Fractional Sliding Mode Control Research Articles

Adaptive reinforcement learning interval type II fuzzy fractional nonlinear observer and controller for a fuzzy model of a wind turbine

This article presents an innovative control technique for doubly fed induction generator (DFIG) based wind turbine. A DFIG equation is initially presented using fractional order Takagi and Sugeno interval type II fuzzy modeling. Moreover, fault and disturbance are considered in the DFIG model. Then, to design an observer that estimates both fault and disturbance, the fuzzy model of DFIG is decoupled into three subsystems using a different linear coordinate transformation: the state subsystem without disturbance and fault, the subsystem of fault without disturbance, and the subsystem of disturbance without fault. In the following, using the state subsystem, an adaptive reinforcement learning TS interval type II fuzzy fractional sliding mode observer is introduced. The observer gains are adjusted by applying proximal policy optimization, which is a new application of reinforcement learning. Robustness against uncertainties, fast convergence speed of estimation, high degree of freedom and precise estimation are among features of the suggested observer. In addition, only by utilizing the estimated state subsystem and obtained mathematical relationships, the actuator faults and disturbance are estimated. A fractional order sliding mode controller is proposed for the DFIG speed controller. Low chattering characteristics and accurate response are achieved owing to the fractional speed controller. Also, to compensate the influence of disturbances and faults, an adaptive interval type II fuzzy fractional sliding mode controller is used for rotor current regulations, which employs the estimated fault and disturbance. High robustness, fast response time, low tracking error and chattering are some of the advantages of the proposed fault tolerant controller (FTC). The closed-loop stability of controllers is proved by using the Lyapunov theorem. Simulations is accomplished to evaluate the effectiveness of the proposed method. The proposed controller is compared with other controllers. Robustness against parameter uncertainty is also investigated.

Fractional-order robust fixed-time sliding mode control for deployment of tethered satellite

Tether deployment of the space tether system is the first step of related on-orbit experiments, which requires an advanced and reliable control scheme to realize rapid deployment without overshoot. In this paper, we propose a fractional-order fixed-time controller based on hierarchical sliding mode control to be applied to the deployment process of the tether system. The application of fractional calculus improves the local effect of the controller. Through strict mathematical derivation, we prove that the proposed control law satisfies the global fixed-time stability. So the closed-loop system has the performance of fixed-time convergence. Part of the simulation uses a fractional sliding mode control law for comparison, which further illustrates the superiority of the control law proposed in this paper. In view of the uniqueness of tether system dynamics, the research ideas in this paper are also of reference value to similar under-actuated systems.

Erratum: “New Compound Fractional Sliding Mode Control and Super-Twisting Control of a MEMS Gyroscope” [ASME Lett. Dyn. Sys. Control, 2022, 2(4), p. 040904; DOI: 10.1115/1.4055878

Abstract Due to a family emergency, this paper could not be presented at the 2022 ASME International Mechanical Engineering Congress and Exposition (IMECE).

New Compound Fractional Sliding Mode Control and Super-Twisting Control of a MEMS Gyroscope

Abstract This research proposes a new compound fractional sliding mode control (FOSMC) and super-twisting control (FOSMC + STC) to control a microelectromechanical systems gyroscope. A new sliding mode surface has been defined to design the proposed new sliding mode controller. The main advantages of a FOSMC are its high tracking performance and robustness against external perturbation, but creating a chattering phenomenon is its main drawback. By applying a super-twisting control (STC) method with FOSMC, the chattering phenomenon is eliminated, the singularity problem is solved, and systems robustness has significantly improved. Simulation results validate the effectiveness of the proposed control approach.

Finite-time lag projective synchronization of nonidentical fractional delayed memristive neural networks

Without considering identical systems, this paper investigates the finite-time lag projective synchronization of nonidentical fractional delayed memristive neural networks (FDMNN) by designing a novel fractional sliding mode controller (SMC). Due to the existence of memristor, the research is under the framework of Filippov solution. We firstly construct a fractional integral sliding mode surface (SMS). Based on sliding mode control theory and Lyapunov stability theorem, a novel fractional SMC is proposed to realize the lag projective synchronization of nonidentical FDMNN in finite time, and the synchronization setting time is less conservative than the existing results. As the special cases, some sufficient conditions are extended to projective synchronization, lag synchronization, anti-lag synchronization of nonidentical FDMNN in finite time, which improve and enrich some existing results. At last, a simulation example is given to prove the validity of the conclusions.

Performance-guaranteed fractional-order sliding mode control for underactuated autonomous underwater vehicle trajectory tracking with a disturbance observer

This paper proposes a fractional-order sliding mode control method for an underactuated autonomous underwater vehicle (AUV) with random disturbances. First, a new fractional-order sliding mode disturbance observer (FOSMDO) is designed to estimate the random disturbance and unknown AUV’s model based on adaptive and fixed time . A strategy based on adaptive fractional sliding mode control is designed for motion control, and a line-of-sight guidance law with time-varying look-ahead distance is applied to achieve path following. Then, a new fractional-order sliding model controller is designed by constructing a fractional-order mode surface and proposing a prescribed performance function to ensure the control performance. The closed-loop stability is proved and analyzed, and the effectiveness and robustness of the controller are demonstrated by numeric simulations.

Improved model-free fractional-order intelligent proportional–integral fractional-order sliding mode control with anti-windup compensator

In addition to the difficulty of system modeling, every physical system faces actuator saturation, making the real control different from the controller output (desired control input). When this occurs, the controller output does not regulate the system properly and errors occur as a result of incorrect updating. This is known as the windup phenomenon. In the event that the controller is configured to override actuator saturation, it can lead to a failure in the controller’s performance, such as large overshoots, high response time, and even system instability in the worst case. Therefore, in this paper, a new robust model-free controller method is proposed. It is a combination of four nonlinear control techniques, namely model-free controller, fractional-order sliding mode controller, fractional integral–proportional (PI) controller, and anti-windup compensator, which gives rise to the new model-free controller algorithm called hybrid fractional-order intelligent PI fractional sliding mode controller with an anti-windup compensator termed (MF-FOiPI-FOSMC-AW). However, to illustrate the effectiveness of the new proposed MF-FOiPI-FOSMC-AW method, simulation and experimental results compared to classical PI and iPI controllers (with and without an anti-windup compensator) on a hydraulic system are presented in the presence or absence of external disturbances for different types of references. Finally, simulation is conducted through an experimental comparison of the proposed approach with other strategies such as the classical anti-windup PI controller and the anti-windup intelligent PI controller, which is carried out for this purpose.

A Novel Fixed-Time Trajectory Tracking Strategy of Unmanned Surface Vessel Based on the Fractional Sliding Mode Control Method

A novel sliding mode control method is proposed to achieve the trajectory tracking of the Unmanned Surface Vessel (USV) and effectively deal with the unmodeled dynamics and external unknown disturbances. First, a fixed-time fractional-order sliding mode control (FTFOSMC) strategy is proposed, combined with the fixed-time control theory and fractional-order control theory based on the sliding mode control method. The FTFOSMC strategy can improve the convergence velocity of the system, and effectively track the desired path, weakening the “chattering” effect in sliding mode control systems. Second, a fixed-time fractional-order sliding mode control strategy combined with the radial basis function neural network (RBF-FTFOSMC) was designed, which can effectively estimate the lumped uncertainties, such as the disturbance of external wind, wave, and current, and the unmodeled dynamics of the USV model. Then, the stability and effectiveness of the designed control strategy are guaranteed by the Lyapunov theory and the corresponding lemmas. Finally, a rigorous simulation experiment is designed to validate the effectiveness and stability of the proposed control strategy. The simulation results show that the control strategy can effectively achieve trajectory tracking of the USV, reduce the “chattering” phenomenon of sliding mode, and effectively estimate the lumped uncertainties.

Optimal fractional sliding mode control for the frequency stability of a hybrid industrial microgrid

<abstract> <p>The rising proportion of inverter-based renewable energy sources in current power systems has reduced the rotational inertia of overall microgrid systems. This may cause high-frequency fluctuations in the system leading to system instability. Several initiatives have been suggested concerning inertia emulation based on other integrated external energy sources, such as energy storage systems, to combat the ever-declining issue of inertia. Hence, to deal with the aforementioned issue, we suggest the development of an optimal fractional sliding mode control (FSMC)-based frequency stabilization strategy for an industrial hybrid microgrid. An explicit state-space industrial microgrids model comprised of several coordinated energy sources along with loads, storage systems, photovoltaic and wind farms, is considered. In addition to this, the impact of electric vehicles and batteries with adequate control of the state of charge was investigated due to their short regulation times and this helps to balance the power supply and demand that in turn brings the minimization of the frequency deviations. The performance of the FSMC controller is enhanced by setting optimal parameters by employing the tuning strategy based on an iterative teaching-learning-based optimizer (ITLBO). To justify the efficacy of the proposed controller, the simulated results were obtained under several system conditions by using a vehicle simulator in a MATLAB/Simulink environment. The results reveal the enhanced performance of the ITLBO optimized fractional sliding mode control to effectively damp the frequency oscillations and retain the frequency stability with robustness, quick damping, and reliability under different system conditions.</p> </abstract>

Speed sensorless control of a bearingless induction motor with combined neural network and fractional sliding mode

To address the problem of speed and flux observation in sensorless control of a bearingless induction motor under the influence of parameter changes and external disturbances, a speed sensorless control strategy combining radial basis function (radial basis function, RBF) neural network and fractional sliding mode is proposed. According to the current error, fractional sliding mode control rate is designed to reduce the speed-observed chatter of the bearingless induction motor and its adverse effect on the rotor suspension stability. Then, combined with the theory of RBF neural network, the new optimal control rate is obtained by using its approximation ability. At the same time, the stability of two control rate is proved. Thus, the flux linkage and speed under normal operation, parameter change and external disturbance are observed and the new speed sensorless control is realized. The simulation and experimental results show that the proposed joint RBF neural network approximation algorithm and fractional sliding mode speed sensorless control system of the bearingless induction motor can not only effectively identify the flux and speed under three conditions of no-load, load disturbance and speed change, but also ensure the good suspension of the motor rotor in the x-axis and y-axis directions.

Adaptive parallel fractional sliding mode control

SummaryFractional sliding mode schemes possess the ability of compensating a large sort of continuous but not necessarily integer‐order differentiable disturbances; however, the adjustment of the control parameters is usually difficult and is based on a heuristic process. Motivated by the approximation capabilities of fractional sliding modes, this article proposes a parallel controller, which results as a linear combination of fractional‐order integral functions. The weight of each action of control is computed online by means of an adaptation algorithm. The stability of the closed‐loop system is demonstrated in the Lyapunov framework and a simulation study is presented to highlight the reliability of the proposed controller.

Fractional Order Adaptive Fast Super-Twisting Sliding Mode Control for Steer-by-Wire Vehicles with Time-Delay Estimation

It is difficult to model and determine the parameters of the steer-by-wire (SBW) system accurately, and the perturbation is variable with complex and changeable tire–road conditions. In order to improve the control performance of the vehicle SBW system, an adaptive fast super-twisting sliding mode control (AFST-SMC) scheme with time-delay estimation (TDE) is proposed. The proposed scheme uses TDE to acquire the lumped dynamics in a simple way and establishes a practical model-free structure. Then, a fractional order (FO) sliding mode surface and a fast super-twisting sliding mode control structure were designed on the basic super-twisting sliding mode to ensure fast convergence and high control accuracy. Since the uncertain boundary information of the actual system is unknown, a novel adaptive algorithm is proposed to regulate the control gain based on the control errors. Theoretical analysis concerning system stability is given based on the Lyapunov theory. Finally, the effectiveness of the method is verified through comparative experiments. The results show that the proposed TDE-AFST-FOSMC control scheme has the advantages of model-free, fast response and high accuracy.

Bridge-Ship Collision Avoidance Control Based on AFSMC with a FRNN Estimator

For collision avoidance and maneuvering control in bridge areas, an adaptive fractional sliding mode control with fractional recurrent neural network (FRNN-AFSMC) is proposed. The uncertainties are estimated by FRNN, and the fractional gradient is adopted to improve the recurrent neural network (RNN). Its convergence has been proven. The influence of fractional order on algorithm performance is analyzed, and the simulation platform of ship collision avoidance control is built. Dynamic collision avoidance of multiple ships is simulated and verified. The results show the feasibility and effectiveness of dynamic autonomous collision avoidance motion control in a dynamic ocean environment.

Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness

This paper considers the Mittag-Leffler projective synchronization problem of fractional-order coupled systems (FOCS) on the complex networks without strong connectedness by fractional sliding mode control (SMC). Combining the hierarchical algorithm with the graph theory, a new SMC strategy is designed to realize the projective synchronization between the master system and the slave system, which covers the globally complete synchronization and the globally anti-synchronization. In addition, some novel criteria are derived to guarantee the Mittag-Leffler stability of the projective synchronization error system. Finally, a numerical example is given to illustrate the validity of the proposed method.

Fractional sliding mode control for an autonomous two-wheeled vehicle equipped with an innovative gyroscopic actuator

Balancing two-wheeled autonomous vehicles at low forward speeds is one of the primary challenges in the development of such vehicles. Gyrostabilizers can be used as actuators to make the balance; however, conventional gyros are not typically able to maintain constant moments and directions to stabilize against constant ‘heel’. In this paper, we present an innovative gyrostabilizer including a twin-flywheel arrangement that can provide any desired gyroscopic roll moment. The dynamical model of a bicycle together with the gyrostabilizer is derived using Newton–Euler method. The actuator dynamics is included when designing the control system. A robust non-integer sliding mode controller is then developed to guarantee perfect trajectory tracking in the presence of roll disturbance. Extensive comparative simulations (based on the experimentally measured parameters of a typical bike) are conducted to evaluate the method and to show the impact of introducing the novel actuator. Results demonstrate that the proposed system offers superior performance while the control effort also remains within the capacity of normal actuators.

A new fractional sliding mode controller based on nonlinear fractional-order proportional integral derivative controller structure to synchronize fractional-order chaotic systems with uncertainty and disturbances

This study presents a new fractional sliding mode controller based on nonlinear fractional-order proportional integral derivative controllers to synchronize fractional-order chaotic systems with uncertainties and affected by disturbance. According to the proposed control approach, a new fractional order control law is presented which ensures robust and stable synchronization of chaotic systems in the presence of uncertainties of the master and slave systems and bounded disturbance according to Lyapunov theorem. The proposed sliding mode controller is used to synchronize two non-smooth chaotic jerk systems affected by disturbance and uncertainty. Simulation results verify effectiveness and robustness of the proposed control law.

Fractional Dynamic Sliding Mode Control for Uncertain Chaotic Systems Applied to a Chaotic Robot Arm Under Dynamic Load

Background: A novel type of control strategy is presented for the control of chaotic systems, particularly a chaotic robot in joint and workspace, which is the result of applying fractional calculus to dynamic sliding mode control. Objectives: To guarantee the sliding mode condition, a control law is introduced based on the Lyapunov stability theory. Methods: A control scheme is proposed for reducing the chattering problem in finite time tracking and robust in the presence of system matched disturbances. Results: Qualitative and quantitative characteristics of the chaotic robot are all proven to be viable thru simulations. Conclusion: In addition, all of the chaotic robot’s qualitative and quantitative characteristics have been investigated. Numerical simulations indicate the viability of our control method.

Design and HIL implementation of a new robust fractional sliding mode control of microgrids

Microgrid inverters in the presence of faults, unavoidable modelling uncertainties, disturbance and harmonic current resulting from nonlinear loads should have small steady state tracking error, small THD and high robustness hence this subject has turned one of the motivations of this investigation. To achieve the stated goals, fractional adaptive sliding mode controller (FASMC) is proposed in this paper. The proposed controller increases the robustness, flexibility and degree of freedom. As far as in practice it is not easy to define the bounds of disturbances and guarantee the system stability, hence in next step, to overcome this challenge the adaptation laws are suggested. Then for the problem of determining the controller parameters, Particle Swarm Optimization (PSO) algorithm is used. The performance of the proposed technique is investigated for an islanded microgrid under different disturbances, also to verify the advantages of the proposed controller, the results are compared with other controllers. Finally, the proposed controller and PID controller are implemented experimentally on Arduino mega 2560 microcontroller.

Mitigating subsynchronous control interaction using fractional sliding mode control of wind farm

This paper proposes a fractional sliding mode control (FSMC) based on direct torque control to mitigate subsynchronous control interaction (SSCI) in doubly-fed induction generator (DFIG)-based wind farm. The proposed FSMC realizes chattering attenuation and SSCI mitigation simultaneously. Moreover, FSMC improves the system robustness and convergence property, which make contributions to achieving effective damping of SSCI under different operating points. Given the high number of control parameters of FSMC, genetic algorithm (GA) is adopted to optimize control parameters. Impedance-based analysis, time-domain simulation, and experimental test are conducted to test the performance of FSMC as compared to subsynchronous damping control (SSDC) and terminal sliding mode control (TSMC). Results confirm the better damping capability of FSMC under different compensations and wind speeds. FSMC also shows strong robustness against parametric uncertainty and disturbance.

Optimal Projective Synchronization of Non-identical Fractional-Order Chaotic Systems with Uncertainties and Disturbances Using Fractional Sliding Mode Control with GA and PSO Algorithms

This work presents an optimal projective synchronization of non-identical fractional-order chaotic systems (FOCS) in the presence of uncertainties and external disturbances using a fractional sliding mode controller (FSMC). For the first time, and based on Lyapunov stability theory, fractional-order sliding surfaces are proposed to design signal controllers for forcing errors behavior to zero and to make the states of the FOCS asymptotically stable. Then, to obtain optimal control parameters, GA and PSO algorithms will be introduced. An example of non-identical FOCS are proposed to demonstrate the effectiveness of the proposed optimal FSMC approach compared with the integer one. The simulation results show the applicability and efficiency of the proposed scheme.