Fractional-order Sliding Mode Control Research Articles

Intelligent fractional-order sliding mode control based maneuvering of an autonomous vehicle

Intelligent fractional-order sliding mode control based maneuvering of an autonomous vehicle

Adaptive Hierarchical Fractional-Order Sliding Mode Control Strategy for Multi-terminal VSC-HVDC System with Wind Farm

In this paper, an adaptive hierarchical fractional-order sliding mode controller (AHFSMC) for a multi-terminal Voltage Source Converter (VSC) based High Voltage Direct Current (HVDC) Integrated with a wind farm (WF) system is designed. Multi-terminal VSC-HVDC (MtVDC) connected to wind farms has received several attentions in the power sector because of its numerous benefits. The effectiveness of MtVDC, on the other hand, is dependent on the control scheme used. To achieve this goal, a hierarchical sliding mode control method by fractional-order calculus is used. The controller parameters are adjusted according to a suitable adaptation method to enhance the proposed controller's robustness compared to the system uncertainties coefficient. An appropriate Lyapunov-based approach is used to achieve the adaptation rule. This paper discusses a scheme to design additional controllers in MtVDC systems to damp electromechanical oscillations, one of several features of HVDC presently under active study. Numerical simulations validate the proposed control strategy's feasibility and efficiency. This novel approach is employed for the upgrading of system stability with the dynamic properties of the MtVDC in a variety of operative conditions.

A Sliding-Mode Current Decoupling Control Strategy for an Active Power Filter Based on an Internal Model

With the ongoing development of electronic power technologies, harmonic pollution in the power grid has become a topic of great concern. This study takes a substation as its background. The safe and steady operation of the station’s equipment was impacted by a 10 kV bus’s harmonic current, which was significantly higher than the required amount. We propose a sliding-mode current decoupling control strategy based on an internal model to address the problems of complex harmonic current detection and distortion in the power supply current when there are nonlinear load changes in hybrid active power filters. By establishing a mathematical model for a HAPF, our proposed strategy can be used for inner current loops with the goal of stability, decoupling control between the d- and q-axes, fast-tracking harmonic reference currents, and optimizing the controller by enhancing the system’s anti-jamming performance to ensure that the system operates stably when line parameter ingressions or step changes in the load demand occur. The outer voltage loop uses the fractional-order sliding-mode control method to keep the capacitor voltage smooth and to dynamically adjust when the load changes suddenly. Finally, this filter is compared with a filter controlled by a PI in MATLAB/Simulink, and the feasibility and effectiveness of the proposed control strategy are verified based on a diode-embedded three-level parallel-type HAPF platform. The simulation and experimental results show that our sliding-mode current decoupling control strategy based on the internal mode is characterized by simplicity, stability, and fast responses.

A Mathematical Structural Modulation Method for Neutral-Point Potential Balancing of Three-Level Neutral-Point-Clamped Converters

To achieve the fast neutral-point potential balance of three-level neutral-point-clamped (3L-NPC) converters, a mathematical structural modulation method is presented in this paper, featuring fast balance capability, low computation, and easy implementation. In this method, the duty cycle is decomposed into the differential-mode component (DMC) and the common-mode component (CMC). The CMC is used to synthesize the AC output voltage while the DMC is adopted to control the neutral-point potential. Based on the fractional-order sliding-mode control theory, the DMC is constructed. As a result, neutral-point potential balancing in a pre-calculated time is achieved. Finally, the effectiveness of the proposed method is verified by experimental results.

Stabilization of chaotic fractional-order Lu ̈ system using sliding mode control

In this paper a fractional-order sliding mode controller (FOSMC) is proposed to control the chaotic fractional-order l’s system. Sliding mode control is a robust controller and its objective is to allo the system states to move to the sliding surface and remain on it. The stability analysis for the proposed control is performed based on the Lyapunov stability theorem. Simulation results show the ability of the proposed controller to improve the system performance.

An intelligent optimized fractional order sliding mode controller for biological system

An intelligent optimized fractional order sliding mode controller for biological system

Passivity-based Rieman Liouville fractional order sliding mode control of three phase inverter in a grid-connected photovoltaic system.

Photovoltaic (PV) system parameters are always non-linear due to variable environmental conditions. The Maximum power point tracking (MPPT) is difficult under multiple uncertainties, disruptions and the occurrence of time-varying stochastic conditions. Therefore, Passivity based Fractional order Sliding-Mode controller (PBSMC) is proposed to examine and develop a storage function in error tracking for PV power and direct voltage in this research work. A unique sliding surface for Fractional Order Sliding Mode Control (FOSMC) framework is proposed and its stability and finite time convergence is proved by implementing Lyapunov stability method. An additional input of sliding mode control (SMC) is also added to a passive system to boost the controller performance by removing the rapid uncertainties and disturbances. Therefore, PBSMC, along with globally consistent control efficiency under varying operating conditions is implemented with enhanced system damping and substantial robustness. The novelty of the proposed technique lies in a unique sliding surface for FOSMC framework based on Riemann Liouville (R-L) fractional calculus. Results have shown that the proposed control technique reduces the tracking error in PV output power, under variable irradiance conditions, by 81%, compared to fractional order proportional integral derivative (FOPID) controller. It is reduced by 39%, when compared to passivity based control (PBC) and 28%, when compared to passivity based FOPID (EPBFOPID). The proposed technique led to the least total harmonic distortion in the grid side voltage and current. The tracking time of PV output power is 0.025 seconds in PBSMC under varying solar irradiance, however FOPID, PBC, EPBFOPID, have failed to converge fully. Similarly the dc link voltage has tracked the reference voltage in 0.05 seconds however the rest of the methods either could not converge, or converged after significant amount of time. During solar irradiance and temperature change, the photovoltaic output power has converged in 0.018 seconds using PBSMC, however remaining methods failed to converge or track fully and the dc link voltage has minimum tracking error due to PBSMC as compared to the other methods. Furthermore, the photovoltaic output power converges to the reference power in 0.1 seconds in power grid voltage drop, whereas other methods failed to converge fully. In addition power is also injected from the PV inverter into the grid at unity power factor.

Fractional-Order Control Method Based on Twin-Delayed Deep Deterministic Policy Gradient Algorithm

In this paper, a fractional-order control method based on the twin-delayed deep deterministic policy gradient (TD3) algorithm in reinforcement learning is proposed. A fractional-order disturbance observer is designed to estimate the disturbances, and the radial basis function network is selected to approximate system uncertainties in the system. Then, a fractional-order sliding-mode controller is constructed to control the system, and the parameters of the controller are tuned using the TD3 algorithm, which can optimize the control effect. The results show that the fractional-order control method based on the TD3 algorithm can not only improve the closed-loop system performance under different operating conditions but also enhance the signal tracking capability.

Barrier Function-Based Backstepping Fractional-Order Sliding Mode Control for Quad-Rotor Unmanned Aerial Vehicle Under External Disturbances

Barrier Function-Based Backstepping Fractional-Order Sliding Mode Control for Quad-Rotor Unmanned Aerial Vehicle Under External Disturbances

Fractional-Order Sliding-Mode Control and Radial Basis Function Neural Network Adaptive Damping Passivity-Based Control with Application to Modular Multilevel Converters

This paper proposes a hybrid control scheme that combines fractional-order sliding-mode control (FOSMC) with radial basis function neural network adaptive damping passivity-based control (RBFPBC) for modular multilevel converters (MMC) under non-ideal operating conditions. According to the passive control theory, we establish the Euler–Lagrange (EL) models of positive and negative sequences based on the unbalanced grid. A passivity-based controller that satisfies the energy dissipation law is designed. To enable rapid convergence of the system energy storage function, a radial basis function neural network (RBFNN) is introduced to adjust the injection damping adaptively. Additionally, a fractional-order sliding-mode controller (FOSMC) is designed. The fractional-order sliding mode surface used can improve tracking performance, and effectively suppressed the undesirable chattering phenomenon compared to the traditional sliding-mode control (SMC). Finally, combining the two control methods can effectively solve the issue of passivity-based control (PBC) being too dependent on parameters. The proposed hybrid control scheme enhances the ability of the system to resist disturbances, and improves its overall robustness. Simulation results demonstrate the feasibility and effectiveness of this control method.

Nonlinear variable order system of multi-point boundary conditions with adaptive finite-time fractional-order sliding mode control

Nonlinear variable order system of multi-point boundary conditions with adaptive finite-time fractional-order sliding mode control

Fixed-time convergence of second-order nonlinear systems based on nonsingular fractional sliding mode

In this paper, a fixed-time convergence scheme for fractional sliding modes is proposed for nonlinear second-order systems. Firstly, a fixed-time fractional-order sliding mode surface is designed by combining the fixed-time theory with fractional-order sliding mode control, which has a faster convergence rate and less chattering. Secondly, the proposed sliding mode controller is applied to a class of second-order nonlinear systems subject to uncertainties and external perturbations to ensure that the system is globally robust fixed-time stable. Then, a continuous fractional order approach law is designed and the proposed sliding mode controller is shown to converge in fixed time by Lyapunov function and the convergence time is related to the choice of controller parameters. Finally, the fixed-time fractional-order sliding mode control strategy is applied to a second-order nonlinear magnetic levitation system system, and the simulation results verify the effectiveness of the proposed method.

Reactive power control of micro-grids using FOSMC for grid code compliance during asymmetrical voltage sags

Application of micro-grids (MGs) as a solution for future energy systems are significantly increasing in recent years. On the other hand, more stringent requirements are added to grid codes (GCs) of low-voltage distribution networks. Accordingly, this paper proposes a low-voltage ride-through (LVRT) control scheme for four-wire multi-source MGs. The novel strategy is composed of two layers for controlling each phase of the grid-connected sources independently. The primary layer contains a reverse-droop function for each phase and fractional-order sliding-mode-control (FOSMC). The secondary layer determines the total requested reactive power for each phase during symmetrical and asymmetrical voltage drops. Then, the mentioned power is shared among the phases of each inverter based on the reactive power-sharing strategy and GC requirements. Based on the proposed grid-following controller, the voltage of faulty phases is compensated by reactive power injection. In addition, power quality indexes are kept in acceptable ranges during abnormalities, and the FOSMC performs better than the conventional methods. The effectiveness of the proposed scheme is verified through offline simulations in MATLAB/Simulink as well as validation by real-time results.

ON THE ASYMPTOTIC STABILITY OF A NEW FRACTIONAL-ORDER SLIDING MODE CONTROL WITH APPLICATION TO ROBOTIC SYSTEMS

This paper presents an advanced control strategy based on Fractional-Order Sliding Mode Control (FO-SMC), which introduces a robust solution to significantly improve the reliability of robotic manipulator systems and increase its control performance. The proposed FO-SMC strategy includes a two-key term-based Fractional Sliding Function (FSF) that presents the main contribution of this work. Additionally, a fractional-order-based Lyapunov stability analysis is developed for a class of nonlinear systems to guarantee the asymptotic stability of the closed loop system. Four FSF-based versions of the designed FO-SMC are studied and discussed. Various scenarios of the proposed control strategy are tested on a 3-degree-of-freedom SCARA robotic arm and compared to recent FO-SMC works, demonstrating the effectiveness of the new proposed control strategy to (i) ensure the asymptotic stability, (ii) achieve a smooth start-up, (iii) cancel the static error, giving a good tracking trajectory, and (iv) reduce the control torques, yielding a consumed energy minimization.

Fractional-Order Sliding Mode Load Frequency Control and Stability Analysis for Interconnected Power Systems With Time-Varying Delay

The universal use of open communication networks in interconnected power systems has changed the constant delay in the formerly dedicated channels into time-varying delay. The delay will deteriorate the dynamic performance of the load frequency control and lead to system frequency instability. This paper presents a fractional-order sliding mode controller for interconnected power systems with time-varying delay and performs stability analysis based on the Lyapunov direct method. Firstly, fractional-order integral sliding mode control is used to improve the stability of interconnected power systems containing time-varying delay. This expands the delay margin by taking advantage of the scalability of the fractional-order to the sliding mode surface. Then, the Riemann-Liouville fractional-order Lyapunov functional is introduced to stability analysis. This reduced the conservatism of the stability analysis by adjusting the upper limit of the functional integral. Lastly, combining Lyapunov's theory and integral inequality to obtain the stability conditions of the time-varying delay power system described by linear matrix inequality, and bring the stability margin of the system. The simulation results show that the designed controller can guarantee that the maximum delay time of the system is less than a predefined upper limit. The proposed control strategy obtains a larger stability margin than the other four scenarios. Additional simulation study was also conducted to verify its robustness to load variations and wind fluctuations.

Dynamic Analysis and Suppression Strategy Research on a Novel Fractional-Order Ferroresonance System

Ferroresonance is characterized by overvoltage and irregular operation in power systems, which can greatly endanger system equipment. Mechanism analysis of the ferroresonance phenomenon depends mainly on model accuracy. Due to the fractional-order characteristics of capacitance and inductance, fractional-order models are more universal and accurate than integer-order models. A typical 110 kV ferroresonance model is first established. The influence of the excitation amplitude on the dynamic behavior is analyzed. The fractional-order ferroresonance model is then introduced, and the effects of the fractional order and flux-chain order on the system’s motion state are studied via bifurcation diagrams and phase portraits. In order to suppress the nonlinear dynamic behavior of fractional-order ferroresonance systems, a novel fractional-order fast terminal sliding mode control method based on finite-time theory and the frequency distributed model is proposed. A new fractional-order sliding mode surface and control law using a saturation function are developed. A robust fractional-order sliding mode controller could achieve finite-time stabilization and tracking despite model uncertainties and external disturbances. Compared with conventional sliding mode methods, the simulation results highlight the effectiveness and superiority. The research provides a theoretical basis for ferroresonant analysis and suppression in large-scale interconnected power grids.

Parametric fractional-order analysis of Arneodo chaotic system and microcontroller-based secure communication implementation

Chaotic systems are often used in cryptology applications thanks to their complex dynamic structures. By increasing the dynamic diversity of chaotic systems through fractional-order analysis, more complex systems for data security can be obtained. In this study, fractional calculus analyses of the Arneodo chaotic jerk system with cubic nonlinearity and its microcontroller-based chaotic masking application are presented. Numerical analyses such as bifurcation diagrams, spectral entropy complexity, and Lyapunov spectra are performed to examine the dynamic characteristics of the fractional-order system. The parametric analysis indicates the presence of chaotic states in the system for nearly all fractional-order values ranging from 0.55 to 1. In this manner, the study focuses on investigating the minimum applicable fractional-order value for use in secure communication applications, constituting the main contribution of this research. Consequently, the dynamic diversity and unpredictability of the cubic system are greatly increased. Moreover, two fractional-order Arneodo chaotic (FOAC) systems with distinct initial conditions are synchronized using a single-state fractional-order sliding mode controller (FOSMC). Finally, an innovative secure communication system based on a microcontroller is designed and implemented by employing the chaotic masking method. As anticipated, the voltage outputs of the microcontroller-based secure communication application demonstrated good agreement with the numerical simulations.

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.