Fractional Order Sliding Mode Research Articles

VIBRATION SUPPRESSION OF A ROTATING HUB-BEAM SYSTEM WITH A FLEXIBLE SUPPORT USING FRACTIONAL ORDER SLIDING MODE CONTROL

In this paper, a rotating hub-blade system with a flexible support which represents a wide range of industrial applications is considered for modelling and control. The flexible blade is assumed as an Euler–Bernoulli beam. In addition, three piezoelectric layers are mounted on the blade as sensors and actuators to reduce vibrations of the blade attached to the hub. For modelling, the Lagrange’s method is utilized to obtain the equations of motion of the system. In order to simultaneously suppress vibrations of the system and track the desired angular position of the hub, designing an appropriate controller is carried out. In this regard, a fractional order sliding mode (FOSM) controller is proposed to fulfil these objectives and then the comparison between FOSM controller and the classical sliding mode controller is presented in order to investigate the effectiveness of the proposed controller. The simulation results indicate the superior performance of the fractional order controller in compare to the integer order sliding.

Optimized Fractional Order Sliding Mode Controller for Water Level in Irrigation Canal Pool

Water level regulation of irrigation canals represents a major challenge for control systems design. Those systems exhibit large dynamic variations in their operating conditions. To overcome this fact, robust controllers should be applied. The sliding mode control paradigm reveals this ability which make it a suitable candidate to be incorporated in the irrigation canal control loop. Moreover, its flexibility can be further potentiated by extending the ordinary formulation by adding fractional-order integro-differential operations. In this work, fractional-order sliding mode control is applied to the above mentioned problem. This application represents a novelty and, according to the obtained simulation results, leads to an accurate and proper performance when compared to its integer-order counterpart and to a fractional proportional-integrative controller, recently proposed for this problem.

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.

Robust fractional order sliding mode control of doubly-fed induction generator (DFIG)-based wind turbines

Wind power plants have nonlinear dynamics and contain many uncertainties such as unknown nonlinear disturbances and parameter uncertainties. Thus, it is a difficult task to design a robust reliable controller for this system. This paper proposes a novel robust fractional-order sliding mode (FOSM) controller for maximum power point tracking (MPPT) control of doubly fed induction generator (DFIG)-based wind energy conversion system. In order to enhance the robustness of the control system, uncertainties and disturbances are estimated using a fractional order uncertainty estimator. In the proposed method a continuous control strategy is developed to achieve the chattering free fractional order sliding-mode control, and also no knowledge of the uncertainties and disturbances or their bound is assumed. The boundedness and convergence properties of the closed-loop signals are proven using Lyapunov׳s stability theory. Simulation results in the presence of various uncertainties were carried out to evaluate the effectiveness and robustness of the proposed control scheme.

Fuzzy Fractional Order Sliding Mode Control for Automatic Clutch of Vehicle AMT

The automatic clutch driving system of vehicle automated manual transmission (AMT) is a typical nonlinear system. A fast and accurate position control is difficult to achieve because of the nonlinearity of the load changes caused by the clutch diaphragm spring, the cushion spring, and other nonlinear components and because of the uncertainty of the load changes caused by the cushion spring deformation in the clutch engagement process at varying temperatures on the friction surface. In this paper, based on the theory of fractional calculus and traditional sliding mode control, the method of fuzzy fractional order sliding mode control (FFOSMC) is proposed for clutch control. By selecting the fractional order sliding surface, the laws of control are designed; and self-tuning of the switch gain is realized with the fuzzy controller. Theoretical analysis and numerical simulation revealed that compared with the traditional fuzzy integer order sliding mode controller, FFOSMC achieves better dynamic performance in position control and better robustness against load disturbance and other uncertain factors.

Finite-time Adaptive Synchronization of Two Different Fractional-order Gyroscope Systems with Dead-zone Nonlinear Inputs

This paper proposes a novel fractional-order Sliding Mode Control (SMC) technique to synchronize two difierent fractional-order gyroscope systems. We assumed that all parameters of both master and slave system are fully unknown in advance. Moreover, the efiects of dead-zone nonlinear inputs are taken into account. In order to deal with these unknown parameters, some adaption laws are given. On the basis of SMC technique and flnite-time theory, a robust controller is designed to synchronize two fractional-order gyroscope systems in flnite time. Finally, simulation results are presented to verify the efiectiveness and applicability of the proposed flnite-time SMC scheme.

Direct Torque Control of PMSM Based on Fractional Order Sliding Mode Variable Structure and Experiment Research

A direct torque control method based on fractional order sliding mode variable structure (DTC-FOSMVS) was proposed for the speed control of a permanent magnet synchronous motor (PMSM). The proposed method in which the space vector pulse width modulation (SVPWM) with fixed switch frequency is applied, reduces the torque and flux ripple, and improves the speed control performance. In order to improve the energy efficiency and reduce the demagnetization effect, the DTC-FOSMVS method with dynamic flux reference was designed. The stability of the control method is proved by Lyapunov theory. The performance of the proposed method is verified through experiment which is based on hardware in loop and Simulink/QuaRC real time control software. The experiment results show the robustness and effectiveness of the proposed method.

Development of a Novel Fractional Order Sliding Mode Controller for a Gun Control System

To solve the nonlinearity phenomenon of a Gun Control System (GCS), a novel Fractional order Sliding Mode Control (FoSMC) strategy is proposed in this study. By inducing the fractional order calculus, a Fractional Order PID (FOPID) type sliding surface is especially designed and consequently an equivalent control discipline with fractional order dynamics is induced. The saturation function is employed as the switch function. By numerical simulation, the dynamic characteristics of the FoSMC based control system are analyzed and compared with Conventional Sliding Mode Control (CSMC) system. The results demonstrate that the FoSMC system could reach up to the equilibrium state more smoothly, which shall significantly suppress the inherent chatter effects. Besides, the FoSMC based gun control system is of high response rate, better positioning accuracy and high robustness, which is suitable for fast, smooth and accurate adjustments of the gun.

A Sufficient Condition for Checking the Attractiveness of a Sliding Manifold in Fractional Order Sliding Mode Control

AbstractStability issues of fractional order sliding mode control laws are analyzed in this paper. For differentiation orders less than unity, it is shown that a stable reaching law in the fractional order case corresponds to a stable reaching law in the integer order case. The contribution of the current study is to explain the stability of the closed loop by the use of the Caputo and Riemann‐Liouville definitions of fractional order differentiation.Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society