Fractional Order

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Yangquan Chen - One of the best experts on this subject based on the ideXlab platform.

  • Fractional Order proportional resonant controller
    Advances in Computing and Communications, 2018
    Co-Authors: Hadi Malek, Sara Dadras, Chun Yin, Yangquan Chen
    Abstract:

    In this paper, a Fractional Order synchronous frame controller and its equivalent model, stationary frame control named Fractional Order proportional resonant controller, have been introduced using Fractional Order theory. Compared conventional proportional resonant controller, the proposed controller troller not only ensures a zero steady-state error for AC control systems, but also provides more robustness against fluctuations of resonant (center) frequency. Having a wider bandwidth and higher gain in the neighborhood of resonant frequency enhance the capability of this controller to deal with resonant frequency variations and furthermore, improve the time domain transient performance of these systems. Analog and digital implementions of this novel controller have been discussed. In addition, stability of the proposed controller has been investigated. Finally, the proposed Fractional Order control strategy is successfullyapplied to a grid-connected system as current regulator.

  • Fractional-Order modeling of permanent magnet synchronous motor speed servo system
    Journal of Vibration and Control, 2015
    Co-Authors: Weijia Zheng, Yangquan Chen, Ying Luo, Youguo Pi
    Abstract:

    A Fractional-Order modeling approach for a permanent magnet synchronous motor speed servo system is proposed applying a method combining electromagnetic part modeling and mechanical part modeling. Based on the proposed Fractional-Order model and system identification scheme, system identification experiments are performed on the electromagnetic part and the mechanical part of the permanent magnet synchronous motor speed servo system, respectively. The Fractional-Order model parameters of these two parts are identified with these experimental results, and the Fractional-Order model of the permanent magnet synchronous motor speed servo system is integrated from these two parts. Simulations and experiments in open-loop and closed-loop are performed based on the obtained Fractional-Order model and integer-Order model. The advantage of the proposed Fractional-Order model for the permanent magnet synchronous motor speed servo system is demonstrated by the simulation and experimental results.

  • digital Fractional Order savitzky golay differentiator
    IEEE Transactions on Circuits and Systems Ii-express Briefs, 2011
    Co-Authors: Dali Chen, Yangquan Chen, Dingyu Xue
    Abstract:

    This brief proposes a design method for a digital Fractional Order Savitzky-Golay differentiator (DFOSGD), which generalizes the Savitzky-Golay filter from the integer Order to the Fractional Order for estimating the Fractional Order derivative of the contaminated signal. The proposed method calculates the moving window's weights using the polynomial least-squares method and the Riemann-Liouville Fractional Order derivative definition, and then computes the Fractional Order derivative of the given signal using the convolution between the weights and the signal, instead of the complex mathematical deduction. Hence, the computation time is greatly improved. Frequency-domain analysis reveals that the proposed differentiator is essentially a Fractional Order low-pass filter. Experiments demonstrate that the proposed DFOSGD can accurately estimate the Fractional Order derivatives of both noise-free signal and contaminated signal.

  • experimental study of Fractional Order proportional derivative controller synthesis for Fractional Order systems
    Mechatronics, 2011
    Co-Authors: Ying Luo, Yangquan Chen
    Abstract:

    Abstract In recent years, studies on real systems have revealed inherent Fractional Order dynamic behavior, and Fractional Order systems have attracted more and more attentions. It is intuitively true that these Fractional Order models require the corresponding Fractional Order controllers to achieve desired performance. In this paper, an experimental study of the Fractional Order proportional and derivative (FO-PD) controller systematic design is presented, to validate the control performance for the Fractional Order systems with generalized Fractional capacitor membrane model. The performance of the designed FO-PD controller is compared with both the integer Order and Fractional Order controllers which are designed based on the approximate integer Order system. This comparison results are presented both in the simulation and the hardware-in-the-loop experiment.

  • Fractional Order iterative learning control for Fractional Order linear systems
    Asian Journal of Control, 2011
    Co-Authors: Yan Li, Yangquan Chen
    Abstract:

    In this paper, we discuss in time domain the convergence of the iterative process for Fractional-Order systems. Fractional Order iterative learning updating schemes are considered. For the linear time invariant (LTI) system case, the convergence conditions of the Fractional-Order and integer-Order iterative learning schemes are proved to be equivalent for D=0. It has been proved by theory and verified by MATLAB/SIMULINK that the tracking speed is the fastest when the system and iterative learning scheme have the same Fractional Order. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Cheng Lu - One of the best experts on this subject based on the ideXlab platform.

  • Adaptive Fractional Order sliding mode controller with neural estimator
    Journal of the Franklin Institute, 2018
    Co-Authors: Juntao Fei, Cheng Lu
    Abstract:

    In this study, an adaptive Fractional Order sliding mode controller with a neural estimator is proposed for a class of systems with nonlinear disturbances. Compared with traditional sliding mode controller, the new proposed Fractional Order sliding mode controller contains a Fractional Order term in the sliding surface. The Fractional Order sliding surface is used in adaptive laws which are derived in the framework of Lyapunov stability theory. The bound of the disturbances is estimated by a radial basis function neural network to relax the requirement of disturbance bound. To investigate the effectiveness of the proposed adaptive neural Fractional Order sliding mode controller, the methodology is applied to a Z-axis Micro-Electro-Mechanical System (MEMS) gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed control system can improve tracking performance as well as parameter identification performance.

Ye Chen - One of the best experts on this subject based on the ideXlab platform.

  • synchronization for Fractional Order neural networks with full under actuation using Fractional Order sliding mode control
    International Journal of Machine Learning and Cybernetics, 2018
    Co-Authors: Heng Liu, Yongping Pan, Ye Chen
    Abstract:

    This paper considers synchronization between two Fractional-Order neural networks (FONNs). To handle the case of full/under-actuation, i.e. the dimension of the synchronization controller is equal to or less than that of the FONNs, a novel Fractional-Order integral sliding surface is designed, and the feasibility of the proposed approach is shown by solving two linear matrix inequalities. Then, based on the Fractional Lyapunov stability criterion, a Fractional-Order sliding mode controller equipped with Fractional-Order adaptation laws is constructed to guarantee the synchronization error converging to an arbitrary small region of the origin. The effectiveness of the proposed control method is verified by two simulation examples.

  • adaptive fuzzy backstepping control of Fractional Order nonlinear systems
    IEEE Transactions on Systems Man and Cybernetics, 2017
    Co-Authors: Heng Liu, Yongping Pan, Ye Chen
    Abstract:

    Backstepping control is effective for integer-Order nonlinear systems with triangular structures. Nevertheless, it is hard to be applied to Fractional-Order nonlinear systems as the Fractional-Order derivative of a compound function is very complicated. In this paper, we develop an adaptive fuzzy backstepping control method for a class of uncertain Fractional-Order nonlinear systems with unknown external disturbances. In each step, a complicated unknown nonlinear function produced by differentiating a compound function with a Fractional Order is approximated by a fuzzy logic system, and a virtual control law is designed based on the Fractional Lyapunov stability criterion. At the last step, an adaptive fuzzy controller that ensures convergence of the tracking error is constructed. The effectiveness of the proposed method has been verified by two simulation examples.

Jinde Cao - One of the best experts on this subject based on the ideXlab platform.

Juntao Fei - One of the best experts on this subject based on the ideXlab platform.

  • Adaptive Fractional Order sliding mode controller with neural estimator
    Journal of the Franklin Institute, 2018
    Co-Authors: Juntao Fei, Cheng Lu
    Abstract:

    In this study, an adaptive Fractional Order sliding mode controller with a neural estimator is proposed for a class of systems with nonlinear disturbances. Compared with traditional sliding mode controller, the new proposed Fractional Order sliding mode controller contains a Fractional Order term in the sliding surface. The Fractional Order sliding surface is used in adaptive laws which are derived in the framework of Lyapunov stability theory. The bound of the disturbances is estimated by a radial basis function neural network to relax the requirement of disturbance bound. To investigate the effectiveness of the proposed adaptive neural Fractional Order sliding mode controller, the methodology is applied to a Z-axis Micro-Electro-Mechanical System (MEMS) gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed control system can improve tracking performance as well as parameter identification performance.