Terminal Sliding Mode Surface Research Articles

Active Fault Tolerant Nonsingular Terminal Sliding Mode Control for Electromechanical System Based on Support Vector Machine

Effective fault diagnosis and fault-tolerant control method for aeronautics electromechanical actuator is concerned in this paper. By borrowing the advantages of model-driven and data-driven methods, a fault tolerant nonsingular terminal sliding mode control method based on support vector machine (SVM) is proposed. A SVM is designed to estimate the fault by off-line learning from small sample data with solving convex quadratic programming method and is introduced into a high-gain observer, so as to improve the state estimation and fault detection accuracy when the fault occurs. The state estimation value of the observer is used for state reconfiguration. A novel nonsingular terminal sliding mode surface is designed, and Lyapunov theorem is used to derive a parameter adaptation law and a control law. It is guaranteed that the proposed controller can achieve asymptotical stability which is superior to many advanced fault-tolerant controllers. In addition, the parameter estimation also can help to diagnose the system faults because the faults can be reflected by the parameters variation. Extensive comparative simulation and experimental results illustrate the effectiveness and advancement of the proposed controller compared with several other main-stream controllers.

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

Fixed-Time Aircraft Spin Recovery Control Based on a Nonsingular Integral Terminal Sliding Mode Approach

This paper introduces a control strategy to recover from various spin motions to level trim flight conditions, utilizing a fixed-time nonsingular terminal sliding mode approach to minimize altitude loss. Firstly, an integral terminal sliding mode surface is constructed to guarantee the tracking errors of the spin recovery system converge to the origin within a fixed time and avoid the singularity problem. Next, a fixed-time type reaching law is proposed to weaken the chattering phenomenon and guarantee terminal sliding hyperplanes converge to zero in a fixed time. Furthermore, the stability analysis indicates the fixed-time convergence stability of the spin recovery control system and provides an accurate calculation of the settling time. Finally, comparative simulations are performed to validate the effectiveness and superiority of the developed spin recovery control scheme.

Finite-time attitude tracking control of stratospheric airship in the presence of multiple disturbances

Abstract This paper proposes a composite non-singular fast terminal sliding mode attitude control scheme based on a reduced-order extended state observer for the stratospheric airship’s attitude system affected by multiple disturbances. First, the feedback linearisation method is applied to address the nonlinearity of the attitude motion model and achieve decoupling of the model in three channels. Second, the overall disturbances, encompassing airship parameter perturbations and external disturbances, are treated as an aggregate. A reduced-order extended state observer is designed for each channel to formulate a composite non-singular fast terminal sliding mode surface. In the control design phase, the hyperbolic sine function is adopted as replacement for the sign function to ensure the continuity of the control signal. The estimated disturbances are incorporated in the control law design to directly offset the effects of multiple disturbances on the attitude motion of the airship. Third, based on Lyapunov theory, it has been proven that the control law can drive the attitude tracking error to converge to zero within a finite time. Simulation results demonstrate that the proposed control scheme exhibits favorable disturbance rejection capability, as well as higher tracking accuracy and faster response speed.

Sliding mode coordinated control of hybrid electric vehicle via finite-time control technique

During the transient mode switching process of the hybrid electric vehicle (HEV) from motor driving mode to hybrid driving mode, dynamic coordinated control of different components is essential to improve the vehicle comfort and dynamic performance. The key to highly quality mode switching control includes fast and stable speed and/or displacement tracking of the engine and motor. The transient mode switching stages of the HEV is divided in this paper. On this basis, by combing the nonlinear sliding mode control and the finite-time stability theory, the global fast integral terminal sliding mode controller (GFITSMC) is designed for the transition stages involving clutch slip. The GFITSMC consists of the global fast integral terminal sliding mode surface (GFITSMS) and the non-smooth reaching law (NSRL). In order to improve the controller convergence and anti-disturbance performance, the proposed controller is synthesized from the perspective of finite-time stability. It is proved that, with proper NSRL and GFITSMS parameters, the speed and displacement tracking error of the motor and engine can reach the sliding mode surface and further converge to zero in a finite time. Simulation and hardware-in-the-loop (HIL) tests are performed to validate the effectiveness of the proposed control method. Research results demonstrate that the proposed strategy not only achieves faster transient mode switching by improving the state trajectory tracking performance, but also reduces the longitudinal jerk caused by the transient mode switching significantly.

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.

Fixed-time tracking control of manipulators based on non-singular fast terminal sliding surface

As for the problem of trajectory tracking of a multi-joint serial manipulator, a novel fixed-time control scheme is proposed based on non-singular fast terminal sliding mode control. By employing a fast terminal sliding mode surface, we solve the singularity problem existed in traditional terminal sliding mode surface. In the meantime, in order to improve the rapidity of the system, the fixed-time control is incorporated with the fast terminal sliding mode surface control. Theoretical analysis proves that the proposed control scheme guarantees that better tracking performance is obtained, and its convergence time upper limit is not affected by the initial states. In addition, a reaching law with the exponential approach characteristic is added to the control law, which effectively reduces the chattering phenomenon in the controller design. Finally, the effectiveness and feasibility of the designed controller are verified through a numerical simulation.

Fixed‐time dual sliding mode control for linear synchronous motor maglev systems

AbstractA dual fixed‐time terminal sliding mode control strategy is proposed to address the problems of magnetic coupling, end effects and unknown disturbances in linear synchronous motor maglev systems, which ensures that the system tracking trajectory achieves fixed‐time convergence and high accuracy. First, a fixed‐time integral terminal sliding mode surface is designed to obtain the desired dynamic properties and avoid the singularity problem. Second, based on the dynamic sliding mode theory, a second fixed‐time terminal sliding mode surface is designed to weaken the chattering problem in the controller by replacing the discontinuous switching signal with a continuous switching rule. The proposed controller is theoretically proved to be fixed‐time convergent and the convergence time is independent of the initial conditions by means of the Lyapunov function and the fixed‐time convergence theorem. Finally, simulations and experiments are carried out on a linear maglev experimental platform. Compared with the fixed‐time sliding mode control, the simulation and experimental results show that the proposed strategy improves the tracking accuracy by 37.5%, the convergence speed by 33.3%, and the robustness by 42.1%, which has the advantages of fast convergence speed, strong robustness, and weak chattering.

Assembly-Oriented Finite-Time Coordinated Control of Underactuated Dual Rotary Cranes for Payload Position and Attitude Regulation

With strong load capacity and high maneuverability of payload attitude regulation, dual rotary cranes (DRCs) are widely applied for transportation and assembly tasks in infrastructure construction. For DRCs, to achieve safe and accurate control of the payload position and attitude, it is necessary to enhance the motion synchronization of two cranes, under the premise of controlling more state variables with fewer control inputs based on nonlinear coupling dynamics; moreover, the finite-time convergence of positioning errors is also expected to be guaranteed for high efficiency. To this end, this paper proposes an assembly-oriented finite-time coordinated controller <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> any linearization to the nonlinear crane dynamics, which realizes accurate and stable regulation of the payload position and attitude through coordinated boom motions. To our knowledge, the proposed controller provides the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> closed-loop control solution to realize both horizontal and non-horizontal payload hoisting for DRCs based on practical assembly demands. Theoretically, through elaborate design of the synchronization error and coupling errors, the real-time information exchange between the two cranes is realized for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> time, which enhances the boom motion synchronization while suppressing payload swings. Furthermore, by introducing continuous terminal sliding mode surfaces with a multi-layer nested structure, the finite-time convergence of the boom positioning errors and the synchronization error is ensured with chattering reduction. Additionally, rigorous closed-loop stability analysis is provided based on Lyapunov techniques and Barbalat’s Lemma. Finally, the effectiveness and robustness of the proposed controller are verified by hardware experimental results. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the coordinated motion control problem of dual rotary cranes (DRCs), which aims to achieve safe and accurate control of the payload position and attitude oriented on practical assembly demands. At present, most control methods for DRCs only realize horizontal payload transportation, which not only ignores the requirements of payload attitude regulation in assembly tasks, but also lacks the guarantee for boom motion coordination and the finite-time convergence of state variables. To address these issues, based on the nonlinear crane dynamics <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> any linearization, this paper proposes an assembly-oriented finite-time coordinated controller for DRCs, which achieves precise and stable regulation of the payload position and attitude through coordinated boom motions, and simultaneously enhances the system rapidity by ensuring the finite-time convergence of boom positioning errors. Furthermore, the detailed controller design and stability analysis process is provided, and the effectiveness of the proposed method is verified by hardware experiments. In the future research, we will try to apply the proposed method to practical operations of DRCs for complex assembly tasks of large heavy objects.

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&#x0D;

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.&#x0D;

Model-Free Adaptive Nonsingular Fast Integral Terminal Sliding Mode Control for Wastewater Treatment Plants

The regulation of wastewater treatment plants (WWTPs) is a challenge due to their complex biological and chemical characteristics and their accurate mathematical model is generally not accessible because of the limitation of available measurements. To overcome such challenges, in this paper, a novel model-free adaptive nonsingular fast integral terminal sliding mode control (MFA-NFITSMC) is proposed. Firstly, based on the concept of dynamic linearization, a compact format dynamic linearized (CFDL) data model for the WWTP is established. Secondly, a novel fast integral terminal sliding mode surface is proposed to accelerate the convergence of tracking error and a discrete-time MFA-NFITSMC is created using the CFDL model as a basis; then, its stability is proved by theoretical analysis. Finally, the experimental verification is conducted based on the Benchmark Simulation Model No. 1 and the results show that the proposed method has a higher tracking accuracy and stronger robustness than other methods in the control of WWTPs.

Two-Phase Non-Singular Terminal Sliding Mode Control of Nonlinear Systems

This paper presents a two-phase non-singular terminal sliding mode control scheme for a class of nonlinear systems in the presence of external disturbances. A two-phase terminal sliding mode surface is constructed and utilized, such that our control scheme achieves fast finite-duration convergence in regions both close to and far away from the control objective, by which the transition state is set and a less conservative bound of the settling time is obtained and superior to the existing results. Meanwhile, the singularity is avoided by the utilization of the saturation function, with the simplicity of structure and implementation. Extensions to multi-input multi-output systems are carried out further. The numerical simulation of the single inverted pendulum and the industrial manipulator are conducted to verify the effectiveness of the proposed control strategy.

Finite-time adaptive super-twisting sliding mode control for autonomous robotic manipulators with actuator faults

This paper proposes a new adaptive super-twisting global integral terminal sliding mode control algorithm for the trajectory tracking of autonomous robotic manipulators with uncertain parameters, unknown disturbances, and actuator faults. Firstly, a novel global integral terminal sliding mode surface is designed to ensure that the tracking errors of autonomous robotic manipulators converge to zero in finite time and the global robustness of the system is also enhanced. Then a new adaptive method is devised to deal with the adverse effect of nonlinear uncertainty. To suppress the chattering phenomenon, the adaptive super-twisting algorithm is used in this paper, which can ensure that the control torque is a continuous input signal. Based on the adaptive mechanism, the adaptive super-twisting global integral terminal sliding mode controller is developed to provide superior control performance. The stability analysis of the system is demonstrated by using the Lyapunov method. Ultimately, the effectiveness of the control scheme is confirmed by a simulation study.

Fixed‐time tracking control of manipulators based on a fast variable power reaching law

SummaryAs for the problem of trajectory tracking of a two‐joint series manipulator, a novel fixed‐time control scheme is proposed based on non‐singular fast terminal sliding mode (NFTSM) control and a fast variable power reaching law. The innovation of the proposed method is: (1) by employing the NFTSM surface, we solve the singularity problem existed in traditional terminal sliding mode surface. (2) The convergence rate is increased by 50% by the combination of fixed‐time control and NFTSM surface control. (3) A new fast variable power reaching law is presented, which combines the advantages of the double power reaching law and the fast power reaching law, and it effectively improves the reaching rate and reduces the amplitude by 40–60 N m. Theoretical analysis proves that the better tracking performance is obtained, and its convergence time upper limit is not affected by the initial states of the system. Finally, the effectiveness and feasibility of our controller are verified through a numerical simulation.

Active Physical Interaction Control for Aerial Manipulator Based on External Wrench Estimation

This article investigates the active physical interaction problem of an aerial manipulator in terms of capability, reliability, and costs. Then, an active physical interaction control architecture is presented for the aerial manipulator to achieve both stable motion and interaction behaviors with external wrench estimation. Specifically, an external wrench estimator in absence of the acceleration and wrench measurements is designed to regulate the interaction point of the aerial manipulator with a minimal sensor condition. Next, a force tracking impedance control strategy with variable stiffness is presented to guarantee the contact stability and force tracking of the aerial manipulator with uncertain contact targets. Further, utilizing the knowledge of prescribed performance and terminal sliding mode surface, a pose controller is proposed to implement the dynamic response speed and accuracy control of the aerial manipulator, which provides a prerequisite for the realization of reliable physical interaction tasks. The stability of the proposed control architecture is analyzed through Lyapunov tools. Moreover, the feasibility and performance of the proposed control architecture are validated via simulations and real-world contact experiments.

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.

Integrated optimal control of distributed in-wheel motor drive electric vehicle in consideration of the stability and economy

From the perspective of handling stability and economy, this paper brings forward an integrated optimal control scheme of distributed in-wheel motor drive electric vehicles (IWMDEV). A linear quadratic regulator (LQR) controller is presented according to nominal model and ideal motions firstly. To tackle the uncertain parameters and random disturbance, a novel robust optimal (RO) control strategy is further proposed to design the top level controller by employing the combination of optimal control and high order sliding mode control. By virtue of the integral and terminal sliding mode surface, the resulting robust optimal control method can not only achieve better performance, but also converge in finite time without chattering phenomenon. As for the bottom level controller, an optimal algorithm is developed to determine the weights for each term in objective function of torque allocation dynamically and coordinate the relationship between driving safety and energy-saving performance timely. Finally, joint simulations are carried out. In comparison with LQR control strategy, the results demonstrate that the proposed control scheme could ensure the robustness and effectiveness in the presence of parametric perturbation and external disturbance. Moreover, the torque allocation algorithm, which considers both handling stability and energy consumption, proves to be an effectual approach.

Adaptive super-twisting sliding mode attitude coordination control for spacecraft formation flying with actuator saturation

This paper investigates the attitude coordination control issue for spacecraft formation flying in the presence of actuator saturation and external disturbances with unknown boundaries. Firstly, a super-twisting integral terminal sliding mode surface is developed, which ensures that the sliding mode surface and its first-time derivative converge to zero in finite time. Then, based on the developed sliding mode surface and adaptive technique, a robust anti-saturation distributed attitude coordination controller that enables the attitude and angular velocity to precisely track the desired time-varying command in finite time is devised under the undirected communication topology. Finally, stability analysis and numerical simulations validate the effectiveness and feasibility of the devised control approach.