are developed to omit the requirement of prior knowledge of the upper bound of the lumped uncertainty. In particular, an effective method is provided for the parameters selection to meet a prespecified convergence time. Hence, the convergence time to the origin of the tracking errors can be specified in advance according to the mission requirements. The formulation of the controllers and the stability analysis are verified by Lyapunov theory. Simulation results and comparative studies are presented to demonstrate the effectiveness and the superiority of the proposed algorithms.

ADRC Control System of PMLSM Based on Novel Non-Singular Terminal Sliding Mode Observer

In an attempt to solve the problem of the many parameters of the traditional active disturbance rejection controller (ADRC) and to accurately estimate the mover position and speed required by a permanent magnet synchronous linear motor (PMLSM) system, an improved ADRC and a novel nonsingular fast terminal sliding mode observer (NFTSMO) are proposed. Firstly, the traditional first-order ADRC is simplified, the tracking differentiator (TD) module is removed, and the direct error is used to replace the nonlinear function in the extended state observer (ESO) and nonlinear state error feedback (NLSEF) module. Based on the traditional NFTSMO, the smooth back electromotive force (EMF) is obtained by adding the TD to reduce the phase delay caused by the low-pass filter in the traditional sliding mode observer (SMO), and the actuator position and speed information are modulated from the observed back EMF based on the principle of a phase-locked loop (PLL). Simulation and experiments show that this method not only simplifies the system structure of PMLSM but also optimizes many parameters in ADRC while retaining the original excellent performance. Compared with the traditional NFTSMO, the improved NFTSMO enhances the observation accuracy, reduces the chattering phenomenon of the system, and improves the robustness of the system.

Fixed‐time non‐singular terminal sliding mode control with globally fast convergence

This paper investigates a fixed-time terminal sliding mode (TSM) control scheme of second-order non-linear uncertain systems. A globally fast fixed-time stable system is proposed, and the convergence time is established with the Lyapunov method. Then, a novel non-singular TSM utilising the proposed fixed-time stable system and an auxiliary polynomial function is constructed. Meanwhile, a fixed-time disturbance observer technique is employed to estimate the matched lumped perturbation. Globally fast fixed-time convergence of the closed-loop system is guaranteed with the phase plane analysis and Lyapunov tools, and the upper bound of the settling time independent of the initial conditions can be predefined by the controller parameters. Finally, the simulation results of a single inverted pendulum system are included to confirm the validity of the proposed methodology while comparing with some popular TSM control strategies.

Low-Dimensional-Approximate Model Based Improved Fuzzy Non-Singular Terminal Sliding Mode Control for Rigid-Flexible Manipulators

The dynamic characteristics of rigid-flexible manipulators involve complex rigid-flexible coupling phenomena, which essentially comprise a nonlinear distributed parameter system with infinite degrees of freedom. Consequently, it results in challenges to the manipulator’s precise positioning. This study combined a state feedback module and a fuzzy non-singular terminal sliding mode to suppress vibration and deformation. Using the improved fuzzy strategy and non-singular terminal sliding mode control, an adaptive dynamic supplementary control law is proposed. The results based on MATLAB simulation and a built hardware experiment show that this method is effective and superior. While realizing the accurate positioning of the end of the manipulator, the vibration of the end of the flexible arm is significantly suppressed. This method has a high tracking performance, which enables accurate positioning of the manipulator terminal and provides strong robustness under the action of bounded external interference.

Cooperative Smooth Nonsingular Terminal Sliding Mode Guidance with Tracking Differentiator for Active Aircraft Defense

Aimed at the poor performance of guidance algorithms designed based on a linearized model in active defense under large leading angle deviation, both-way and one-way cooperative sliding mode guidance algorithms based on the smooth nonsingular terminal sliding mode for the defense missile are proposed. The relative kinematics and linearized models of the target, the active defense missile, and the attacking missile are established. In the design process, two smooth nonsingular terminal sliding mode surfaces are constructed based on zero-effort miss distance and zero-effort velocity, as well as their integral values. A tracking differentiator is introduced for excessive initial command deviation to meet the overload constraints of the active missile and the target. The sensitivity of guidance law to the estimated time-to-go error is reduced, and the target is allowed to perform an independent evasive maneuver. The effectiveness of the proposed guidance strategy is verified by numerical simulation and compared to the existing guidance strategies, the high accuracy, anti-chattering, and strong robustness of the proposed guidance algorithm are verified.

Adaptive Nonsingular Terminal Sliding Mode Control for Performance Improvement of Perturbed Nonlinear Systems

In this study, an adaptive nonsingular terminal sliding mode control technique according to the barrier function is designed for the performance improvement and robust stability of nonlinear systems with outdoor disturbances. For this reason, a novel nonlinear sliding surface is presented based on the states of the system. The nonlinear sliding surface forces the states of the system to converge from initial conditions to zero. Subsequently, a non-singular terminal sliding control scheme is advised for the purpose of finite-time stability of the nonlinear switching surface. Finite-time stabilization of the non-singular terminal sliding surface is verified by the Lyapunov theory. For improvement of the system performance against exterior perturbation, the barrier function adaptive technique is employed to estimate the unknown upper bounds of the exterior disturbance. Finally, the advantage and productivity of the recommended control method is investigated based on the simulation results. In the simulation part, the plasma torch jerk chaotic system is considered as a case study, such that the obtained results are given in different scenarios.

Frequency-Response of Non-Singular Terminal Sliding Mode Control With Actuators

Non-singular terminal sliding mode control (NTSMC) is widely popular due to its various industrial applications. In many practical circuit systems, the control input is actually given to an actuator rather than directly to the plant. Therefore, it is important to study the effect of actuators on NTSMC performance. In this brief, frequency-domain characteristics of NTSMC are analyzed using the describing function method. It is shown that in the presence of actuator dynamics, the system exhibits a self-sustained periodic oscillation known as chattering. The relationship between the fundamental frequency, the amplitude of this periodic motion and the NTSMC parameters is explored. The effectiveness of the theoretical analysis is verified via a practical example based on an industrial emulator system.

Nonsingular Terminal Sliding Mode Control-based Prescribed Performance Guidance Law with Impact Angle Constraints

Nonsingular Terminal Sliding Mode Control-based Prescribed Performance Guidance Law with Impact Angle Constraints

Neural Network Non-Singular Terminal Sliding Mode Control for Target Tracking of Underactuated Underwater Robots with Prescribed Performance

This paper proposes a neural network-based nonsingular terminal sliding mode controller with prescribed performances for the target tracking problem of underactuated underwater robots. Firstly, the mathematical formulation of the target tracking problem is presented with an underactuated underwater robot model and the corresponding control objectives. Then, the target tracking errors from the line-of-sight guidance law are transformed using the prescribed performance technique to achieve good dynamic performance and steady-state performance that meet the pre-set conditions. Meanwhile, considering the model’s uncertainties and the external disturbances to the underwater robots, a target tracking controller is proposed based on the radial basis function (RBF) neural network and the non-singular terminal sliding mode control. Lyapunov stability analysis and homogeneity theory prove the tracking errors can converge on a small region that contains the origin with prescribed performance in finite time. In the simulation comparison, the controller proposed in this paper had better dynamic performance, steady-state performance and chattering supression. In particular, the steady-state error of the tracking error was lower, and the convergence time of the tracking error in the vertical distance was reduced by 19.1%.

An Adaptive Nonsingular Fast Terminal Sliding Mode Controller for Dynamic Walking of a 5-Link Planar Biped Robot in Both Single and Double Support Phases

This paper aims to design an improved adaptive nonsingular fast terminal sliding mode controller for a fully actuated planar biped robot with five degrees of freedom in the single support (SSP) and double support (DSP) phases in the presence of external perturbation and uncertainties. A new sliding surface was proposed to avoid singularities and the chattering phenomenon. The proposed controller guarantees fast convergence of error signals in finite time. Unlike similar studies, the presented method considers a whole cycle of one step of walking, including SSP, double impact, and DSP phases. Also, the proposed approach does not require a predefined upper limit to estimate uncertainty using an adaptive law. Notably, dynamic walking was preferred over static walking to achieve more similarity to human walking. The designed trajectories were determined according to the position of the waist and swinging legs ankle, which could then be converted into the position of joints using inverse kinematics equations. The simulation results were used to approve the proposed controller's fast and robust tracking performance in the presence of external disturbances, mass, and inertia uncertainties without predefined knowledge of their upper bounds.

Robust trajectory tracking with non-singular terminal sliding mode control of a mobile manipulator

This effort addresses and uses a robust-trajectory-tracking control system for kinematically redundant location tracking of a mobile manipulator (mobman) in its task space in the presence of parameter uncertainties and external disturbances. It consists of a serial manipulator with four degrees of freedom (DOF) fixed on three DOF mobile bases. A robust tracking control is achieved using the configuration of a non-singular terminal sliding mode (NSTSM) control for the entire non-linear model of a mobman. Because of the non-linear added term in the linear sliding surface, which reflects in the non-linear sliding mode known as terminal sliding mode (TSM), this control preparation satisfies systems states finite time convergence. Similarly, conventional terminal sliding mode control (CTSMC) entail singularity trouble, which is tackled by the control scheme. (Computer based) simulations are used to demonstrate the convenience, feasibility, and robustness of given techniques.

Fixed-time nonlinear homogeneous sliding mode approach for robust tracking control of multirotor aircraft: Experimental validation

This paper presents a robust scheme for fixed-time tracking control of a multirotor system. The aircraft is subjected to matched lumped disturbances, i.e., unmodeled dynamics, parameters uncertainties, and external perturbations besides measurement noise. Firstly, a novel Nonlinear Homogeneous Continuous Terminal Sliding Manifold (NHCTSM) based on the weighted homogeneity theory is presented. The sliding manifold is designed with prescribed dynamics featuring Global Asymptotic Stability (GAS) and fixed-time convergence. Then, a novel Fixed-time Non-switching Homogeneous Nonsingular Terminal Sliding Mode Control (FNHNTSMC) is proposed for the position and attitude loops by employing the developed NHCTSM and an appropriate reaching law. Moreover, the control framework incorporates a disturbance observer to feedforward and compensate for the disturbances. The designed control scheme can drive the states of the system to the desired references in fixed-time irrespective of the values of the Initial Conditions (ICs). Since the existing works on homogeneous controllers rely on the bi-limit homogeneity concept in the convergence proofs, the estimate of the settling-time or its upper-bound cannot be given explicitly. In contrast, this study employs Lyapunov Quadratic Function (LQF) and Algebraic Lyapunov Equation (ALE) in the stability analysis of both controller and observer. Following this method, an expression of the upper-bound of the settling-time is explicitly derived. Furthermore, to assure the Uniform Ultimate Boundedness (UUB) of all signals in the feedback system, the dynamics of the observer and controller are jointly analyzed. Simulations and experiments are conducted to quantify the control performance. The proposed approach achieves superior performance compared with recent literature on fixed-time/finite-time control and a commercially available PID controller. The comparative results witness that the developed control scheme improves the convergence-time, accuracy, and robustness while overcoming the singularity issue and mitigating the chattering effect of conventional SMC.

Recurrent neural network non‐singular terminal sliding mode control for path following of autonomous ground vehicles with parametric uncertainties

Uncertain characteristics along with unknown exterior disturbances are fundamental issues in the path-following control of autonomous ground vehicles (AGVs). Here, a novel robust non-singular terminal sliding mode (NTSM) control method based on a recurrent neural network (RNN) structure is proposed to enhance the path-following performance of AGVs. First, based on the dynamic model and path-following model of AGVs, the robust NTSM steering controller is proposed to ensure that the lateral offset converges to zero within a limited time, and concurrently suppresses the chattering phenomenon that occurs in the regular sliding mode control (SMC) strategy. Then, the RNN is applied to approximate the unknown dynamics section of the system online. With an implied feedback loop, its study ability precedes the regular neural network to catch up with the dynamic response. In addition, the adaptive learning algorithms of the parameters in the RNN are derived using the Lyapunov stability theorem and Taylor linearisation technique to ensure the stability of the closed-loop system. Finally, the robustness and effectiveness of the proposed control approach against parametric uncertainties and unknown external disturbances are verified in the Simulink-CarSim simulation platform by comparison with selected reported control methods.

Applied Mechatronics: On Mitigating Disturbance Effects in MEMS Resonators Using Robust Nonsingular Terminal Sliding Mode Controllers

This investigation attempts to study a possible controller in improving the dynamic stability of capacitive microstructures through mitigating the effects of disturbances and uncertainties in their resultant dynamic behavior. Consequently, a nonsingular terminal sliding mode control strategy is suggested in this regard. The main features of this particular control strategy are its high response speed and its non-reliance on powerful controller forces. The stability of the controller was investigated using Lyapunov theory. For this purpose, a suitable Lyapunov function was introduced to prove the stability of a controller, and the singularity conditions and methods to overcome these conditions are presented. The achieved results proved the high capability of the applied technique in stabilizing of the microstructure as well as mitigating the effects of disturbances and uncertainties.

Path Tracking of a Four-Wheel Independently Driven Skid Steer Robotic Vehicle Through a Cascaded NTSM-PID Control Method

Four-wheel independently driven skid steer robotic vehicles (IDSSRVs) have been widely applied in many fields. However, limited by small size and low power consumption, many sensors and high-performance processors cannot be equipped into four-wheel IDSSRVs, which makes path tracking more complex. The nonsingular terminal sliding mode (NTSM) is a good choice for small robotic vehicles because of its strong robustness, fast convergence, and low complexity. However, the performance of the NTSM is easily affected by vehicular weight and road friction because a four-wheel IDSSRV has no steering devices and its driving behavior is completed by adjusting the velocity of the four wheels based on the wheel–ground interaction. Furthermore, a minor instability caused by the output difference of the motors can bring extra torque on the vehicle and ultimately lead to a tracking deviation for the NTSM controller. To resolve these problems, a dynamic model of a four-wheel IDSSRV is analyzed first. Subsequently, a cascaded NTSM-proportional–integral–derivative (PID) method is proposed, in which a conversion function based on compensating the sideslip angle is raised to improve the NTSM controller performance of antidisturbance and tracking accuracy with the limitations of the sensors and processors, and a joint PID controller simultaneously optimizing the motor output error and vehicular yaw error is designed to eliminate the imbalance of motor output and to reduce the deviation of the NTSM controller. Finally, comparative experiments are conducted, and the results highlight the benefits of the proposed approach by reducing the tracking error by approximately 80% compared with the dynamic model predictive control (MPC) method and reducing the tracking error by over 30% compared with the pure NTSM method.