Fixed-time Sliding Mode Control Research Articles

Compliant variable admittance adaptive fixed-time sliding mode control for trajectory tracking of robotic manipulators

Abstract This paper presents a compliant variable admittance adaptive fixed-time sliding mode control (SMC) algorithm for trajectory tracking of robotic manipulators. Specifically, a compliant variable admittance algorithm and an adaptive fixed-time SMC algorithm are combined to construct a double-loop control structure. In the outer loop, the variable admittance algorithm is developed to adjust admittance parameters during a collision to minimize the collision time, which gives the robot compliance property and reduce the rigid collision influence. Then, by employing the Lyapunov theory and the fixed-time stability theory, a new nonsingular sliding mode manifold is proposed and an adaptive fixed-time SMC algorithm is presented in the inner loop. More precisely, this approach enables rapid convergence, enhanced steady-state tracking precision, and a settling time that is independent of system initial states. As a result, the effectiveness and improved performance of the proposed algorithm are demonstrated through extensive simulations and experimental results.

Neural network-based practical fixed-time nonsingular sliding mode tracking control of autonomous surface vehicles under actuator saturation

The article considers the fixed-time tracking control of autonomous surface vehicles (ASVs) subject to actuator saturation. A novel sliding variable with state-dependent exponents is first constructed to alleviate chattering and overcome the singularity. By using the proposed fixed-time sliding variable and the neural network (NN), an NN-based fixed-time sliding mode control (SMC) scheme is developed. Besides, an auxiliary system is utilized to solve the input saturation constraint. Unlike some existing results for ASVs with input saturation, the designed fixed-time SMC law does not require assumptions on a priori upper bound of the lumped disturbances. Through Lyapunov analysis, it is proven that the tracking error can converge to a bounded region in a fixed time. Simulation examples are given to show the validity of the proposed control scheme.

Adaptive Third-Order Fixed Time Sliding Mode Control with Chattering Free for Mobile Loading Arm Systems

Adaptive Third-Order Fixed Time Sliding Mode Control with Chattering Free for Mobile Loading Arm Systems

Predictor-based constrained fixed-time sliding mode control of multi-UAV formation flight

In this work, a predictor-based fixed-time sliding mode control is designed to tackle the problem of achieving precise trajectory tracking control of multiple unmanned aerial vehicle formation flight. The proposed approach simultaneously addresses various practical requirements, such as optimality, constraints, fixed-time convergence, external interferences, and computational burden. Initially, using the Taylor series concept, we derive the predictive models for the fixed-time sliding surface and reaching law. Subsequently, we formulate a constrained performance index by integrating these predictions with the control input. Ultimately, the optimal control input is computed through solving the constrained quadratic optimization problem. An outstanding feature of this study is the theoretical guarantee of closed-loop fixed-time system stability in the presence of external disturbances and constraints. Furthermore, the comparative analysis with sliding mode predictive control law and fixed-time sliding mode control methods demonstrates that the proposed approach achieves a straightforward control method with improved performance and acceptable accuracy. Finally, an experimental test is conducted to demonstrate the algorithm's potential for hardware implementation by employing the Hardware-in-the-Loop test.

Optimal Fixed-Time Sliding Mode Control for Spacecraft Constrained Reorientation

Optimal Fixed-Time Sliding Mode Control for Spacecraft Constrained Reorientation

A Novel Disturbance Observer Based Fixed-Time Sliding Mode Control for Robotic Manipulators with Global Fast Convergence

A Novel Disturbance Observer Based Fixed-Time Sliding Mode Control for Robotic Manipulators with Global Fast Convergence

Sensorless Fixed-Time Sliding Mode Control of PMSM Based on Barrier Function Adaptive Super-Twisting Observer

Sensorless Fixed-Time Sliding Mode Control of PMSM Based on Barrier Function Adaptive Super-Twisting Observer

Satellite Attitude Control Using Faulty Double Gimbal Variable Speed Control Moment Gyroscope

A rigid satellite attitude control requires stable finite-time attitude convergence in the presence of rotation unwinding, external disturbances, and actuator faults. To achieve this, a new nonsingular fast fixed-time sliding mode controller is proposed to ensure finite-time convergence independent of the initial conditions of the system. Rotation unwinding is addressed using the body and shadow pair of the Modified Rodrigues Parameters (MRPs). Convergence behavior of the states errors in the neighborhood of the MRPs switching surface is also addressed. Attitude control is achieved using a double-gimbal variable-speed control moment gyro (DGVSCMG). For the first time, a DGVSCMG having all possible electrical and mechanical faults is considered for control design. A novel nonsingular fast fixed-time anti-unwinding fault-tolerant sliding control using a new sliding surface is proposed. This eliminates switching of the sliding surfaces and minimizes control chattering. Four new propositions are proposed and proved to establish fast fixed-time global stability of the system for tracking maneuver in fault and fault-free conditions with anti-unwinding. Simulation results are presented and compared with existing fixed-time sliding control approaches. The results show superiority of the proposed anti-unwinding fault-tolerant fast fixed-time control for the tracking maneuver in terms of convergence time, energy efficiency, and fault tolerance.

Fixed-Time Sliding Mode Control for Linear Motor Traction Systems with Prescribed Performance

In this research, we propose a fixed-time sliding mode controller using a prescribed performance control approach to address the speed tracking problem in linear motor traction systems, which are powered by high-power permanent magnet linear synchronous motors (PMLSMs). Initially, to tackle the issue of the convergence time and dynamic response associated with traditional finite-time sliding mode controllers, we introduce a fixed-time sliding mode controller. This controller guarantees that the system state converges to the origin within a specified upper time limit. Subsequently, to enhance the dynamic response of the PMLSM and minimize speed errors, we integrate the prescribed performance control strategy with a fixed-time sliding mode controller. This effectively limits the motor’s speed error within the predefined function boundaries, reduces system overshoo, and mitigates system jitter to a certain degree. Finally, simulation results are presented to validate that the proposed control strategy significantly enhances precision of speed tracking in PMLSMs.

Singularity-free fixed-time sliding mode control for a class of nonlinear systems

In this paper, the fixed-time control for a class of second-order nonlinear system is investigated. Considering that the presented fixed-time controllers in most existing results are singular, we aim to develop a fixed-time sliding mode controller without singularity. The contribution of this work is not only developing a novel cosine function-based sliding function to ensure the fixed-time convergence of system states on the sliding surface but also designing a novel sliding mode controller to guarantee the fixed-time stability of the obtained closed-loop system without singularity. First, it is proven that the system trajectories converge to the origin in a fixed time on the novel proposed cosine function-based sliding surface. It is further proven by Lyapunov theory that the obtained closed-loop system under the presented controller is fixed-time stable. Moreover, the chattering problem is settled by slightly modifying the presented controller. It is also proven that the system trajectories converge into a small neighborhood of the origin in a fixed time. The results are illustrated in the simulation.

A nonlinear system of hybrid fractional differential equations with application to fixed time sliding mode control for Leukemia therapy

In this article, a coupled nonlinear problem of hybrid fractional differential equations (HFDEs) is presented for the qualitative work and numerical results. Two types of operators are involved in the research problem. One of them is DβrR which represent Riemann–Liouville's (RL) fractional derivatives while the operator L(DϱrR) is a series operator and DϱrR's are RL operators such that βr,ϱr∈(0,1]. These operators are joined by Φp operator. As a result, we have a nonlinear coupled system of FDEs. The newly established nonlinear system is studied for the existence, uniqueness criteria, stability of the solutions, and numerical computations. For the theoretical results, we take help from the available literature about the fixed point (FP) techniques. Then a computational scheme is developed with the help of Lagrange's interpolation technique. An application of the problem as a particular case is presented in the sense of the Leukemia mathematical model. The model presents the infection propagation. Leukemia can be managed by providing a chemotherapeutic treatment generally accepted to be safe, and a fractional-order fixed-time terminal sliding mode control has been developed to achieve this goal of removing Leukemic cells while keeping a sufficient number of normal cells. In order to evaluate the proposed controller stability, the fixed-time Lyapunov stability theory is employed. To better illustrate the study, comparison simulations are shown, demonstrating that the suggested control approach has higher tracking and convergence performance.

Adaptive non-singular fixed-time sliding mode control of moving-base underwater flexible manipulators

Adaptive non-singular fixed-time sliding mode control of moving-base underwater flexible manipulators

Reactive human–robot collaborative manipulation of deformable linear objects using a new topological latent control model

Real-time reactive manipulation of deformable linear objects is a challenging task that requires robots to quickly and adaptively respond to changes in the object’s deformed shape that result from external forces. In this paper, a novel approach is proposed for real-time reactive deformable linear object manipulation in the context of human–robot collaboration. The proposed approach combines a topological latent representation and a fixed-time sliding mode controller to enable seamless interaction between humans and robots. The introduced topological control model offers a framework for controlling the dynamic shape of deformable objects. By leveraging the topological representation, our approach captures the connectivity and structure of the objects’ shapes within a latent space. This enables improved generalization and performance when handling complex deformable shapes. A fixed-time sliding mode controller ensures that the object is manipulated in real-time, while also ensuring that it remains accurate and stable during the manipulation process. To validate our proposed framework, we first conduct motor-robot experiments to simulate fixed human interaction processes, enabling straightforward comparisons with other approaches. We then follow up with human–robot experiments to demonstrate the effectiveness of our approach.

Adaptive Disturbance Observer-Based Local Fixed-Time Sliding Mode Control With an Improved Approach Law for Motion Tracking of Piezo-Driven Microscanning System

Adaptive Disturbance Observer-Based Local Fixed-Time Sliding Mode Control With an Improved Approach Law for Motion Tracking of Piezo-Driven Microscanning System

Distributed fixed-time formation control for heavy haul trains based on sliding mode control

The problem of distributed fixed-time formation control for heavy haul trains is proposed in this paper. Firstly, a train-following model of multiple heavy haul trains with considering uncertain resistance and unknown disturbances is established, and the information transmission between heavy haul trains follows a predecessor-following topology. Then, based on fixed-time sliding mode control and adaptive control theories, a novel distributed fixed-time formation controller for heavy haul trains is designed. Finally, the control effects of the proposed controller are verified and analyzed by simulations. It is shown that the proposed fixed-time formation controller has more advantages in terms of convergence speed and convergence accuracy compared to the nonfinite-time formation controller. Besides, the convergence time is not affected by the initial state of the trains.

Fixed time adaptive fault tolerant sliding mode control of PEMFC air supply system

Guaranteeing rapid management of oxygen excess ratio (OER) for proton exchange membrane fuel cells (PEMFC) under load variations is a challenge with practical significance. To improve the controller response of PEMFC air supply system, a fixed time fault-tolerant control strategy is proposed in this paper. A fixed convergence time of PEMFC air supply control system is quantified and guaranteed by the proposed method and the control response can be accelerated by reducing the setting time. The contributions of this paper is fourfold. Firstly, the manifold leakage fault is estimated by fixed time fault observer, which can improve the real-time fault tracking performance of the control system. Secondly, a hierarchical fixed time sliding mode controller is proposed to regulate the OER rapidly. Furthermore, a novel adaptive term is employed to reduce the effects of the chattering from fault observer in the outer loop. Finally, the effectiveness of the proposed method is verified on a real-time PEMFC simulation platform. Experimental results on a Hardware-in-the-loop (HIL) platform show that the proposed fixed time fault tolerant control strategy has the characteristics of fast response and high robustness.

Improved Fixed-Time Convergence Guidance Scheme Design and Its Application to Missile

This study presents a fixed-time convergence guidance scheme for impact time and angle control. First, two improved fixed-time stable systems are presented, which have smaller initial control command and better terminal convergence.16 An improved fixed-time extended state observer is proposed to provide accurate estimation of system states and disturbance, which effectively solves peaking value problem. Furthermore, an improved fixed-time sliding mode controller is derived, which avoids the singular problem and achieves faster convergence rate with smaller initial control command. Second, a new guidance scheme with impact angle and impact time constraints is proposed for intercepting a stationary target. By introducing a virtual target, the guidance process is divided into two stages. The proposed fixed-time controller is employed in the first stage. The method with a virtual leader ensures that the missile intercept the virtual target with desired line-of-sight angles at a specific time. By using the proportional navigation guidance law, the missile keeps travelling with desired flight-path angles to hit the real target in the second stage,17 so as to achieve the impact time and angle control. Finally, the feasibility and effectiveness of the proposed guidance scheme in different engagement scenarios are verified by numerical simulations with comparisons.

Fixed-time control for free-floating space manipulators with prescribed constraints and input saturation

Abstract This paper investigates the issue of tracking control for a free-floating space manipulator with prescribed performance constraints, considering the inertia uncertainties, internal disturbances and input saturation. An inherently continuous adaptive controller is proposed by incorporating non-singular fixed-time sliding mode control, prescribed performance control (PPC), and auxiliary compensation. First, a modified non-singular fast fixed-time terminal sliding surface is constructed, which has a shorten convergence time than the conventional fixed-time sliding surface. Unlike the existing complicated PPCs, a simple structure controller is developed to satisfy prescribed performance constraints through a unique tangent-type PPC technique. The input saturation is then compensated adaptively by an auxiliary mechanism. The Lyapunov theory thoroughly validates the stability and fixed-time convergence of the closed-loop tracking system. With the suggested control scheme, the system states can converge quickly to a small neighbourhood around the origin within a preassigned time, while the position tracking error can be confined within a prescribed performance bounds even in the presence of input saturation. Compared to the existing tracking methods, the suggested control approach has the advantages of faster transient convergence, higher steady-state tracking precision, and stronger robustness. Simulation comparisons demonstrate the effectiveness and superiority of the proposed controller.

Disturbance observer–based fixed-time sliding mode trajectory tracking control for marine surface vehicles with uncertain dynamics

In this paper, a fixed-time sliding mode control scheme is developed to fulfill the trajectory tracking task of a marine surface vehicle with unknown dynamics. To restrain the adverse effects of the unknown dynamics including the parameter inaccuracy and exogenous disturbances, a fixed-time disturbance observer is designed to estimate the lumped uncertainties using the bi-limit homogeneous theory without requiring any knowledge of the model uncertainties. Then, a nominal tracking controller is proposed to stabilize the error dynamic model in the sense of fixed-time Lyapunov stability, based on which a novel integral-type sliding mode manifold with bi-limit homogeneity is constructed to drive tracking error convergence in fixed time. To enhance the robustness of the vessel control system, a disturbance observer–based fixed-time integral sliding mode tracking controller is finally proposed, and the chattering phenomenon is effectively alleviated by direct estimation compensations. The analysis of Lyapunov stability indicates that the closed-loop system is fixed-time stable. Numerical simulations on a model vessel are carried out to validate theoretical results of the proposed control scheme.

Quenching chaos in a power system using fixed-time fractional-order sliding mode controller

The aim of this paper is to study the unwanted chaotic oscillation that can severely affect the reliable and safe operation of electrical power systems. The dynamical behavior of a benchmark three-bus nonlinear electrical power system model is explored using modern nonlinear analysis methods, where the Lyapunov exponents spectrum, bifurcation diagram, power spectral density and bicoherence are used to investigate the chaotic oscillation in the power system. The analysis shows the existence of critical parameter values that may drive the power system to an unstable region and can expose the system to bus voltage collapse and angle divergence or blackout. To eliminate the chaotic oscillation, a fractional-order fixed time sliding mode controller has been used to control the power system in a finite time that can be predetermined by the designer. The Lyapunov theorem has been used to prove the stability of the controlled power system. The results confirm the superiority, robustness, and effectiveness of the suggested control algorithm.