Nonsingular Sliding Mode Control Research Articles

Unified Sufficient Conditions for Predefined-Time Stability of Non-Linear Systems and Its Standard Controller Design

This paper presents a unified Lyapunov-based predefined-time stability theorem that includes three sufficient conditions. The standard theoretical analysis method for achieving predefined-time stability of non-linear systems using this theorem is provided within the framework of Lyapunov theory. The developed Lyapunov-based theorem facilitates the establishment of equivalence between the existing Lyapunov theorems concerning predefined-time stability. Furthermore, when the presented sufficient conditions are relaxed, the predefined-time stability conclusion for non-linear systems degenerates into a finite-time one. Consequently, a standard non-singular sliding mode control framework based on the unified Lyapunov-based theorem is developed for a Lagrangian system to ensure its predefined-time stability. Exemplary numerical simulation results are subsequently given, in order to illustrate the convergence behavior of the system states and confirm that the controlled systems are predefined-time stable.

Predefined-Time Nonsingular Sliding Mode Control and Its Application to Nonlinear Systems

Predefined-Time Nonsingular Sliding Mode Control and Its Application to Nonlinear Systems

Designing a fixed-time observer-based adaptive non-singular sliding mode controller for flexible spacecraft

This paper investigates the stabilization problem with a fixed-time approach for a flexible spacecraft subject to vibrations of flexible modes, unknown bounded disturbance, and inherent uncertainty. To estimate the modal variables of a flexible spacecraft which are often unmeasurable in practice, an observer with guaranteed fixed-time convergence is designed. Using the estimated modal variables, a fixed-time non-singular sliding mode controller is designed so that the desired attitude can be reached before a pre-specified time threshold regardless of the spacecraft's initial attitude. By incorporating the estimated modal variables in the control design, significant reduction in the steady-state error of the system response is achieved. The proposed control system is further enhanced with an adaptive law to increase robustness against unknown external disturbances and uncertainties. Stability analysis based on Lyapunov theory guarantees the convergence of observer estimation error and spacecraft attitude error to a pre-determined set before a fixed threshold. Simulation results validate the promising performance of the proposed control system, highlighting its effectiveness in achieving accurate and robust attitude control for flexible spacecraft.

Fixed‐time sliding mode consensus tracking for second‐order nonlinear multi‐agent system with persistent dwell‐time switching topologies

AbstractThis article investigates the problem of fixed‐time sliding mode consensus tracking for nonlinear second‐order multi‐agent system, in the presence of disturbances and actuator attacks. The interaction topology graph of multi‐agent system is directed and switched, and the switching topologies satisfy a more general persistent dwell‐time switching mechanism. To account for the disturbances, actuator attack, and switching topologies, a nonsingular sliding mode control law with distributed switching scheme is constructed to guarantee the fixed‐time reachability to a sliding surface. By using multiple Lyapunov functions, some new sufficient criteria are derived for fixed‐time consensus tracking of the multi‐agent system with persistent dwell‐time switching topologies. To illustrate the proposed approach, we present a numerical example and a physical example of the single pendulum model.

Predefined-time stability and its applications using non-singular sliding mode control

In this work, a Lyapunov-like sufficient condition for predefined-time stability PDTS is presented for a class of dynamical systems. In addition, the proposed Lyapunov-like condition allows us to deduce some prior results on PDTS. Based on the proposed scheme, non-singular predefined-time controllers are designed for first-order systems. Further, a predefined-time terminal sliding surface PDTSS and corresponding non-singular predefined-time terminal sliding mode control NPDTSM strategy have been proposed for the second-order systems. These controllers have several advantages: (i) The control scheme can withstand the effects of bounded, non-vanishing disturbances and is non-singular in the whole state space. (ii) The convergence time can be specified by a constant defined by the user in advance. Along with the predefined-time synchronization of the Φ6 duffing oscillator, a two-dimensional chaotic system, some examples are provided to justify the numerical inferences of the proposed scheme.

Coordinated trajectory tracking control for mining excavator with oscillating external disturbance

AbstractThe mining excavator is a significant type of field robot, however, its ability to track excavation trajectories accurately is limited by model uncertainties and fast‐changing external digging force. This paper presents a novel trajectory tracking coordinate control approach for mining excavators by utilizing cross‐coupling control (CCS). The approach begins by defining the coordination error based on the motion relationship. A super‐twisting nonsingular sliding mode controller is then combined with an adaptive radial basis function neural network to compensate for the unknown nonlinear term that includes model uncertainties and external excavating forces. Moreover, CCS is introduced to enhance the coordination of different actuators. Finally, the effectiveness of the proposed scheme is validated through comparative simulations and experiments.

Position-attitude coupling guidance and control for asteroid landing with a flexible lander

Landing on an asteroid is a highly valuable endeavor accompanied by significant challenges, making it a promising area for further research. This paper aims to present a flexible lander specifically designed for asteroid landing missions while also studying the guidance and control techniques involved in its descent phase. Firstly, the paper briefly introduces the mission simulation model and asteroid environment from previous work. It then provides a detailed exposition on the guidance model which facilitates trajectory planning and the attitude control model used for managing the lander's attitude. The parametric trajectory is subsequently applied to obtain the position-attitude coupling trajectory that allows for the flexible lander's trajectory planning. The generating set search method is used to optimize the parametric trajectory under the appropriate constraints, ensuring high efficiency. In tracking the proposed trajectory, an open-loop control is applied for position tracking, while a closed-loop attitude controller is proposed for attitude control. An attitude control technique involving a combination of the nonsingular sliding mode control method with RBF to capture perturbations and unmodeled dynamics is adopted, and its global stability is proven using a Lyapunov-based approach. Monte Carlo simulation is conducted to test the performance of the proposed trajectory planning technique with results showing that real-time trajectory generation and refreshing are achieved. The feasibility and accuracy of the proposed guidance and control technique are further verified with another set of Monte Carlo simulation. Finally, the paper highlights one successful scenario including the descent and touching phases of asteroid landing with the flexible lander, illustrating its feasibility further.

Appointed‐time nonsingular sliding mode control of spacecraft attitude stabilization

AbstractThis paper investigates the appointed‐time attitude stabilization problem of a rigid spacecraft under disturbance and parametric uncertainty. A continuous appointed‐time sliding mode disturbance observer is presented to observe the synthetical disturbance term. To circumvent the singularity problem in terminal sliding mode control, a new nonsingular appointed‐time sliding mode surface is designed by employing the concept of switching control. Based on the observation information deriving from the proposed disturbance observer, an observer‐based nonsingular sliding mode control scheme is developed to stabilize the attitude control system within appointed time which is given by the user. And also, the undesired control chattering phenomenon can be attenuated. The appointed‐time stability of the controlled attitude system is proved by the Lyapunov criteria. The simulation results show that the proposed attitude stabilization control scheme is valid.

Fixed-time leader-follower formation control of underactuated unmanned surface vehicles with unknown dynamics and ocean disturbances

This paper investigates the formation control problem of underactuated unmanned surface vehicles with unknown dynamics and ocean disturbances. To tackle the leader-follower configuration, an improved fixed-time velocity controller is proposed for the virtual vehicle to guide the followers efficiently. For the tracking control of the follower vehicles, a concise controller is designed by borrowing on backstepping and nonsingular sliding mode control techniques. A novel adaptive filter is developed to address the so called “explosion of complexity” problem in the traditional backstepping framework, which could simplify the control structure and facilitate the implementation of the proposed controller in practical engineering. Furthermore, the radial basis function neural network is employed to identify the unknown dynamics of the vehicle model. A bounded-feedback adaptive law is developed to estimate the upper bound of the ocean disturbances. That could greatly enhance the robustness and accuracy of the controller. Finally, a rigorous proof has been given to guarantee the practical fixed-time stability of the closed-loop system. Two examples are provided to demonstrate the effectiveness and superiority of the theoretical results.

Fractional-order Fixed-time Non-singular Sliding Mode Control for Nonlinear Robotic Manipulators

In this study, fractional-order non-singular fixed-time terminal sliding mode control (FoFxNTSM) for nonlinear robotic manipulators in the existence of uncertainties and external disturbances is examined. To begin, the concept of fractional-order fixed-time non-singular terminal sliding mode control is introduced. This method combines the benefits of NTSM (which provides fast convergence speed, smooth and singularity-free control inputs) with the advantages of a fractional-order constants (which improves position tracking effectiveness). Lyapunov analysis yields the fixed-time stability of the closed-loop system. To evaluate and illustrate the performance of the proposed strategy, the relevant simulation results are presented.

Adaptive fixed-time quantized fault-tolerant attitude control for hypersonic reentry vehicle

This paper focuses on the adaptive fixed-time quantized fault-tolerant attitude tracking problem for hypersonic reentry vehicle (HRV). Due to the strong nonlinearity, tight coupling, uncertain characteristics and potential actuator faults, the attitude control of HRV poses a considerable challenge. By resorting to feedback linearization technique, the inherently nonlinear attitude model of HRV is decoupled into a linear control-oriented model, where the actuator malfunction, quantization nonlinearities and multiple disturbances are incorporated into the lumped disturbance. Then a fixed-time neural network disturbance observer is designed to estimate the lumped disturbance, with the practical fixed-time stability of the observation error ensured independent of initial conditions. Subsequently, by using a hyperbolic-tangent-like function, a novel paradigm is proposed for achieving adaptive fixed-time convergence and based on the paradigm, an adaptive fixed-time nonsingular sliding mode controller is proposed. The main features of the controller include: 1) The controller gain is adjusted adaptively following the current magnitude of the output variable to obtain high transient performance. 2) The tracking error can converge to zero within a fixed time even in the case of actuator faults and signal quantization. 3) A hysteretic quantizer is implemented in the attitude control loop such that the on-board communication load can be significantly reduced. Moreover, the proposed fault-tolerant control scheme design is non-recursive, rendering the controller structure simple. Ultimately, the effectiveness of the proposed method is demonstrated by numerical simulations.

Adaptive Fault Tolerant Non-Singular Sliding Mode Control for Robotic Manipulators Based on Fixed-Time Control Law

This paper presents a fault tolerant scheme employing adaptive non-singular fixed-time terminal sliding mode control (AFxNTSM) for the application of robotic manipulators under uncertainties, external disturbances, and actuator faults. To begin, non-singular fixed-time terminal sliding mode control (FxNTSM) is put forth. This control method uses non-singular terminal sliding mode control to quickly reach fixed-time convergence, accomplish satisfactory performance in tracking, and produce non-singular and non-chatter control inputs. Then, without knowing the upper bounds beforehand, AFxNTSM is used as a reliable fault tolerant control (FTC) to estimate actuator faults and unknown dynamics. The fixed-time stability of the closed-loop system is established by the theory of Lyapunov analysis. The computer simulation results of the position tracking, control inputs, and adaptive parameters are presented to verify and illustrate the performance of the proposed strategy.

Finite time non-singular sliding mode control for spinning tether system with prescribed performance under artificial gravity mission

In this paper, the spinning tether system (STS) is applied to produce the artificial gravity overload with a proposed spin-up scheme in elliptical transfer orbits. To improve the comfort of the astronauts during spinning, the combined control scheme with tension and thrust is designed for spin-up. Then, based on the novel performance function and sliding mode technology, a finite time prescribed performance controller is proposed to track angular velocity for the desired artificial gravity overload. Compared with the existing works, the tracking error is controlled within the preset transient performance and converged to the origin within finite time even in the presence of unknown external disturbance. The stability of closed-loop tracking system is proved by Lyapunov theorem. Finally, the numerical simulations are given to demonstrate the effectiveness and robustness of the proposed controllers in the artificial gravity mission.

Coordinated Control after Grasping the Space Targets Using Controllable Damping Mechanism

Compliant capture of the space non-cooperative targets is a key technology in on-orbit services. A great challenge is that the multi-dimensional contact force generated by the tumbling space target can destabilize the spacecraft-manipulator system (SMS), which may eventually cause failure of the capture task. A full-dimensional controllable damping mechanism (FDCDM) with gyroscopic structure is introduced into the joint of the SMS to buffer the multi-dimensional contact forces during capture. The six-dimensional damping force outputs by the FDCDM can be equivalent to the actuator outputs in the end joint, which could form a coordinated control system with the torque of base flywheel and active joints. The whole-body dynamic model of SMS with FDCDM is established using the Kane method. Furthermore, a backstepping non-singular sliding mode control is proposed to optimize the momentum distribution and impact absorption. The characteristics of collision process for the above SMS-FDCDM system is analyzed in the ADAMS workspace, and the experiments performed in MATLAB demonstrate that the full-dimensional damping mechanism and coordinated control can greatly reduce the vibration caused by the impact force, and the attitude of SMS is quickly stabilized after capture, which proves the feasibility of its application in non-cooperative target capturing tasks.

Predefined-Time Nonsingular Attitude Control for Vertical-Takeoff Horizontal-Landing Reusable Launch Vehicle

This paper presents a novel predefined-time nonsingular tracking control system for a vertical-takeoff horizontal-landing (VTHL) reusable launch vehicle (RLV) in the face of parameter uncertainties, model couplings and external disturbances. Firstly, this paper proposes a novel predefined-time prescribed performance function (PTPPF) with desired steady-state and transient performance. The convergence time of PTPPF from the transient state to the steady state can be flexibly adjusted by changing one parameter. Moreover, the decreasing rate of PTPPF in the transient phase can also be adjusted by changing one parameter on the premise of not changing the convergence time of PPF to reach steady state. A novel predefined-time terminal sliding mode surface (SMS) is designed to avoid the singularity, and the attitude tracking errors on SMS are predefined-time stable. By utilizing PTPPF and error transformation, this paper designs a novel nonsingular sliding mode controller to guarantee the attitudes of RLV with desired tracking performance. Without using piecewise functions, the phenomenon of singularity can be avoided. The Lyapunov method is used to verify the stability of the controller. Lastly, a numerical simulation is presented to validate the efficiency of the proposed controller.

Practical Tracking of Permanent Magnet Linear Motor Via Logarithmic Sliding Mode Control

This article focuses on the fast position tracking problem for the permanent magnet linear motor (PMLM) system under a chattering-reduced sliding mode control signal. To this end, a class of globally nonsingular sliding mode control (SMC) laws, called logarithmic sliding mode (LnSM) control, is proposed in this article. Using the natural logarithm function, a high gain is established at the equilibrium of the sliding mode reduced-order system, which leads to a higher tracking precision and a faster local convergence rate than those of some classical SMCs. In addition, a super-twisting algorithm-based LnSM (ST-LnSM) control is constructed to reduce the chattering typical for first-order SMC, while stabilizing the position tracking system rapidly. Since only a few parameters need to be adjusted, and the employed natural logarithm function is conventionally integrated into most PMLM drivers, the proposed control law is easy to implement in PMLM systems or other industrial servo systems.

Finite-time convergence of perturbed nonlinear systems using adaptive barrier-function nonsingular sliding mode control with experimental validation

In this study, an adaptive barrier procedure is combined with nonsingular sliding mode control (SMC) technique at the aim of the fast stabilization of nonlinear system with external disturbances. It is verified that the barred function-based control law leads to the fast convergence of state errors to a region near origin. Furthermore, the suggested method eradicates the requirement for the knowledge of upper bounds of exterior perturbations which are frequently required in SMC scheme. The stability analysis confirms fast convergence of the error states to a predetermined region. In order to demonstrate the validity of the planned method, a mass-spring system is examined as the case study. Finally, simulation and experimental outcomes on a mass-spring system are given to prove the efficacy and success of the advised methodology.

Nonsingular fixed-time attitude coordinated tracking control for multiple rigid spacecraft

This paper investigates the problem of fixed-time attitude coordinated control for multi-spacecraft systems with unknown external disturbance. Firstly, a distributed fixed-time observer is introduced to estimate the states of the virtual leader. The observer can track the leader completely in a fixed time without dependence on the initial conditions of the leader and observer. Then, we propose a novel nonsingular fixed-time sliding mode tracking controller to address the fixed-time attitude tracking problem. It is noteworthy that the requirement on initial conditions of spacecraft is removed in the proposed nonsingular sliding mode controller. Due to the robustness of sliding mode control, the influence of external disturbance can be eliminated, such that each spacecraft can track desired attitude trajectories precisely in a fixed time. Hence, the fixed-time attitude coordination for multiple spacecraft can be achieved. Finally, numerical simulation results and comparisons reveal the effectiveness of the proposed algorithms.

Barrier function-based adaptive nonsingular sliding mode control of disturbed nonlinear systems: A linear matrix inequality approach

In this study, a novel barrier function-based adaptive non-singular terminal sliding mode control methodology is suggested for robust stability of disturbed nonlinear systems. It is proved that the barrier function-based control method can force the state trajectories to converge to a region near origin in the finite time. A sufficient criterion is derived using Lyapunov stability theorem and linear matrix inequalities (LMIs) to satisfy the asymptotic stability of state trajectories. In addition, the design eliminates the necessity to have any knowledge about the upper bounds of external disturbances; a common requirement in sliding mode control implementation. The stability analysis verifies that the system states, under the designed control scheme, can asymptotically converge to a pre-defined region. Lastly, simulation studies are presented to confirm the efficacy and robustness of proposed approach.

Finite-Time Sliding Mode Control With Unknown Control Direction

In this paper, a global nonsingular sliding mode controller is developed for a second order system with unknown control direction. A novel terminal sliding mode hypersurface is presented to compensate for the sign uncertainty in the control input and avoid the singularity issue present in the traditional terminal sliding mode control. In contrast to the Nussbaum gain approach where the equilibrium point is reached asymptotically in the presence of input sign uncertainty, the proposed controller guarantees that the equilibrium point can be reached from any initial state in finite time. Simulation results are provided to validate the proposed controller.