Adaptive Fractional-order Sliding Mode Control Research Articles

Control of SMES systems in distribution networks with renewable energy integration: A perturbation estimation approach

Electrical energy storage system (EESS) plays a crucial role to handle the intermittency and randomness of renewable energy, such that the power reliability can be significantly enhanced. This paper attempts to design an adaptive fractional-order sliding-mode control (AFOSMC) approach for a typical EESS technology, e.g., superconducting magnetic energy storage (SMES) systems, to improve its dynamical responses against varirous operation conditions. At first, a sliding-mode state and perturbation observer (SMSPO) is applied to estimate the combined effect of unmodelled dynamics, parameter uncertainties, and external disturbances of SMES systems. Then, a fractional-order sliding-mode control (FOSMC) is utilized to completely compensate the perturbation estimat, such that a noticeable robustness can be achieved. Moreover, only the dq-axis currents need to be measured while the perturbation estimate replaces its upper bound, thus AFOSMC be easily achieved with appropriate control costs. For the purpose of validating its control performance, a distribution network involving SMES system with renewable energy penetration is studied. The control performance of conventional proportional-integral-derivative (PID) control, interconnection and damping assignment passivity-based control (IDA-PBC), sliding-mode control (SMC), and fractional-order sliding-mode control (FOSMC) is compared to that of AFOSMC under three scenarios. Simulation results show that AFOSMC can greatly outperform other approaches in both tracking speed and overall costs, e.g., its active power error is only 63.55%, 83.44%, 69.60%, and 76.67% of that of PID control, IDA-PBC, SMC, and FOSMC under reactive and active power supply, while the required control costs is only 76.69%, 91.28%, 83.50, and 86.76% to the above three controllers. Finally, a hardware-in-the-loop (HIL) test based on dSpace is implemented to verify its practicability under various scenarios.

Active fault-tolerant synchronisation of fractional-order chaotic gyroscope system

In this paper, a fractional-order adaptive sliding mode controller is designed to synchronise a fractional-order chaotic gyroscope with fractional dynamics. To this end, the error dynamic is defined first and then the adaptive sliding mode synchroniser is designed using through defining a proper sliding surface and estimating uncertainty parameters of the master and slave system and its stability is proved using the Lyapunov theorem. The important point is the efficiency of the controller against input disturbance and uncertainty. Finally, the proposed controller is simulated in MATLAB and the results indicate that the introduced fractional-order chaotic system using an adaptive sliding mode controller is able to synchronise the fractional-order chaotic gyroscope.

Adaptive fractional-order blood glucose regulator based on high-order sliding mode observer.

Type I diabetes is described by the destruction of the insulin-producing beta-cells in the pancreas. Hence, exogenous insulin administration is necessary for Type I diabetes patients. In this study, to estimate the states that are not directly available from the Bergman minimal model a high-order sliding mode observer is proposed. Then fractional calculus is combined with sliding mode control (SMC) for blood glucose regulation to create more robustness performance and make more degree of freedom and flexibility for the proposed method. Then an adaptive fractional-order SMC is proposed. The adaptive SMC protect controller against disturbance and uncertainties while the fractional calculus provides robust performance. Numerical simulation verifies that the proposed controllers have better performance in the presence of disturbance and uncertainties without chattering.

Fractional-order two-component oscillator: stability and network synchronization using a reduced number of control signals

In this paper, a fractional-order version of a chaotic circuit made simply of two non-idealized components operating at high frequency is presented. The fractional-order version of the Hopf bifurcation is found when the bias voltage source and the fractional-order of the system increase. Using Adams–Bashforth–Moulton predictor–corrector scheme, dynamic behaviors are displayed in two complementary types of stability diagrams, namely the two-parameter Lyapunov exponents and the isospike diagrams. The latest being a more fruitful type of stability diagrams based on counting the number of spikes contained in one period of the periodic oscillations. These two complementary types of stability diagrams are reported for the first time in the fractional-order dynamical systems. Furthermore, a new fractional-order adaptive sliding mode controller using a reduced number of control signals was built for the stabilization of a fractional-order complex dynamical network. Two examples are shown on a fractional-order complex dynamical network where the nodes are made of fractional-order two-component circuits. Firstly, we consider an ideal channel, and secondly, a non ideal one. In each case, increasing of the coupling strength leads to the phase transition in the fractional-order complex network.Graphical abstract

Two Novel Approaches of NTSMC and ANTSMC Synchronization for Smart Grid Chaotic Systems

The presence of uncertainties and external disturbances is one of the unavoidable problems with various practical systems which might be unavailable in real-time. Sliding Mode Control (SMC) is one of the effective robust control methods to deal with these uncertainties and external disturbances. In this paper, two novel controllers are designed by using Nonsingular Terminal SMC (NTSMC) and Adaptive Nonsingular Terminal SMC (ANTSMC) methods for synchronization of dual smart grid chaotic systems with various uncertainties and external disturbances. Indeed, both adaptive and non-adaptive controllers based on NTSMC are proposed to provide two alternatives which can adjust by changing operating conditions and dynamics. The concept of SMC method guarantees controller robustness against various uncertainties and external disturbances. Elimination of the undesirable chattering phenomenon is addressed in this study which is one of the common deficiencies with conventional SMC method. Additionally, finite time concept is used to speed up the convergence rate. Finite time stability proof is performed by using Lyapunov stability theory. The numerical simulation is carried out in Simulink/MATLAB to reveal the validity of the proposed controllers for the smart grid chaotic system. A comprehensive comparison is made by performing simulation for the Fractional Order Adaptive Sliding Mode Control (FOASMC) controller and defining three performance criteria, among the proposed controllers in this study and FOASMC controller.

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.

Synchronization of the Chaotic Fractional-Order Genesio–Tesi Systems Using the Adaptive Sliding Mode Fractional-Order Controller

This paper introduces an adaptive fractional-order sliding mode controller for synchronization of two chaotic Genesio–Tesi systems with fractional dynamics. For this purpose, first the error dynamics is defined; then the adaptive sliding mode synchronization controller is designed through defining suitable sliding surface and estimating uncertainty parameters and stability of the control system is verified using related theorems. Robustness against input uncertainty and disturbance is considered as a primary design objective. Simulation results using MATLAB show that the proposed adaptive fractional-order sliding mode controller is able to synchronize the mentioned chaotic system with acceptable performance.

FPGA implementation of adaptive sliding mode control and genetically optimized PID control for fractional-order induction motor system with uncertain load

In this paper, we investigate the control of 4-D nonautonomous fractional-order uncertain model of a PI speed-regulated current-driven induction motor (FOIM) using a fractional-order adaptive sliding mode controller (FOASMC). First, we derive a dimensionless fractional-order model of the induction motor from the well-known integer -model of the induction motor. Various dynamic properties of the fractional-order induction motor, such as stability of the equilibrium points, Lyapunov exponents, bifurcation, and bicoherence, are investigated. An adaptive controller is derived to suppress the chaotic oscillations of the fractional-order model of the induction motor. Numerical simulations of the adaptive chaos suppression methodology are depicted for the fractional-order uncertain model of the induction motor to validate the analytical results of this work. A genetically optimized fractional-order PID (FOPID) controller is also derived to stabilize the states of the FOIM system. FPGA implementation of the proposed FOASMC is also presented to show that the proposed controller is hardware realizable.

Dynamic analysis and fractional-order adaptive sliding mode control for a novel fractional-order ferroresonance system**Project supported by the National Natural Science Foundation of China (Grant No. 51507134) and the Science Fund from the Education Department of Shaanxi Province, China (Grant No. 15JK1537).

Ferroresonance is a complex nonlinear electrotechnical phenomenon, which can result in thermal and electrical stresses on the electric power system equipments due to the over voltages and over currents it generates. The prediction or determination of ferroresonance depends mainly on the accuracy of the model used. Fractional-order models are more accurate than the integer-order models. In this paper, a fractional-order ferroresonance model is proposed. The influence of the order on the dynamic behaviors of this fractional-order system under different parameters n and F is investigated. Compared with the integral-order ferroresonance system, small change of the order not only affects the dynamic behavior of the system, but also significantly affects the harmonic components of the system. Then the fractional-order ferroresonance system is implemented by nonlinear circuit emulator. Finally, a fractional-order adaptive sliding mode control (FASMC) method is used to eliminate the abnormal operation state of power system. Since the introduction of the fractional-order sliding mode surface and the adaptive factor, the robustness and disturbance rejection of the controlled system are enhanced. Numerical simulation results demonstrate that the proposed FASMC controller works well for suppression of ferroresonance over voltage.

Chaos Control in Fractional Order Smart Grid with Adaptive Sliding Mode Control and Genetically Optimized PID Control and Its FPGA Implementation

We investigate a specific smart grid system and its nonlinear properties. Lyapunov exponents are derived to prove the existence of chaos and bifurcation and bicoherence contours are investigated to show the parameter dependence and existence of quadratic nonlinearities, respectively. A fractional order model of the smart grid system (FOSG) is then derived and bifurcation of the FOSG system with variation in the commensurate fractional order of the system is investigated to show that largest Lyapunov exponent of the system exists in fractional order. Hence we proposed two different control methods to suppress the chaotic oscillations. In the first method we derive fractional order adaptive sliding mode control (FOASMC) algorithm to control chaotic oscillations and in the second method we used genetically optimized fractional order PID controllers (GAFOPID) for chaos control. Numerical simulations are conducted to show the effectiveness of the controllers and also to prove that GAFOPID controllers are more effective than FOASMC controllers for fractional order systems. The GAFOPID controllers are then realized in FPGA to show that the proposed methodology is hardware realizable.

Stabilization of the Two-Axis Gimbal System Based on an Adaptive Fractional-Order Sliding-Mode Controller

ABSTRACTThis paper introduces an adaptive fractional-order sliding-mode controller for stabilization of a two-axis gimbal platform in the presence of the torque disturbance effects. To tend the angular velocities of the inner gimbal in the elevation and azimuth axes to zero, an adaptive fractional-order sliding-mode approach is utilized. To achieve this goal, fractional-order sliding surfaces in both azimuth and elevation axes and the corresponding adaptive controllers with adjustable parameters tuned according to Lyapunov-based adaptation mechanisms are employed. The optimal value of the fractional order is obtained through an integral square error performance index minimization. The moments products uncertainties are incorporated in the design procedure. The numerical simulations demonstrate that the proposed control approach is robust against the moments products variations.

Stabilisation of commensurate fractional‐order polytopic non‐linear differential inclusion subject to input non‐linearity and unknown disturbances

In this study, a fractional-order adaptive-sliding mode control (SMC) scheme is proposed to stabilise commensurate fractional-order polytopic non-linear differential inclusion systems containing sector and dead-zone nonlinearities in the control inputs and unknown bounded disturbances. The suggested control method is composed of fractional-order sliding surfaces, adaptive-SMC inputs and adaptation laws for unknown bounds of disturbances. The Lyapunov stability theorem is used to prove the stability of the closed-loop system. A practical system and two numerical examples are simulated to show the effectiveness and performance of the proposed control technique.