Finite-time Sliding Mode Control Research Articles

Chattering Free Sliding-Mode Controller Design for Underactuated Tower Cranes With Uncertain Disturbance

Tower cranes are widely used in various industrial sites and require a high level of anti-disturbance performance from the crane controller due to the variability of the application environment. Although sliding mode control is a typical anti-disturbance control method, most sliding mode controllers suffer from output chattering and do not reflect well under severe external disturbances. To address these issues from a practical application perspective, a finite time sliding mode control method using the super-twisting algorithm (STA) is proposed for underactuated tower cranes operating in the presence of external disturbances. The proposed method includes a finite-time chattering-free sliding mode controller that eases the output torque chattering problem and a finite-time sliding mode observer based on STA to observe the uncertain disturbances. The observed values are then applied to the controller through feedforward compensation. Experimental results show that the proposed control method effectively weakens output torque chattering, compensates for disturbance quickly, and accurately completes control tasks.

Robust finite-time sliding mode control of unmanned surface vehicle with active compensation of pose estimation uncertainty

Robust control of Unmanned Surface Vehicles (USVs) is crucial for their safe and reliable navigation. The control methods of USV generally regard the results of pose estimation (such as GNSS/INS) as an accurate reference, but GNSS/INS is usually fluctuating and uncertain in the open water, which easily leads to large tracking errors or even control failure of USV. To this end, a robust sliding mode control of USV considering the active compensation of pose estimation uncertainty is innovatively presented, which can ensure the stability and accuracy of USV's control. The distinctive features of the proposed method are twofold: (i) To improve the pose estimation accuracy and obtain accurate uncertainty evaluation, an improved adaptive Kalman filtering considering the time-varying solution state is presented, which utilizes the convergence characteristics of INS and the time-varying features of GNSS solution state; (ii) By integrating pose estimation uncertainty assessment and active compensation, a Robust Finite-Time Sliding Mode Control (RFT-SMC) for a twin-propeller unmanned surface vehicle is developed to enhance tracking accuracy and anti-disturbance capability, and its convergence is established using a Lyapunov function, ensuring reliable operation of the USV even in the presence of uncertain pose estimation. Finally, verification experiments are offered to verify the effectiveness of the presented RFT-SMC method.

Asynchronous finite-time extended dissipative sliding mode control for semi-Markovian jump master–slave neural networks

This paper aims to investigate the finite-time extended dissipative asynchronous sliding mode control (SMC) on semi-Markovian jump master–slave neural networks (MSNNs) subject to event-triggering scheme (ETS) and packet dropout. Considering ETS, packet dropout and network-induced delays, the asynchronous finite-time SMC which is more realistic is designed. Sufficient conditions are obtained that closed-loop system is extended dissipative stochastic finite-time bound. Meantime, we present novel results for closed-loop system on extended dissipative stochastic finite-time contractive bound. Finally, the biological neural network is presented to illustrate the validness of methods.

Protocol-based SMC for singularly perturbed switching systems with sojourn probabilities

This paper focuses on the finite-time sliding mode control for singularly perturbed switching systems in the presence of sojourn probabilities. To effectively capture the dynamic behavior of singularly perturbed switching systems, a generalized framework of piecewise-homogeneous sojourn probabilities is established. Additionally, a novel event-triggered protocol is introduced to alleviate transmission frequency, making use of dynamic quantization and adjustable triggering thresholds to accommodate system state fluctuations. Besides, an asynchronous sliding mode control law is designed, using a suitable sliding function and hidden-Markov model strategy, to ensure the trajectory of the resulting singularly perturbed switching systems reaches the predefined sliding surface within a finite-time interval. Finally, the proposed method is validated using a numerical example and two practical models, demonstrating its effectiveness and practicality.

Fractional-order finite-time sliding mode control for uncertain teleoperated cyber–physical system with actuator fault

The stability of the teleoperated cyber–physical system with model uncertainty, external disturbance, and actuator fault is addressed in this study by using a suitable fractional-order sliding mode control (SMC) strategy. First, the sliding surface is designed to ensure the better tracking performance of the system. Second, the suggested control method combines SMC with an adaptive strategy to ensure that the system is stable in finite time. Third, neural network (NN) and fuzzy logic system (FLS) are used to estimate the model uncertainty, time-varying delay, external disturbance and unknown coefficient matrices of sliding mode surface, respectively. Finally, the advantages of the proposed control scheme are confirmed by the simulation example.

Super-twisting sliding mode finite time control of power-line inspection robot with external disturbances and input delays

An adaptive super-twisting sliding mode control (AST-SMC) is proposed for the power-line inspection (PLI) robot system with two degrees of freedom and single control input underactuated with multiple balances. Firstly, the nonlinear dynamic equation of PLI robot is established, and the model is linearized at the nominal equilibrium point. Secondly, a special transformation is introduced to transform the original input delay system into a delay-free model, and an equilibrium manifold linearization (EML) model is established by using scheduling variables to expand the operating range of the controlled system, as a result of which the disturbance observer control (DOC) is designed to estimate the external disturbance. Thirdly, in order to achieve fast convergence and continuous control, the super-twisting sliding mode control(ST-SMC) method is proposed to decrease chattering in the control law. Finally, it can be verified by Lyapunov stability theory that the system reaches the sliding mode surface in finite time and the trajectory tracking error converges to zero in finite time. The simulation results verify that the combination of DOC and AST-SMC has a optimal disturbance approximation and control convergence ability, clarifying the effectiveness and robustness of the proposed control scheme.

A generalized coupled system of fractional differential equations with application to finite time sliding mode control for Leukemia therapy

In this article, a general nonlinear system of functional differential equations for two types of operators is considered. One of them includes RDβi which are n-operators in the Riemann–Liouville’s sense of derivative while the second is based on a series operator L(RDϱi) where all the RDϱi’s are Riemann–Liouville’s fractional operators with the assumption of βi,ϱi∈(0,1]. These two types of operators are combined with the help of a nonlinear Φp-operator. This novel construction is more useful in scientific problems. The novel system of FDEs is studied for the solution existence, uniqueness analysis, stability analysis and numerical computation is also carried out. For an application of the presumed general coupled system, a fractional order Leukemia therapy model with its numerical simulations and optimization, is given. The Leukemia model describes the propagation of infected cells. A fractional-order finite-time terminal sliding mode control is designed to control Leukemia for the fractional-order dynamics for eliminating Leukemic cells while maintaining an adequate number of normal cells by the application of a chemotherapeutic agent that is considered as safe. The Lyapunov stability theory has been employed to analyze the controllers. The comparative simulations are presented for a better illustration of the work and show the superior tracking and convergence performance of the proposed control method.

Strict finite-time sliding mode control for a tethered space net robot

Tethered Space Net Robot (TSNR) is considered to be a promising approach for space debris removal, and accordingly it is also an interesting control problem due to its time-varying disturbances caused by an elastic and flexible net and a main connected tether. In this situation, the control scheme should be robust enough, low-frequency, and finite-time convergent in presence of external disturbances. In this paper, a robust controller with an advanced adaptive scheme is proposed. To improve robustness, the disturbance is skillfully involved in the adaptive scheme. It is strictly proven that the closed-loop system can converge to the desired trajectory in finite time in both reaching and sliding processes. Based on the theoretical proof, adaptive gains and corresponding dynamic stability characteristics are further discussed. Finally, the efficiency of the proposed control scheme is numerically proven via a TSNR. The proposed control scheme utilizes small and continuous control forces to compensate for the disturbance efficiently and track the desired trajectory quickly.

Adaptive event-triggered finite-time sliding mode control for singular T–S fuzzy Markov jump systems with asynchronous modes

This paper investigates the finite-time asynchronous control issue for singular fuzzy Markov jump systems (SFMJSs) with mode-dependent derivative-term coefficient through the sliding mode control (SMC) approach. Firstly, a new adaptive event-triggered scheme (ETS), which satisfies the system conditions by changing the threshold, is adopted to further reduce the communication consumption. Meanwhile, a mode-dependent fuzzy sliding surface (SS) function on account of hidden Markov model is designed. Based on a state observer, an asynchronous SMC law is proposed in accordance with the adaptive ETS to ensure that SFMJSs are finite-time boundedness (FTB). Finally, two examples are provided to certify the availability and practicability of the presented results.

Adaptive fractional tracking control of robotic manipulator using fixed-time method

This paper proposes an adaptive fractional-order sliding mode controller to control and stabilize a nonlinear uncertain disturbed robotic manipulator in fixed-time. Fractional calculus is used to construct a fractional-order sliding mode controller (FtNTSM) that suppresses chattering to help the robotic manipulator converge to equilibrium in a fixed-settling time based on fixed-time stability theory. Then, adaptive control is introduced and combined with FtNTSM to overcome the unknown system dynamics. The convergence time of the proposed fixed-time fractional-order sliding mode controller (AFtNTSM) is independent of beginning circumstances and can be precisely assessed, unlike the finite-time control approach. Finally, numerical simulations show that the adaptive fractional-order sliding mode controller outperforms finite-time sliding mode controller.

Finite-time sliding mode control methods for a class of non-integer-order systems with input saturations and its application

Control and synchronization of chaotic dynamical systems is a key issue in engineering that has numerous applications in the applied sciences. In this research, single input finite-time sliding mode (FTSMC) control algorithms are developed to synchronize and stabilize a class of three-dimensional non-integer order systems where input saturation is present. Using the non-integer version of the Lyapunov stability theory (LST) and the dynamic-free idea, techniques are devised to suppress the improper behavior of the aforementioned fractional-order (FO) chaotic systems without unpleasant chattering phenomena. The proposed FTSMC approach can be utilized to stabilize and synchronize systems that include model uncertainty, external disturbances, and input saturation. The developed single input techniques have the benefits of being model-free, robust to uncertainty, user-friendly, and establishing equilibrium in a finite amount of time. In addition, the efficacy and applicability of the FTSMC approaches are shown by synchronizing two different industrial FO chaotic systems and chaos suppressing of the PMSM chaotic system utilizing these methods.

Finite-Time Sliding Mode Control Based on Unknown System Dynamics Estimator for Nonlinear Robotic Systems

This article proposes an unknown system dynamics estimator (USDE) based finite-time sliding mode control for nonlinear robotic systems with unknown dynamics. First, an USDE with only one tuned parameter is designed by using filter operations and invariant manifold to estimate the unknown system dynamics. Second, a novel sliding mode surface with faster response time is designed. By incorporating the USDE into the sliding mode surface, a composite sliding mode control (CSMC) is proposed to achieve better dynamic performance. With simple parameter turning, the CSMC can realize the high precision trajectory tracking control of robotic systems. Finally, simulation results illustrate the superiority of the proposed control strategy.

A Finite-Time Sliding Mode Control Approach for Constrained Euler–Lagrange System

This paper investigates a general control strategy to track the reference trajectory for the constrained Euler–Lagrange system with model uncertainties and unknown external disturbances. Unlike the disturbances assumed to be upper-bounded by a constant in other papers, we consider the disturbances to be bounded by a function of the system states, which are more realistic. First, the nominal controller was designed based on the nonsingular fast terminal sliding mode control, and global fast finite-time convergence to the sliding surface was guaranteed. As the system is state-constrained in this paper, we introduce the control barrier function approach to formulate the constraints and ensure the system does not break the restrictions. The proposed control strategy was numerically assessed on a two-link robot manipulator system, and the simulation results illustrate the effectiveness of the proposed control strategy.

A finite-time sliding mode control technique for synchronization chaotic fractional-order laser systems with application on encryption of color images

In recent years, fractional order Laser chaotic systems have gained popularity in both theory and applications, and various classes of these systems have been introduced. This paper presents a dynamic-free sliding mode control (SMC) methodology to synchronize a class of unknown fractional order (FO) Laser chaotic systems with input saturation. The proposed method uses a defined continuous function instead of the discrete sign function and is based on the FO version of the Lyapunov stability theorem. The result is a novel finite-time SMC (FTSMC) methodology that effectively suppresses chaotic behavior in FO Laser chaotic systems without undesirable chattering. This approach is designed to take advantage of the boundedness feature of the FO chaotic system. The efficacy of the FTSMC is demonstrated by applying the method to a chaotic FO Laser system at two different non-integer orders, and its practical applicability is demonstrated by using it to encrypt/decrypt color pictures. The suggested encryption/decryption methodology uses an adaptation of the pre-diffusion permutation-diffusion structure to increase security. Performance and security analyses, including histogram analysis, neighboring pixel correlation analysis, and information entropy analysis, provide further support for the suggested encryption system's superiority.

Continuous Adaptive Finite-Time Sliding Mode Control for Fractional-Order Buck Converter Based on Riemann-Liouville Definition.

This study proposes a continuous adaptive finite-time fractional-order sliding mode control method for fractional-order Buck converters. In order to establish a more accurate model, a fractional-order model based on the Riemann-Liouville (R-L) definition of the Buck converter is developed, which takes into account the non-integer order characteristics of electronic components. The R-L definition is found to be more effective in describing the Buck converter than the Caputo definition. To deal with parameter uncertainties and external disturbances, the proposed approach combines these factors as lumped matched disturbances and mismatched disturbances. Unlike previous literature that assumes a known upper bound of disturbances, adaptive algorithms are developed to estimate and compensate for unknown bounded disturbances in this paper. A continuous finite-time sliding mode controller is then developed using a backstepping method to achieve a chattering-free response and ensure a finite-time convergence. The convergence time for the sliding mode reaching phase and sliding mode phase is estimated, and the fractional-order Lyapunov theory is utilized to prove the finite-time stability of the system. Finally, simulation results demonstrate the robustness and effectiveness of the proposed controller.

Finite-time sliding mode attitude control design for a coaxial tilt-rotor UAV

In this article, a finite-time sliding mode controller (FTSMC) is designed with the aim of attitude tracking of the coaxial tilt-rotor UAV (CTRUAV) under external disturbance. The CTRUAV is a multi-input multi-output (MIMO) and highly coupled system, which leads to the complexity of the controller design. Based on the dynamic model of the CTRUAV, an FTSMC is designed to improve the tracking performance of attitude control and robustness under uncertain disturbance, the stability of FTSMC is proved based on Lyapunov theory, and the power distribution is adjusted to solve the control-allocation problem of the CTRUAV. At last, simulation results are provided to show the effectiveness of FTSMC.

Observer-Based Finite-Time Sliding-Mode Control of Robotic Manipulator with Flexible Joint Using Partial States

This paper addresses the control problem of the flexible joint manipulator (FJM) with unmeasurable system states and mismatched uncertainties. First, the control system is transformed as a matched uncertain system with unmeasurable states based on differentiation method. Then, the uncertainties and unmeasurable states are estimated by designing a fixed-time observer (FTO). Based on the integral sliding-mode control (SMC), the bi-limit homogeneity technique and the estimation of FTO, a finite-time SMC is proposed for FJM. Compared with the existing finite-time SMC method for FJM, the most attractive feature of the proposed method is that not only the finite-time convergence is guaranteed but also the two angular velocity sensors for rotation angles of link and motor are simplified. Moreover, the proposed SMC can suppress the mismatched and matched uncertainties by using chattering-free control input. The fixed-time stability of FTO and finite-time stability of proposed controller are proved. Finally, the efficiency of proposed scheme is shown by the numerical simulation.

Satellite Attitude Control Using Double-Gimbal Variable-Speed Control Moment Gyroscope: Single-Loop Control Formulation

A single-loop control architecture is proposed to achieve singularity-free attitude control of satellites actuated using a double-gimbal variable-speed control moment gyroscope (DGVSCMG). Satellite and DGVSCMG combined rotational dynamics is modeled in the framework of geometric mechanics. It is shown that the combined attitude dynamics is in control-affine form when the motor torques of the DGVSCMG are taken as control inputs. A single-loop hybrid robust nonsingular fast finite-time sliding mode control (NFFTSMC) is designed to ensure an unwinding-free attitude maneuver. In the proposed single-loop formulation, the respective motor torques of the DGVSCMG are computed directly using only one NFFTSMC without requiring the steering law, resulting in mathematical singularity-free attitude control. A novel sliding surface is also proposed to ensure that the rotor angular speed converges to its nominal value after the maneuver. This eliminates the need of repeated desaturation of the rotor spin rate, unlike all the steering-law-based control architecture. Unwinding-free global stability of the system using the proposed hybrid NFFTSMC is proved for the sliding and reaching phases. Simulation results are presented to substantiate the claim made, assuming the rigid satellite to be equipped with only one DGVSCMG.

Disturbance-observer-based finite time sliding mode controller with unmatched uncertainties utilizing improved cubature Kalman filter

Complex reactions are difficult to control as the reactants not only produce desired product but may also further undergo unwanted reactions or the original reactants may degrade through alternate paths. This can be improved by selecting proper measurement and control. In this paper, a robust augmented derivative-free Kalman filter (augmented cubature Kalman filter, ACKF) is propounded for the continuous stirred tank reactor (CSTR) carrying out Van-de-Vusse type complex reactions where the intermediate is the desired product in the midst of consecutive and parallel reactions. Non-isothermal CSTR shows strong non-linearity with inherent challenges as the reaction kinetics depends on process temperature through Arrhenius laws and accompanies non-ideal flow behaviour and unmeasurable disturbances. First, the process exhibits inverse or non-minimum phase behaviour. Second, to control product temperature and concentration, a finite time sliding mode controller (FSMC) is suggested which effectively tracks servo response to the desired set point. Third, a disturbance filter has been proposed in association with FSMC, which constructively eliminates the input disturbances. Realistic simulations for servo-regulatory compliance, elimination of measurement noise, impact on large perturbation, and parametric uncertainty with a state-of-the-art simulator ensure the efficacy of the proposed controller. The results are analysed further with a derivative-free FSMC control approach, considering various performance indices (root mean square error (RMSE), total variation (TV), mean square deviation (MSD)) to assess the goodness of the newly developed control strategy. It has been found that improved control law (improved augmented cubature Kalman filter (IACKF)-FSMC) yields better RMSE (7.2645e–05) than ACKF-FSMC (7.5814e–05).

FTESO-based Nonsingular Fast Integral Terminal Sliding Mode Finite Time Control for the Speed and Tension System of the Cold Strip Rolling Mill

FTESO-based Nonsingular Fast Integral Terminal Sliding Mode Finite Time Control for the Speed and Tension System of the Cold Strip Rolling Mill