Fractional-order Sliding Mode Control Research Articles

Adaptive sliding mode tracking control of underwater vehicle-manipulator systems considering dynamic disturbance

This paper proposes an adaptive sliding mode tracking control method with a nonlinear disturbance observer (NDO-ASMTC) to solve the trajectory tracking problem of the underwater vehicle-manipulator system (UVMS) in the presence of large dynamic uncertainties and severe external disturbances. The proposed NDO-ASMTC method employs an adaptive control law, an improved fractional-order sliding mode, and a nonlinear disturbance observer to achieve excellent tracking performance of the UVMS. To obtain a fast response speed in the sliding mode phase and eliminate static error in the reaching phase, a modified fractional-order sliding mode control scheme is proposed. An adaptive auto-tuning law of switching gains is presented to overcome the problem that the fixed switching gain may lead to obvious tracking performance degradation under lumped uncertainty. In addition, a nonlinear disturbance observer is implemented to maintain the robustness and stability of the control scheme under severe disturbances. Moreover, the proposed adaptive control scheme has been proved to be stable using the Lyapunov theorem. Simulations and experiments show that the proposed control scheme can meet the design requirements of the UVMS in terms of tracking accuracy, system stability, and interference attenuation under the application of external disturbances.

Fault-tolerant adaptive fractional order sliding mode control for a quadrotor using disturbance observer

An adaptive fractional-order sliding mode control method using a disturbance observer is proposed for position tracking of a quadrotor. The mathematical model of the quadrotor considering disturbance is derived using the Euler–Lagrange equations. The model is divided into two fully actuated and underactuated subsystems. The proposed controller as the result of combining fractional calculus and the sliding mode method is designed for both subsystems separately. Furthermore, a disturbance observer is designed which deals with actuator fault, uncertainty, and wind disturbance. The stability of the closed-loop system is proved using Lyapunov theory and finite-time convergence of the variables to the desired values is guaranteed. In the numerical simulation, position tracking despite the actuator faults and effects of load and wind disturbance are investigated. Finally, the simulation results validate the superior performance and robustness of the proposed controller against actuator fault and wind disturbance and the results of controllers are compared.

One new composite control based smooth nonlinear fractional order sliding mode algorithm and disturbance compensation for PMSM with parameter uncertainties

To achieve high-quality control of PMSM with parameter uncertainties, a nonlinear smooth fractional order sliding mode composite control (NSFOSMCC) strategy is designed in this paper. This approach incorporates a novel nonlinear smooth fractional order sliding mode controller, a novel adaptive super-twisting (AST) algorithm, and a modified nonlinear extended state observer (ESO) to achieve enhanced motor performance. To effectively overcome the disadvantages of simplicity and toughness associated with the conventional fractional order sliding mode controller, a novel nonlinear smooth fractional order sliding mode controller is designed. A novel AST technique is introduced to effectively weaken chattering issues. The modified nonlinear ESO is used to estimate the uncertainty parameters of the PMSM. By combining the modified nonlinear ESO with the latest sliding mode controller, a new composite controller called NSFOSMCC strategy is developed for PMSM. The proposed NSFOSMCC strategy, utilizing a combination of “feedforward plus feedback,” is implemented for PMSM with parameter uncertainties. The reliability and stability of the controller are thoroughly established through the utilization of the Lyapunov stability theorem. Furthermore, comparative results show strong evidence supporting the effectiveness of the novel composite control strategy.

Self-Constructing Fuzzy Neural Fractional-Order Sliding Mode Control of Active Power Filter.

In this article, a fractional-order sliding mode control (FOSMC) scheme is proposed for mitigating harmonic distortions in the power system, whereby a self-constructing recurrent fuzzy neural network (SCRFNN) is used to weaken the effect of compound nonlinearity caused by unknown uncertainties and environmental fluctuations. The fractional-order sliding mode controller (SMC) is constructed to maintain the control system to be asymptotically stable and a fractional-order calculus is introduced into an SMC to soften the sliding manifold design and realize chattering reduction. Considering parameter variations existing in the power system model, SCRFNN is adopted to approximate the unknown dynamics, which is able to dynamically update network structure by optimizing the fuzzy division, and a feedback connection is incorporated into the feedforward neural network, which is regarded as a storage unit to enhance the capability of coping with temporal problem. The control scheme combining the FOSMC with the SCRFNN can make the tracking error and its time derivative converge to zero. Experimental studies demonstrate the validity of the designed scheme, and comprehensive comparisons illustrate its superiority in harmonic suppression and high robustness.

A robust super twisting fractional-order sliding mode-based control of vehicle longitudinal dynamic subjected to a constant actuator fault

This paper deals with the design and analysis of a super twisting fractional-order sliding mode controller (ST-FOSMC) to adjust the vehicle longitudinal dynamic when braking. While vehicle loading, road types, and modeling uncertainties are time-varying parameters, the control law must be robust against these disturbances. Also, the aging of the brake plate may introduce a difference between the control output and the actuator response that should be considered. The proposed control strategy has been used to enable the anti-lock braking system (ABS) to track the desired wheel slip value despite the presence of disturbances and constant actuator fault. The design of this controller is presented and the system stability is guaranteed by applying the Lyapunov theory. We carried out a simulation example that makes a comparison between our controller and the one based on the fractional-order sliding mode control to investigate which one of them outperforms the other. The results exhibit the superiority of the super twisting fractional order controller over the traditional fractional-order sliding mode controller during the braking phase.

Fractional order sliding mode control for linear maglev synchronous motor based on an adaptive fixed-time extended state observer

In order to improve the tracking accuracy of the linear maglev synchronous motor maglev system with non-linear, strongly coupled, and other uncertainty problems, a fixed-time fractional order terminal sliding mode control (FFTSMC) strategy based on adaptive fixed-time extended state observer (AFxESO) is proposed. Firstly, a fast AFxESO is constructed and an adaptive law is designed to dynamically adjust the gain to reduce the estimation error and measurement noise, which enables the observer to accurately estimate the perturbation of the unknown boundary in a fixed-time. Secondly, a new FFTSM controller is designed by applying the theory of fractional order calculus, which can speed up the system convergence and suppress the chattering problem in SMC. Then, using the Lyapunov stability theory, it is demonstrated that the proposed AFxESO-FFTSM control scheme can guarantee the global fixed-time convergence of the system to equilibrium and the convergence time is dependent on the selection of the controller parameters, which effectively overcomes the drawbacks of finite-time control. Finally, the feasibility and superiority of the proposed strategy are verified on the linear maglev synchronous motor system experiment platform.

Extended state observer based fractional order sliding mode control for steer‐by‐wire systems

AbstractIn this paper, an extended state observer based fractional‐order sliding mode control strategy is studied for vehicle steer‐by‐wire systems (SBWSs). The parameter perturbation and external interference are considered in the dynamic model of SBWSs. A fractional‐order sliding mode control scheme is designed to solve the tracking problem and improve the control performance. An extended state observer is further used to estimate the lumped disturbance, and then the estimated value is considered as a feedforward compensation to reduce the chattering phenomenon. Finally, comparison simulation results show that the excellent steering tracking and strong robustness performance have been achieved by the proposed control strategy for SBWSs.

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.

A Novel Data-Driven Self-Tuning SVC Additional Fractional-Order Sliding Mode Controller for Transient Voltage Stability With Wind Generations

This paper proposes a novel data-driven self-tuning additional sliding mode controller for power system transient voltage stability enhancement considering wind integration. We first develop a new additional fractional-order sliding mode controller (FOSMC) for the static var compensator (SVC). The tuning of FOSMC parameter settings is then reformulated as a Markov decision process (MDP) and solved by the deep reinforcement learning (DRL) algorithm. In addition, a data-driven estimation method is proposed for the identification of an equivalent transfer function that is further used to calculate reward during the training process, yielding the model-free training. After that, the well-trained agent allows us to tune the controller parameters considering system uncertainties and achieve robustness against various operating conditions. Comparative results with other state-of-art methods demonstrate that the proposed method can effectively suppress the chattering issue of the sliding mode controller and ensure transient voltage stability under different operating conditions.

Fractional order sliding mode control for an omni-directional mobile robot based on self-organizing interval type-2 fuzzy neural network

Four-wheeled omnidirectional mobile robots (FM-OMR) are widely used in various fields due to their excellent steering ability and adaptability. As application scenarios expand, higher requirements are placed on their trajectory tracking capabilities. FM-OMR is highly complex and difficult to model accurately, and the system contains uncertainties. Therefore, achieving accurate trajectory tracking in the presence of system uncertainty is a pressing problem. Traditional control methods struggle to accurately estimate uncertainty, and existing controllers often rely on model parameters, resulting in poor transferability. To address this issue, this paper proposes a new control method based on an online self-organizing interval type II fuzzy neural network (SOIT2FNNFSMC). This method employs an online self-organizing algorithm to dynamically compensate for uncertainty, providing greater flexibility and accuracy compared to traditional approximation networks in terms of network construction and approximation performance. A new combined reaching law is proposed based on the characteristics of traditional reaching laws, resulting in improved chattering reduction. Additionally, fractional calculus is introduced to enhance the dynamic characteristics of the controller. Simulation and experimental results demonstrate the effectiveness of this method in achieving precise trajectory tracking while handling uncertainty and not relying on model parameter features. The self-organizing algorithm proposed in this method also provides a reference for the application of SOIT2FNN in FM-OMR.

Fixed-Time Fractional-Order Sliding Mode Control for UAVs under External Disturbances

The present paper investigates a fixed-time tracking control with fractional-order dynamics for a quadrotor subjected to external disturbances. After giving the formulation problem of a quadrotor system with six subsystems like a second-order system, a fractional-order sliding manifold is then designed to achieve a fixed-time convergence of the state variables. In order to cope with the upper bound of the disturbances, a switching fixed-time controller is added to the equivalent control law. Based on the switching law, fixed-time stability is ensured. All analysis and stability are proved using the Lyapunov approach. Finally, the higher performance of the proposed controller fixed-time fractional-order sliding mode control (FTFOSMC) is successfully compared to the two existing techniques through numerical simulations.

Recurrent-Neural-Network-Based Fractional Order Sliding Mode Control for Harmonic Suppression of Power Grid

A continuous fractional order sliding mode controller (CFOSMC) based on a developed output feedback feature selection neural network (OFFSNN) for an active power filter (APF) is studied in this paper to effectively compensate grid harmonic current and improve power quality. A fractional order sliding mode manifold is introduced firstly. Then a continuous fractional order sliding mode controller is adopted to resolve the shortcoming of chattering phenomenon in the conventional one by designing a continuous control law. Furthermore, considering the unknown part of APF system, a new neural structure called OFFSNN is established to estimate the unknown dynamic characteristic with high precision and low computational burden. Compared with general neural network, the proposed OFFSNN is adept at adjusting neural structure and parameters by selecting beneficial nodes as well as deleting useless ones. To demonstrate the effectiveness and superiority of the presented scheme, experiments in various cases on the APF platform are given.

Double-hierarchical fuzzy exponential convergence law fractional-order sliding mode control for PMSM drive control in EV

In the vector control of permanent magnet synchronous motor (PMSM), the speed overshoot and torque pulsation phenomena need to be solved. There are two prerequisites for the drive control of PMSM in electric vehicle (EV). The first is that the vehicle control has to be ensured as a whole. The second is, to ensure the economy of the vehicle control while ensuring the stable control of the motor. Therefore, this paper first proposes the fuzzy exponential convergence law fractional-order sliding mode control (F-CFSMC), it is constructed with the purpose of online correction of the exponential convergence law of the fractional-order sliding mode surface. It is expressing the arrival time and convergence speed of the fractional-order sliding mode surface explicitly with parameters. The stability of the F-CFSMC is proved to be derived using the Lyapunov equation. The F-CFSMC is applicable to PMSMs with different parameters. Next, the fuzzy controller that considers the battery parameter factor in EV is introduced to combine the lithium battery and PMSM to enhance energy utilization. At this point, the double-hierarchical fuzzy exponential convergence law fractional-order sliding mode control (DF-CFSMC) build is complete. Moreover, comparative simulations and experiments using the DF-CFSMC and the conventional PMSM control are conducted, and the results are performed in PMSM hierarchical. Simulations are also performed in the EV hierarchical application to show the universality, repeatability and advantages of DF-CFSMC.

Adaptive Control Design for Euler–Lagrange Systems Using Fixed-Time Fractional Integral Sliding Mode Scheme

This paper presents an adaptive fixed-time fractional integral control for externally disturbed Euler–Lagrange systems. In the first step of the control design, the approach of fractional-order fixed-time integral nonsingular terminal sliding mode control (FoIFxTSM) is introduced. This scheme combines the benefits of fractional calculus with integral sliding mode control, resulting in fast convergence, smooth nonsingular control inputs, and fixed-time stability. By integrating an adaptive scheme, the proposed method is used to control the dynamical system in the presence of uncertainty and external perturbations. The findings of the fixed-time stability using Lyapunov analyses are provided for the closed-loop system. The simulation results are compared with the adaptive fractional-order sliding mode control scheme, and they show the better tracking and convergence performance of the proposed method.

Ship roll stabilization using an adaptive fractional-order sliding mode controller

The current study designs an adaptive fractional-order sliding mode controller (AFOSMC) to diminish the undesirable effects caused by the ship roll motions. The ship roll dynamics combined with the fin actuator are employed for the controller design. The design steps are given as follows. At first, a non-integer sliding surface is utilized to design a fractional-order sliding mode controller (FOSMC). Then, an appropriate Lyapunov-based adaptation mechanism is designed to construct the adaptive version of the FOSMC. A Lyapunov candidate function is adopted to attain the ship roll stabilization through this adaptive control approach. The designed controller is robust to uncertain parameters in the ship roll dynamics and the fin actuator. Moreover, the effect of sea waves is reduced, as well. The robust performance of the AFOSMC is shown through numerical simulations.

Fractional order neural sliding mode control based on the FO-Hammerstein model of piezoelectric actuator

Piezoelectric actuators (PEA) are extensively utilized in high-precision micro-measurement and operation. However, owing to the rate-dependent nature of its hysteresis, its accuracy in certain applications would suffer significantly, and the system would become unstable. To address this issue, a new method for developing a feedback control system that can reduce the rate-dependent impacts of PEA on the positioning system is provided using PEA as the research object. This strategy is based on the fractional order Hammerstein model (FO-Hammerstein). For the fractional order model, a novel fractional order integral sliding mode surface is proposed here that can accurately delineate the dynamic characteristics of PEA. This sliding mode surface is composed of a fractional polynomial and an integral term, which can better minimize static errors and monitor reference signals, and it is built using a fractional neural sliding mode control (BP-FSMC) method. The control technique can be extensively utilized in various systems, such as FO-Hammerstein and those described by the fractional transfer function. The research introduces a neural network and an artificial bee colony algorithm (DeC-ABC) that are used to alter the system’s parameters. The study’s findings reveal that a system with high resilience can follow the signals from both composite and single input sources. Compared with the fractional order sliding mode control approach on the basis of extended state observer, the fractional order sliding mode control method based on single parameter adaptive law and the proportional integral sliding mode control method on the basis of feedforward compensation, this method has a quicker response time and lower tracking error.

Research on Path Tracking and Yaw Stability Coordination Control Strategy for Four-Wheel Independent Drive Electric Trucks

Achieving accurate path tracking and vehicle stability control for four-wheel independent drive electric trucks under complex driving conditions, such as high speed and low adhesion, remains a major challenge in current research. Poor coordination control may cause the vehicle to deviate from its intended path and become unstable. To address this issue, this article proposes a coordinated control strategy consisting of a three-layer control framework. In the upper layer controller design, establish a linear quadratic regulator (LQR) path tracking controller to ensure precise steering control by eliminating steady-state errors through feedforward control. The middle layer controller utilizes the fractional order sliding mode control (FOSMC) yaw moment controller to calculate the additional yaw moment based on the steering angle of the upper input, utilizing the error of yaw rate and sideslip angle as the state variable. To collectively optimize the control system, establish a coordinated optimization objective function and utilize the hybrid genetic-particle swarm optimization algorithm (GA-PSO) to optimize the weight coefficient of LQR and sliding mode parameters of FOSMC, effectively improving the performance of the controller. In the lower layer torque distribution controller, use the quadratic programming method to achieve real-time optimal torque distribution based on tire utilization, which improves vehicle stability control. Through simulations conducted under four different working conditions, the proposed control scheme demonstrates a 15.54% to 23.17% improvement in tracking performance and a 10.83% to 23.88% optimization in vehicle driving stability compared to other control methods. This scheme provides a theoretical reference for path tracking and stability control in four-wheel independent drive electric trucks.

Embedded adaptive fractional-order sliding mode control based on TSK fuzzy system for nonlinear fractional-order systems

An adaptive fractional-order sliding mode control (AFOSMC) is proposed to control a nonlinear fractional-order system. This scheme combines the features of sliding mode control and fractional control for improving the response of nonlinear systems. The structure of AFOSMC includes two units: fractional-order sliding mode control (FOSMC) and the tuning unit that employs a certain Takagi–Sugeno–Kang fuzzy logic system for online adjusting the parameters of FOSMC. Tuning the parameters of the FOSMC improves its performance with various control problems. Moreover, stability analysis of the proposed controller is studied using Lyapunov theorem. Finally, the developed control scheme is introduced for controlling a fractional-order gyroscope system. The proposed AFOSMC is implemented practically using a microcontroller where the test is carried out using the hardware-in-the-loop simulation. The practical results indicate the improvements and enhancements introduced by the developed controller under external disturbance, uncertainties and random noise effects.

Quadrotor Robust Fractional-Order Sliding Mode Control in Unmanned Aerial Vehicles for Eliminating External Disturbances

Quadrotors, commonly known as drones or unmanned aerial vehicles (UAVs), play an important role in load transportation. The complex vehicles used for transporting loads and surveillance purposes can be replaced through the ease of use and mechanical simplicity of the quadrotors. This study aims to introduce a new way of controlling the slung load system of the quadrotor after applying the fractional-order sliding mode control (FOSMC) method for performance enhancement. This method in the presence of external disturbances is likely to help stabilize and track the quadrotor with minimized swinging of the attached load. The results of this study prove the robustness of FOSMC through analysis, outcomes, and graphical representations that show the effect with various angles for a clear and conceptual understanding. The present study contributes to the literature by designing a robust FOSMC for a quadrotor with the help of external disturbances. The results of this study could be applied to the development of the design of upcoming drones which can increase the efficiency as well as the accuracy of load transportation. Further applications in the fields of rescue, agriculture, construction, research, and advancement of the fraction calculus-based control method are recommended using the FOSMC method.

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.