Nonsingular Terminal Sliding Mode Surface Research Articles

Ultralocal Model-Free Adaptive Supertwisting Nonsingular Terminal Sliding Mode Control for Magnetic Levitation System

The magnetic levitation technology has attracted blooming attention from all walks of life thanks to its superiorities such as non-contact and active control. While the intrinsic features of open-loop instability and strong nonlinearity, along with the uncertain external disturbance make the levitation control particularly significant and difficult. For speeding up the convergence and obtaining a better stability and disturbance robustness, this paper proposes an ultra-local model-free adaptive super-twisting nonsingular terminal sliding mode control (ULMF-ASTNTSMC) strategy for the magnetic levitation system. Different from the conventional model-based control, ultra-local model-free control breaks the constraint of a precise system model. Therefore, an improved second-order ultra-local model is established for the magnetic levitation system. For the benefit of finite time convergence and non-singularity, the nonsingular terminal sliding mode surface is chosen. As a second-order algorithm, super-twisting (ST) algorithm can fundamentally suppress the chattering effect of the sliding mode control (SMC). An adaptive super-twisting algorithm is designed for the further improvement of the system dynamic response. The stability of the proposed scheme is strictly verified based on the Lyapunov stability theory. Simulation and experimental comparisons with the existing control methods validate the exceeding performance of the proposed strategy under various operating conditions.

Fixed-time nonsingular terminal sliding mode control for trajectory tracking of uncertain robot manipulators

Fixed-time nonsingular terminal sliding mode control for trajectory tracking of uncertain robot manipulators

Application of Backstepping Control With Nonsingular Terminal Sliding Mode Surface Technique to Improve the Robustness of Stator Power Control of Asynchronous Generator-Based Multi-Rotor Wind Turbine System

The conventional backstepping control (CBC) technique for the asynchronous generator (AG) incorporated in a multi-rotor wind turbine (MRWT) system faces several challenges, including torque and stator power ripples, lack of robustness, and low-quality stator currents. Furthermore, the CBC performs poorly under distorted grid voltage conditions. To address these issues, this study proposes applying backstepping nonsingular terminal sliding mode control (BNTSMC). The controller design involves incorporating a NTSMC into the control law of the CBC technique, where Lyapunov theory was used to analyze the stability of the suggested approach. The synthesis of the suggested controller revolves around two sliding mode surfaces, specifically the stator powers of the AG, which are used to determine the final control laws. The advantages of this technique are excellent robustness against internal and external disturbances based on NTSMC, and the controller exhibits asymptotic stability based on the backstepping technique. Simulation tests in MATLAB software on a 1.5 MW AG-based MRWT system clearly demonstrate the advantages of BNTSMC over CBC.

Sensorless control of permanent magnet synchronous motor based on fixed‐time terminal sliding mode observer

AbstractIn the sensorless control of a sliding mode observer (SMO)‐based permanent magnet synchronous motor (PMSM), a large gain is required to ensure the stability of the sliding motion. Nonetheless, this can lead to the unexpected chattering and degrade the precision of position estimation. To overcome this trouble, we have proposed a fixed‐time nonsingular terminal SMO (NTSMO). The convergence time is independent of the initial value. Firstly, a fixed‐time nonsingular terminal sliding mode surface is designed so that the current observation error fixed‐time converges to zero, and the singularity issue can be averted. Secondly, via the phase‐locked loop tactic, the rotor position and speed are calculated from the measured back electromotive force. Thirdly, a Lyapunov function‐based proof is utilized to assure the stability of the observer. Finally, the validity of this method is confirmed by simulation tests and experiment results.

Research on Optimal Fast Terminal Sliding Mode Control of Horizontal Vibration of High-speed Elevator Car System

An optimal fast terminal sliding mode control strategy is proposed to suppress effectively the horizontal vibration of the high-speed elevator car system is caused by uncertainties such as rail unevenness, elevator load variation, and component friction and wear. Firstly, considering the elevator's composition structure and vibration characteristics, a 4-degree-of-freedom car system horizontal vibration active control model with a symmetric distribution of the control center is established. Secondly, considering the nonlinear factors of the rolling guide shoe and the external excitation, an optimal fast terminal sliding mode controller (PFTSMC) based on the sliding mode variable structure control is designed to eliminate the horizontal vibration of the car, define the nonsingular terminal sliding mode surface, and introduce the fast terminal convergence law based on the fast terminal attractor to ensure the accessibility of the sliding mode motion and reduce the jitter vibration. In addition, optimization of controller parameters using random weight particle swarm algorithm (RNW-PSO) to improve the controller's vibration suppression performance and robustness. Finally, the proposed controller can achieve more than 51.2% attenuation of horizontal vibration acceleration and displacement, showing that PFTSMC can effectively reduce the horizontal vibration of high-speed elevator car systems and improve ride comfort.

Robust prescribed performance trajectory tracking control with improved fast nonsingular terminal sliding surface of robot manipulators

This paper investigates the high-precision model-free control of robot manipulators. To this end, a model-free robust prescribed performance controller with an improved fast nonsingular terminal sliding mode surface (IFNTSM) and unknown system dynamics estimator (USDE) has been designed. An USDE method is employed to estimate model informations and further to achieve model-free control, which can avoid complex mathematical model calculation. Compared with some other model-free control methods like time-delay control (TDC) and neural-networks control (NNC), the USED does not require acceleration signal and is easy to implement. Then the prescribed performance control (PPC) has been used to limit error trajectory, which means the error can be pre-limit in a constraint band. A new transform function (TF) is designed for PPC, it has unlimited domain and can still maintain stability although tracking error will exceed PPC boundary sometimes, but the PPC with traditional TF will crash in this case. This is a great improvement for the stability of system compared with traditional TF. An improved fast nonsingular terminal sliding mode surface (IFNTSM) with a new adaptive law is proposed to accelerate convergence rate and improve steady-state accuracy on the sliding manifold. Finally, a practical finite-time controller (PFTC) has been constructed to drive sliding variable to a set centered on zero within a finite time, which means the convergence time can be calculated depending on the initial state. The transient response time can be shorten compared with traditional asymptotic stable. Abundant simulations and experimental results also verified the effectiveness of the proposed scheme.

Finite-Time Fault-Tolerant Control for Swashplate of Integrated Hydraulic Transformer With Uncertain Mismatched Interference

The precision position control for the swashplate servomechanism of the integrated hydraulic transformer (IHT) with mismatched interference is considered in this paper. Compared with the type of port-plate-rotating IHT, the swashplate-rotating IHT has smaller leakage and higher efficiency, but suffers from parameters uncertainty, and time-varying uncertain torque from the plungers. To enhance the robustness of the proposed system, a novel robust control scheme based on a finite-time extended state observer (FTESO) is developed. In the proposed control scheme, the system nonlinearities, parameter uncertainty, actuator failure are both taken into account. And a novel FTESO is established to obtain the state variables, load torque, and failure signals. By introducing the nonsingular terminal sliding mode surface and finite-time technique in each step of the backstepping design, the novel control scheme is able to enhance the robustness of servomechanism and realize finite-time stability of the tracking errors. Finally, the comparative experiment is performed to verify the effectiveness of the controller design.

Model‐free prescribed performance fast nonsingular terminal sliding mode control with practical finite‐time stability of uncertain robot manipulators

AbstractThis paper addresses the problem of robust and high precision trajectory tracking control of uncertain robot manipulators with prescribed performance. Time delay estimation (TDE) technique is employed to estimate system model, then a new self‐adjusting strategy (SAS) is designed to adjust TDE gain online. Prescribed performance control (PPC) method is used to guarantee transient response speed and steady‐state accuracy. Moreover, the transform function of PPC employed in this paper has unlimited domain, which greatly improves the robustness and stability of system. An improved fixed‐time dynamical system is firstly deduced and analyzed, then a new fast nonsingular terminal sliding mode surface is designed to accelerate convergence rate of tracking errors. Finally, the whole system is strictly proven to be practical finite‐time stable, which means that tracking errors can converge to a small neighborhood of zero within a uniformly bounded convergence time. Main advantages of the proposed approach include model‐free, robust, singularity‐free, faster transient response and higher steady‐state tracking precision. Experimental results carried out on the Rethink Sawyer Robot also verified the effectiveness of the proposed scheme.

Dual Jitter Suppression Mechanism-Based Cooperation Control for Multiple High-Speed Trains with Parametric Uncertainty

Parameter uncertainty is one of the key factors that affect the performance of train systems. In order to obtain good tracking and cooperation performances and to improve line utilization, this paper proposes a sliding mode surface-based cooperation control scheme for multiple high-speed trains subject to parameter uncertainty. Based on the single-mass point model, multiple high-speed trains can be modeled as a quasi-multi-agent system with the leader–follower model. Considering the parameter uncertainty of the system, the non-singular terminal sliding mode surface is applied and adaptive control laws are designed to estimate the unknown parameters and external disturbances. A dual jitter suppression mechanism-based cooperation control drive strategy is presented in order to achieve the following objectives: (1) the leading train can track the desired trajectory very well; (2) one train can follow the adjacent train in front at the desired safe interval; and (3) the cooperation performances can be obtained for the quasi multi-agent system. Lyapunov functions are defined to prove the stability of the system, and simulation experiments show that the proposed cooperation control scheme is feasible and effective. According to the presented control scheme applied for multiple high-speed trains, the line utilization rate can be greatly improved.

Cooperative target substitution tracking control of multiple unmanned surface vehicles with substitute USVs

In this paper, the cooperative target substitution tracking problem of multiple unmanned surface vehicles (multi-USVs) with substitute members is studied. The damage and substitution problem of tracking USVs are considered for the first time in the tracking process. Firstly, we propose three substitution tracking strategies to deal with the damaged USVs for the first time. Secondly, the substitute USVs selection algorithm is designed to select appropriate substitute USVs to substitute the damaged USVs. At the same time, the influence of model uncertainty, time varying ocean disturbance and unknown parameter change on underactuated USVs tracking control are considered. Then, a novel tracking error system and a novel nonsingular terminal sliding mode surface are proposed. A novel cooperative distributed fast finite time substitution tracking control law is proposed based on nonsingular terminal sliding mode control and fast power reaching law. Finally, we use Lyapunov stability criterion to verify that the designed control law can achieve fast finite time tracking, and solve the tracking time varies caused by the tracking USVs being damaged and substituted. We also illustrate the correctness of our results by numerical simulations.

Intelligent Attitude Fault-Tolerant Control of Space Tumbling Target Fly-Around Based on RBF Neural Network

The flying around monitoring task of space tumbling target is one of the key links of its on-orbit service. Considering the practical constraints of system inertia uncertainty, external disturbance, actuator saturation, and fault in engineering practice, a robust composite controller based on radial basis function (RBF) neural network is proposed. First, in a new line of sight rotation (RLOS) coordinate system, the relative attitude kinematics and dynamics equations between the tracker and tumbling target based on the error quaternion are established; second, the RBF neural network is used to estimate the additive and multiplicative faults of the system, and the fast nonsingular terminal sliding mode surface (FNTSMS) is combined with the active disturbance rejection control (ADRC) technology to design a finite-time fault-tolerant control (FTC) strategy with high accuracy, strong robustness, and anti-saturation based on the RBF neural network. It is proven that the designed robust fault-tolerant controller can ensure that the system state error converges to a small region containing the origin in a limited time under the Lyapunov framework. Finally, the effectiveness and superiority of the control strategy were verified by numerical simulation.

Disturbance observer-based fractional-order sliding mode control for free-floating space manipulator with disturbance

This paper proposes a fractional-order sliding mode control scheme based on disturbance observer for tracking control of free-floating space manipulators (FFSM), regarding system uncertainties and disturbances. To mitigate the effect of disturbance, a fast fractional-order disturbance observer (FFODOB) is proposed, which can estimate the disturbances in finite time. It relaxes the assumption of first-order differentiable of the disturbances, which is common in many existing disturbance observers, to continuous but not necessarily differentiable, making it more suitable for practical applications. Besides, a new fractional-order nonsingular terminal sliding mode (FONTSM) controller is designed, in which, a fractional-order integral term is introduced into the conventional nonsingular terminal sliding mode surface. The presented FONTSM improves the transient response and tracking precision of FFSM. Stability of the closed-loop system and finite-time convergence are proved theoretically. Simulations are performed for different situations, and the results demonstrate the effectiveness and superiorities of the proposed methods over the existing methods.

Finite-time robust control of robotic manipulator with input deadzone and time-varying disturbance compensation

In this paper, the problem of trajectory tracking for robotic manipulator with input deadzone and time-varying disturbances is investigated using a continuous non-singular terminal sliding mode control (SMC). The robotic manipulator plays a vital role in industrial as well as many other applications. However, it faces numerous problems for accurate and fast trajectory tracking response in the presence of unknown uncertainties and external disturbances, that always have adverse affects on system closed-loop performance. This paper proposes a valid control design scheme to address the aforementioned practical issue. First, a non-singular terminal sliding mode surface is designed. Then, a robust control law is developed to guarantee the finite-time converges of system states to the origin. In addition, the sign function is substituted by saturation function, which can effectively reduce the chattering driven by the high-frequency switching item in the traditional SMC method. Moreover, the Lyapunov stability criterion is used to prove the stability of the closed-loop system. The efficiency of the designed control scheme is validated with numerical simulations.

A Novel Nonsingular Terminal Sliding Mode Observer-Based Sensorless Control for Electrical Drive System

To improve the sensorless control performance of electrical drive systems, a nonsingular terminal sliding mode observer (NTSMO) and adaptive observer are proposed to solve the chattering and phase delay problems. Firstly, by defining a new nonsingular terminal sliding mode surface, the sliding mode observer based on the fast reaching law is designed to estimate the back electromotive force (EMF). The observer enhances the robustness and system performance eliminates the singularity and attenuates the chattering. Next, to obtain the accurate back-EMF signal, an adaptive observer is designed instead of a traditional low-pass filter to filter out the harmonics. The adaptive observer can avoid the phase delay problem and further improve the signal observation accuracy. Then, the rotor position and speed information are accurately tracked. The proposed method is applied to the speed control system of a permanent magnet synchronous motor (PMSM), and the effectiveness and feasibility of the proposed sliding mode observer are demonstrated by the experiment.

Adaptive neural sliding mode control of uncertain robotic manipulators with predefined time convergence

AbstractIn this article, a predefined time convergence adaptive tracking control scheme is designed for a class of uncertain robotic manipulators with input saturation. First, a novel auxiliary dynamic system is proposed to handle the influence of input saturation. Radial basis function neural networks are used to approximate the uncertainty of the closed‐loop system and the neural adaptive law is designed by using the given time constant so that the neural networks have a fast convergence rate. The adaptive tracking controller is constructed by utilizing a nonsingular terminal sliding mode surface. Different from the finite‐time and the fixed‐time sliding mode control methods where the upper bound of the convergence time is related to system parameters, the convergence time upper bound of the proposed sliding mode controller is a given constant. Finally, numerical simulations are performed to illustrate that the proposed control scheme possesses the advantages of fast convergence rate and input saturation elimination.

Cooperative guidance law for multiple missiles simultaneous attacks with fixed-time convergence

This paper considers the problem of multiple missiles to attack a maneuvering target simultaneously. Based on a fixed-time fast nonsingular terminal sliding mode surface (FNTSMS), fixed-time distributed cooperative guidance laws are developed. By designing guidance laws along and perpendicular to line of sight (LOS) direction, both relative velocity and range-to-go are consistent. In addition, a saturation function is introduced to avoid the chattering problem caused by the commonly used sign function. Furthermore, a distributed cooperative guidance law with communication failure is considered and proved theoretically, which shows that the proposed guidance law has excellent performance. Finally, the simulation results not only explain the performance of the distributed guidance law,but also verify the robustness against communication topology switching.

Finite-time active fault-tolerant attitude control for flexible spacecraft with vibration suppression and anti-unwinding

In this paper, a finite-time active fault-tolerant control scheme is designed for a flexible spacecraft’s attitude control experiencing inertial parametric variations, external disturbances, multiple actuator faults, and estimation errors while suppressing the flexible appendages’ vibrations without using smart vibration suppression actuators. First, relative attitude dynamics of a flexible spacecraft with multiple actuator faults are outlined, and a sliding mode observer is designed to estimate flexible appendages-related vibrations. The proposed fault detection and identification (FDI) strategy can efficiently detect actuator faults, avoiding the false alarms caused by uncertainties and disturbances, and accurately estimate the cumulative fault effects on the spacecraft via Chebyshev neural network (CNN) based estimator. Based on a novel fast nonsingular terminal sliding mode surface, a finite-time, unwinding-free, and adaptive fault-tolerant attitude controller is designed to acclimatize the detected faults and uncertainties effectively, also heeding the errors in the estimation of flexible modes and faults. The spacecraft can carry out the coveted control objective in a definable time, and the stability of the proposed controller is corroborated via Lyapunov techniques. Finally, a comparative simulation analysis with the existing results elucidated the proposed scheme’s efficacy.

Fuzzy Approximation-Based Fractional-Order Nonsingular Terminal Sliding Mode Controller for DC–DC Buck Converters

This article presents a simple and systematic approach to synthesize a robust adaptive fuzzy fractional-order nonsingular terminal sliding mode controller (AFFO-NTSMC) to improve the output voltage tracking control performance of the dc–dc buck converters. The hybrid control method of fractional-order (FO) calculus and NTSMC are combined to create a FO-NTSMC, in which a new FO nonsingular terminal sliding mode surface is established. The idea behind this strategy is the increased flexibility achieved by FO calculation, improving robustness to disturbances and parameters variations provided by the traditional sliding mode controllers as well as finite time convergence properties of the output voltage error to the equilibrium point during the output load changes, simultaneously. In addition, a fuzzy logic system with online adaptive learning algorithm is designed to provide smooth chattering in switching control signal. The stability of the closed-loop system is carefully demonstrated by Lyapunov's theorem. Experimental measurements from a laboratory prototype are presented to demonstrate the effectiveness of the proposed AFFO-NSTSMC algorithm.

Event-Triggered Finite-Time Attitude Cooperative Control for Multiple Unmanned Aerial Vehicles.

The finite-time attitude cooperative control problem for a group of multiple unmanned aerial vehicle systems with external disturbances and uncertain parameters is discussed in this paper. The dynamics of the systems is described by quaternion avoiding the singularity. Based on the attitude error and angular velocity error, a novel nonsingular terminal sliding mode surface is proposed for the controller with event-triggered scheme. The lumped disturbances are estimated by neural networks with adaptive law. The communication frequency is decreased by the proposed distributed event-triggered based sliding mode controller. Lyapunov theory is utilized to analyze the stability of the systems, and the Zeno behavior is avoided by rigorous proof. Finally, simulation examples are presented to illustrate the efficiency of the proposed control algorithm.

Fault‐tolerant attitude tracking control with practical finite time convergence for unmanned aerial vehicles under actuation faults

AbstractThis paper presents an adaptive attitude finite time tracking control algorithm for quadrotor unmanned aerial vehicle (UAV) in presence of actuator faults, input saturation and external disturbance. The dynamic model of the quadrotor UAV is characterized with quaternion representation. Subsequently, using nonsingular terminal sliding mode surface, an adaptive fault‐tolerant finite‐time attitude control scheme is proposed. Using Lyapunov stability analysis, it is shown that the proposed method is able to achieve practical finite time attitude tracking convergence in that the attitude tracking error converges to a small residual set within finite time and all signals of the closed‐loop system remain bounded. The effectiveness of the proposed method is confirmed via numerical simulation.