Fractional-order Sliding Mode Control Research Articles

Decentralized Sliding Mode Control of WG/PV/FC Microgrids Under Unbalanced and Nonlinear Load Conditions for On- and Off-Grid Modes

This paper presents a new decentralized robust power/current/voltage/frequency control strategy for islanded and grid-connected modes to enhance power-sharing and small- and large-signal stability of a wind/photovoltaic/fuel cell microgrid and improve its performance for nonlinear and unbalanced loads. First, the distributed energy resources are modeled for unbalanced voltage condition. Then, in order to improve power sharing, regulate voltage and active/reactive powers injected by these resources, and moreover, harmonic and negative-sequence current control in the presence of nonlinear and unbalanced loads, three separate controllers for positive-sequence voltage and power control and negative sequence current control are designed based on the sliding mode control, Lyapunov function theory, and fractional-order sliding mode control, respectively. The theoretical concept of the proposed control strategy, including the mathematical modeling of microgrid components, basic theorems, controller design procedure, and robustness/closed-loop stability analysis, is outlined. Also, this direct power/current/voltage/frequency control scheme is governed by a hierarchical control scheme that exploits a voltage compensation scheme and harmonic virtual impedance loop. To show the effectiveness of the proposed control scheme, offline time-domain simulation studies are performed on a wind/photovoltaic/fuel cell microgrid with nonlinear and unbalanced loads in MATLAB/Simulink environment and the results are verified by OPAL-RT real-time digital simulator.

Fractional-order sliding mode control of uncertain QUAVs with time-varying state constraints

In this paper, a novel robust fractional-order sliding mode (FOSM)-based state constrained control scheme is designed for uncertain quadrotor UAVs (QUAVs). Model uncertainties and wind gust disturbances are taken into consideration. Under the presented framework, the overall QUAV system is decoupled into translational subsystem and rotational subsystem. These two subsystems are connected to each other through common attitude extraction algorithms. For translational subsystem, the robust state variables constrained controller is designed to ensure the position state variables within the given time-varying constraints. For the rotational subsystem, a new robust FOSM controller is constructed to track the desired attitudes with better performances. Finally, the system is proved to be asymptotically stable, and both simulation and experiment results are conducted to validate the feasibility and effectiveness of the proposed control scheme.

Fractional Order Sliding Mode Control of a Class of Second Order Perturbed Nonlinear Systems: Application to the Trajectory Tracking of a Quadrotor

A Fractional Order Sliding Mode Control (FOSMC) is proposed in this paper for an integer second order nonlinear system with an unknown additive perturbation term. A sufficient condition is given to assure the attractiveness to a given sliding surface where trajectory tracking is assured, despite the presence of the perturbation term. The control scheme is applied to the model of a quadrotor vehicle in order to have trajectory tracking in the space. Simulation results are presented to evaluate the performance of the control scheme.

Practical Position Tracking Control of a Robotic Manipulator Based on Fractional Order Sliding Mode Controller

In this study, the practical position tracking control of a robotic manipulator has been performed using the proposed fractional-order sliding mode control scheme (FO-SMC). The designed control technique is composed by fractional calculus and sliding mode control (SMC) to guarantee the fast convergence of the joint positions to their desired values. The main idea behind the design of the FO-SMC control is that, the sliding mode control composed with fractional calculus contributes to reach a robust control performance of a nonlinear system in presence of uncertainties, disturbances and un-modelled dynamics without a complete dynamic model of the system. To validate and demonstrate the performance of FO-SMC method, an industrial robot manipulator with external load has been used in the real time experimental studies. The experimental outcomes demonstrate that the proposed fractional-order sliding mode control strategy has a better trajectory tracking performance in presence of the external payload for tracking tasks compared with the classical SMC.DOI: http://dx.doi.org/10.5755/j01.eie.24.5.21838

Fractional‐order sliding mode control for hybrid drive wind power generation system with disturbances in the grid

AbstractThe proposal of hybrid drive grid‐connected wind turbine based on speed regulating differential mechanism (SRDM) has been made in this paper to generate constant‐frequency power without fully‐ or partially‐rated frequency converters so as well improve electric power quality. However, disturbances in the power grid including sudden load fluctuation and sub‐synchronous resonance (SSR) can lead to the pulsating torque to act on the shaft section between SG and exciter at the main generator collector, such that the speed regulating accuracy of SRDM is seriously affected. As a result, this paper synthesizes a new‐type fractional‐order sliding mode controller (FOSMC) with a load torque observer (LTO) for the high‐accuracy speed control of permanent magnet synchronous motor (PMSM) in SRDM. Taking advantage of ridge regression algorithm, related parameters including rotational inertia and viscous friction coefficient of speed regulating system are calculated accurately. Finally, comparative experiments are carried out under four cases of mean of 5, 10, 13, and 21 m/s wind speeds to verify the satisfactory performances of designed FOSMC with LTO. Comparative experimental results show that FOSMC with LTO can effectively eliminate undesirable chattering effect. Additionally, under operating conditions of changing wind speeds, SSR, and sudden load fluctuation in power grid, the output speed of SRDM that corresponds directly to the frequency output of SG can be steadily and accurately regulated by using proposed control scheme. SRDM equipped with designed controller enables the power frequency to meet the National Standard of PR China perfectly.

Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control

This paper deals with a finite time robust synchronization problem of a class of uncertain fractional chaotic/hyper-chaotic systems with a novel fractional sliding mode control technique. Firstly, a fractional order sliding surface is proposed to mimic the behavior of master chaotic system. Then, a fractional order sliding mode control (FOSMC) methodology is derived analytically for convergence of all the synchronizing errors to zero in finite time. Finally, the derived control strategy is augmented with an auxiliary control based on uncertainty and disturbance estimator (UDE) for ensuring the robustness of the closed loop system dynamics in the presence of system uncertainties. Further, the uncertainties with unknown bounds are tackled for depicting the practical scenario and these results are also applicable to the N-dimensional uncertain chaotic as well as hyper-chaotic systems. Moreover, Mittag-Leffler and fractional order Lyapunov results are utilized to prove the stability and finite time convergence. Also, the proposed method delivers chatter-free control signal which is a major issue in sliding mode. MATLAB simulations are carried out to verify the efficacy and robustness of the derived results by considering two examples from literature.

Robust position-based impedance control of lightweight single-link flexible robots interacting with the unknown environment via a fractional-order sliding mode controller

SUMMARYThis paper presents a fractional-order sliding mode control scheme equipped with a disturbance observer for robust impedance control of a single-link flexible robot arm when it comes into contact with an unknown environment. In this research, the impedance control problem is studied for both unconstrained and constrained maneuvers. The proposed control strategy is robust with respect to the changes of the environment parameters (such as stiffness and damping coefficient), the unknown Coulomb friction disturbances, payload, and viscous friction variations. The proposed control scheme is also valid for both unconstrained and constrained motions. Our novel approach automatically switches from the free to the constrained motion mode using a simple algorithm of contact detection. In this regard, an impedance control scheme is proposed with the inner loop position control. This means that in the free motion, the applied force to the environment is zero and the reference trajectory for the inner loop position control is the desired trajectory. However, in the constrained motion the reference trajectory for the inner loop is determined by the desired impedance dynamics. Stability of the closed loop control system is proved by Lyapunov theory. Several numerical simulations are carried out to indicate the capability and the effectiveness of the proposed control scheme.

Perturbation observer based fractional-order sliding-mode controller for MPPT of grid-connected PV inverters: Design and real-time implementation

In this paper, a robust/adaptive perturbation observer based fractional-order sliding-mode controller (POFO-SMC) is designed for a photovoltaic (PV) inverter connected to the power grid, in which a maximum power point tracking (MPPT) based on variable step size incremental conductance (INC) technique is achieved to harvest the available maximum solar energy from the PV arrays in the presence of various atmospheric conditions. A nonlinear extended state observer (ESO), called sliding-mode state and perturbation observer (SMSPO), is used to efficiently estimate the aggregated effect of PV inverter nonlinearities and parameter uncertainties, unmodelled dynamics, stochastic fluctuation of atmospheric conditions, and external disturbances. Then, a fractional-order sliding-mode controller (FOSMC) is designed to considerably enhance the system robustness via real-time perturbation compensation and to noticeably accelerate the tracking rate compared to the traditional integer-order sliding-mode control (SMC) through employing a fractional-order proportional–derivative (FOPD) sliding surface. In addition, more reasonable control efforts could be realized since the upper bound of perturbation is replaced by its real-time estimate, such that the inherent over-conservativeness of conventional SMC can be effectively reduced. Four case studies are carried out under Matlab/Simulink environment. Simulation results verify the effectiveness and superiority of POFO-SMC compared to that of proportional–integral (PI) control, feedback linearization control (FLC), SMC, robust SMC (RSMC), and FOSMC. Finally, a dSpace based hardware-in-loop (HIL) experiment is undertaken for the purpose of implementation feasibility validation.

Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

Adaptive synchronization for a class of uncertain delayed fractional-order Hopfield neural networks (FOHNNs) with external disturbances is addressed in this paper. For the unknown parameters and external disturbances of the delayed FOHNNs, some adaptive estimations are designed. Firstly, a fractional-order switched sliding surface is proposed for the delayed FOHNNs. Then, according to the fractional-order extension of the Lyapunov stability criterion, a fractional-order sliding mode controller is constructed to guarantee that the synchronization error of the two uncertain delayed FOHNNs converges to an arbitrary small region of the origin. Finally, a numerical example of two-dimensional uncertain delayed FOHNNs is given to verify the effectiveness of the proposed method.

Fractional-Order Sliding Mode Control for D-STATCOM Connected Wind Farm Based DFIG Under Voltage Unbalanced

This paper studies the use of distribution static synchronous compensator (D-STATCOM) integrated with wind farm based on doubly fed induction generators. The short-term energy storage system based on a supercapacitor is introduced in this study to improve the operation of D-STATCOM. The dynamic performances of the grid-connected wind farm with D-STATCOM are enhanced by the proposed control scheme, which is based on fractional-order sliding mode control theory with dual-sequence decomposition technique. Some results of simulation show that, under an unbalanced grid voltage conditions, the proposed control strategy for the D-STATCOM not only eliminates effectively the oscillations of the active and reactive powers exchanged between the wind generator and the grid but also achieves the symmetrical and sinusoidal grid currents with less harmonics.

Passivity-based fractional-order sliding-mode control design and implementation of grid-connected photovoltaic systems

In order to achieve the maximum power point tracking of photovoltaic (PV) systems in the presence of time-varying stochastic operation conditions and various uncertainties/disturbances, a passivity-based fractional-order sliding-mode control (PbFoSMC) scheme is proposed. The design can be classified into two steps, i.e., (a) construct a storage function in terms of the tracking error of DC-link voltage, DC-link current, and q-axis current for the PV system, upon which the actual characteristics of each term is thoroughly analyzed. Moreover, the beneficial terms are carefully retained to enhance the dynamical responses of the closed-loop system while the detrimental terms are fully removed to realize a global control consistency; (b) based on the passivized system, a fractional-order sliding-mode control (FoSMC) is incorporated as an additional input, which can considerably improve the control performance with the aim of rapid uncertainties/disturbances rejection. Four case studies, including the solar irradiance change, temperature variation, power grid voltage drop, and PV inverter parameter uncertainties, are undertaken to evaluate the effectiveness of PbFoSMC in comparison to that of proportional-integral-derivative control, passivity-based control, and sliding-mode control (SMC), respectively. At last, a dSpace based hardware-in-loop test is carried out to validate the implementation feasibility of PbFoSMC.

Adaptive fractional order fast terminal dynamic sliding mode controller design for antilock braking system (ABS)

This article focuses on designing an antilock braking system (ABS) controller to adjust the wheel slip to the preferred value using sliding mode control and fractional calculus. The ABS must be robust against external disturbances such as variations in the friction force between the tire and road caused by changes in the road conditions, loadings and etc. A fractional order PD switching surface is defined, then in order to improve the convergence speed and increase degree of freedom of the controller, a new sliding surface is defined as fast terminal dynamic sliding surface which is formulated using Fractional Calculus. Then, a fractional order fast terminal dynamic sliding mode controller (FOFTDSMC) is designed. Also, for estimating the upper bound value of the lumped uncertainty in the proposed controller, an adaptive FOFTDSMC is designed. The finite time stability of the closed-loop system is guaranteed. Simulation results show the effectiveness of the proposed controller in terms of fast tracking with high robustness when compared to the fractional order sliding mode controller and fractional order fast terminal sliding mode controller.

Fuzzy type-2 fractional Backstepping blood glucose control based on sliding mode observer

A new combination of fractional order (FO) nonlinear control and sliding mode observer (SMO) for blood glucose regulation in type 1 diabetes mellitus is proposed in this paper. An observer estimates the difficult-to-measure process variables that are significant to control law design and to prevent failures. A SMO is proposed to estimate non-measurable states variables of Bergman minimal model by data acquired from a continuous glucose monitoring sensor. At first based on Backstepping method with FO sliding surface a control signal is proposed, and then interval type 2 fuzzy logic is utilized to reduce the chattering phenomenon in control signal. The FO sliding mode control provides robust performance and the Backstepping algorithm protects the controller in front of mismatched and matched uncertainties. Simulation results of the proposed controller are compared with its integer counterpart.

Fractional order sliding mode control via disturbance observer for a class of fractional order systems with mismatched disturbance,

This article proposes a novel fractional order sliding mode control for a class of fractional order and integer order systems with mismatched disturbances. First, a new fractional order disturbance observer is designed to estimate the fractional order differential of the mismatched disturbance directly. Second, the fractional order sliding surface and controller are proposed based on the designed disturbance observer. Our method can deal with mismatched disturbance and has better control performance with faster response speed, lower overshoot, and less chattering effect. The simulations on Quad–Rotor UAV and Maglev suspension systems demonstrate the effectiveness of the proposed method.

Bifurcation, Chaos and its Control in A Fractional Order Power System Model with Uncertainties

AbstractThe paper investigates the complex nonlinear behavior of a fractional order four dimension power system (FOFDPS). The discrete mathematical model of the FOFDPS is derived and presented. The equilibrium points along with the Eigen values of commensurate and incommensurate FOFDPS are presented. The existence of chaotic oscillations are supported by a positive Lyapunov exponent. Bifurcation plots are derived for both parameters and fractional orders to show the impact of the same on the dynamic behavior of FOFDPS. Having shown the existence of such complex behaviors in the FOFDPS, we present an adaptive fractional order sliding mode control (FOASMC) to suppress the chaotic oscillations. Numerical results are presented to support the theoretical results.

Practical tracking control of linear motor via fractional-order sliding mode

In this work, a novel discrete-time fractional-order sliding mode control (SMC) scheme is proposed, which guarantees the desired tracking performance of a linear motor control system. By using Euler’s discretization method, a discrete-time model is firstly established for the linear motor, which includes the nonlinear friction and the uncertainties. Considering the practicability of the engineering application, a new discrete-time fractional-order sliding surface is constructed by taking the Grünwald–Letnikov definition based fractional-order difference of the tracking error into account. Compared to the classical integer-order sliding surface, by the proposed fractional-order sliding surface in this work, a better performance can be achieved due to the memory effect of the fractional calculus. To drive the system trajectories to the predefined sliding surface in finite sampling steps, a novel equivalent control is then designed, which can adjust the switching control input adaptively. Meanwhile, the theoretical analysis for the tracking error of the linear motor system is presented, and the practical reachability of the sliding surface is validated by numerical simulations. Finally, the effectiveness of the proposed control strategy is verified by a group of tracking experiments on a linear motor platform.

Fractional Order Sliding Mode Based Direct Power Control of Grid-Connected DFIG

This paper proposes a fractional order sliding mode control (FOSMC) strategy for grid-connected doubly fed induction generator (DFIG). The novel approach aims to directly control the active/reactive power output of a DFIG-based wind energy conversion system with FOSMC, which has never been utilized in the control of DFIG. The fractional order sliding mode control with disturbance is introduced and the Caputo derivative is employed in constructing the sliding surface. Meanwhile, an enhanced exponential reaching law is utilized in order to mitigate the chattering phenomenon in the sliding stage and accelerate the reaching progress in the meantime. A comparative study is conducted subsequently to verify the superior performance of the proposed FOSMC control scheme over that of the conventional sliding mode control and the vector control approach. A steady state simulation is first conducted to tune the parameters of the FOSMC. A variable wind condition is subsequently simulated to compare the performance of those methods. After that, simulations with background harmonics of the grid voltage and parameter perturbation are considered. Ultimately, an experimental test is conducted to further validate the proposed method. The superior performance and the effectiveness of the FOSMC are fully validated with the above four comparative tests.

Adaptive fractional order sliding mode control for Boost converter in the Battery/Supercapacitor HESS.

In this paper, an adaptive fractional order sliding mode control (AFSMC) scheme is designed for the current tracking control of the Boost-type converter in a Battery/Supercapacitor hybrid energy storage system (HESS). In order to stabilize the current, the adaptation rules based on state-observer and Lyapunov function are being designed. A fractional order sliding surface function is defined based on the tracking current error and adaptive rules. Furthermore, through fractional order analysis, the stability of the fractional order control system is proven, and the value of the fractional order (λ) is being investigated. In addition, the effectiveness of the proposed AFSMC strategy is being verified by numerical simulations. The advantages of good transient response and robustness to uncertainty are being indicated by this design, when compared with a conventional integer order sliding mode control system.

An Adaptive-Fuzzy Fractional-Order Sliding Mode Controller Design for an Unmanned Vehicle

In this paper, speed and direction angle of a four wheel skid-steered mobile robot (4 WD SSMR) has been controlled via adaptive-fuzzy fractional-order sliding mode controller (AFFOSMC) under different speed and angle reference signals. The hybrid control method is designed to combine all advantages that controllers have such as flexibility realized by fractional order calculation, robustness to disturbances and parameters variations provided by sliding mode controller (SMC) as well as adaptation of G constant of SMC via fuzzy controller, simultaneously. Also, a fractional-order SMC is applied to the system for the same reference speed and angle references to show the effects of the changes and adaptation of G constant. Experimental results show that the AFFOSMC has better trajectory tracking performance than the FOSMC.DOI: http://dx.doi.org/10.5755/j01.eie.24.2.20630

Fractional sliding mode control of wind turbine for maximum power point tracking

This paper deals with a nonlinear control algorithm based on a sliding mode theory to reach the maximum power point tracking of a variable-speed wind energy conversion system. The proposed method allows us to combine the sliding mode and fractional-order theory. The fractional-order component of the control law is introduced by a sliding surface. In order to validate this controller, fractional and integer sliding modes are developed. The proposed fractional-order sliding mode control law is tested in a Simulink/Matlab environment. The simulation results show the effectiveness of the proposed scheme, suppression of the chattering phenomenon and robustness of the proposed controller compared to the integer sliding mode control law.