The Experts below are selected from a list of 16101 Experts worldwide ranked by ideXlab platform
Yangquan Chen - One of the best experts on this subject based on the ideXlab platform.
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frequency domain modelling and control of Fractional Order System for permanent magnet synchronous motor velocity servo System
Iet Control Theory and Applications, 2016Co-Authors: Wei Yu, Yangquan Chen, Youguo PiAbstract:This study presents Fractional-Order System modelling and control for a permanent magnet synchronous motor (PMSM) velocity servo System. Fractional-Order model of the PMSM velocity servo System is obtained theoretically for an improved modelling precision. To identify the parameters of the proposed Fractional-Order model, an enhancement of the classic Levy identification method with weights is applied. In a real-time PMSM velocity servo plant, the Fractional-Order model is identified according to the experimental tests using the presented algorithm. The fact that the Fractional model is more accurate than traditional integer-Order model is substantiated using by the mean square error performance index. Two H ∞ stabilising output feedback controllers are designed for velocity servo using a simple scheme according to the identified Fractional-Order model and the traditional integer Order one, respectively. The experimental test performance using these two designed H ∞ controllers is compared to demonstrate the advantage of the proposed Fractional-Order model of the PMSM velocity System.
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Quantitative Analysis of Singularities for Fractional Order Systems
Volume 9: 2015 ASME IEEE International Conference on Mechatronic and Embedded Systems and Applications, 2015Co-Authors: Yangquan ChenAbstract:The singularity is an intrinsic property for various Fractional Order Systems. This paper focuses on the time domain analysis of typical “non-proper” Fractional Order transfer functions, which plays the crucial role in the implementation, stability and control of Fractional Order Systems. To this end, the Fractional Order System is converted into a weak singularity integro-differential equation, where the non-proper property can be clearly presented. A practical strategy is shown to find out the poles in the first Riemann plane, which is especially applicable to small commensurate Order problems. The distributed Order and Order sensitivity problems are discussed as well. A number of examples are illustrated by using some reliable Fractional Order numerical methods.Copyright © 2015 by ASME
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Stability analysis of Fractional-Order Systems with double noncommensurate Orders for matrix case
Fractional Calculus and Applied Analysis, 2011Co-Authors: Zhuang Jiao, Yangquan ChenAbstract:Bounded-input bounded-output stability issues for Fractional-Order linear time invariant (LTI) System with double noncommensurate Orders for the matrix case have been established in this paper. Sufficient and necessary condition of stability is given, and a simple algorithm to test the stability for this kind of Fractional-Order Systems is presented. Based on the numerical inverse Laplace transform technique, time-domain responses for Fractional-Order System with double noncommensurate Orders are shown in numerical examples to illustrate the proposed results.
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Fractional Order proportional and derivative controller synthesis for a class of Fractional Order Systems tuning rule and hardware in the loop experiment
Conference on Decision and Control, 2009Co-Authors: Ying Luo, Yangquan ChenAbstract:In recent years, Fractional Order Systems have attracted more and more attention in various field, studies on real Systems have revealed inherent Fractional Order dynamic behavior. It is intuitively true that these Fractional Order models require the corresponding Fractional Order controllers to achieve excellent performance. In this paper, a Fractional Order PD03BC; controller is designed Systematically, to control a class of Fractional Order Systems, the performance of the proposed PD03BC; controller designed for the Fractional Order System is compared with both the integer Order and Fractional Order controllers which are designed for the approximate integer Order System in the simulation and the hardware-in-the-loop experiment respectively.
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robust stability test of a class of linear time invariant interval Fractional Order System using lyapunov inequality
Applied Mathematics and Computation, 2007Co-Authors: Yangquan Chen, Igor PodlubnyAbstract:This paper provides a new analytical robust stability checking method of Fractional-Order linear time invariant interval uncertain System. This paper continues the authors’ previous work [YangQuan Chen, Hyo-Sung Ahn, I. Podlubny, Robust stability check of Fractional-Order linear time invariant Systems with interval uncertainties, in: Proceedings of the IEEE Conference on Mechatronics and Automation, Niagara Falls, Canada, July, 2005, pp. 210–215] where matrix perturbation theory was used. For the new robust stability checking, Lyapunov inequality is utilized for finding the maximum eigenvalue of a Hermitian matrix. Through numerical examples, the usefulness and the effectiveness of the newly proposed method are verified.
Xiaozhong Liao - One of the best experts on this subject based on the ideXlab platform.
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Robust stability criterion of Fractional-Order functions for interval Fractional-Order Systems
IET Control Theory & Applications, 2013Co-Authors: Zhe Gao, Xiaozhong LiaoAbstract:This study presents a sufficient and necessary stability condition for the stability of interval Fractional-Order Systems. An effective constructive method of the value set on the disturbance function of an interval Fractional-Order System is investigated to reduce the burden of computations for the redundant vertices and edges. Based on the zero exclusion principle, a test function and terminal conditions are proposed to verify the stability of interval Fractional-Order Systems. Finally, a numerical example is given to illustrate the effectiveness of this proposed stability theorem.
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Rational approximation for Fractional-Order System by particle swarm optimization
Nonlinear Dynamics, 2011Co-Authors: Zhe Gao, Xiaozhong LiaoAbstract:In this paper, a rational approximation me-thod is proposed for the Fractional-Order System using the particle swarm optimization (PSO). Firstly, the approximation method for the Fractional-Order operator is studied, because a Fractional-Order System consists of many Fractional-Order operators. The coefficients of the transfer function are calculated using PSO with a fitness function under the continued fraction expansion (CFE) framework in the frequency domain. The average velocity of the particle swarm is defined to reflect the real state of particle swarm. To improve the global optimization and achieve a more satisfactory fitting result, comparing with the linear PSO, the chaotic optimization is combined with PSO. The numerical examples of Fractional-Order Systems demonstrate the effectiveness of this method.
Zhe Gao - One of the best experts on this subject based on the ideXlab platform.
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Robust stability criterion of Fractional-Order functions for interval Fractional-Order Systems
IET Control Theory & Applications, 2013Co-Authors: Zhe Gao, Xiaozhong LiaoAbstract:This study presents a sufficient and necessary stability condition for the stability of interval Fractional-Order Systems. An effective constructive method of the value set on the disturbance function of an interval Fractional-Order System is investigated to reduce the burden of computations for the redundant vertices and edges. Based on the zero exclusion principle, a test function and terminal conditions are proposed to verify the stability of interval Fractional-Order Systems. Finally, a numerical example is given to illustrate the effectiveness of this proposed stability theorem.
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Rational approximation for Fractional-Order System by particle swarm optimization
Nonlinear Dynamics, 2011Co-Authors: Zhe Gao, Xiaozhong LiaoAbstract:In this paper, a rational approximation me-thod is proposed for the Fractional-Order System using the particle swarm optimization (PSO). Firstly, the approximation method for the Fractional-Order operator is studied, because a Fractional-Order System consists of many Fractional-Order operators. The coefficients of the transfer function are calculated using PSO with a fitness function under the continued fraction expansion (CFE) framework in the frequency domain. The average velocity of the particle swarm is defined to reflect the real state of particle swarm. To improve the global optimization and achieve a more satisfactory fitting result, comparing with the linear PSO, the chaotic optimization is combined with PSO. The numerical examples of Fractional-Order Systems demonstrate the effectiveness of this method.
Yong Wang - One of the best experts on this subject based on the ideXlab platform.
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Time-domain response of nabla discrete Fractional Order Systems
arXiv: Dynamical Systems, 2018Co-Authors: Songsong Cheng, Yong WangAbstract:This paper investigates the time--domain response of nabla discrete Fractional Order Systems by exploring several useful properties of the nabla discrete Laplace transform and the discrete Mittag--Leffler function. In particular, we establish two fundamental properties of a nabla discrete Fractional Order System with nonzero initial instant: i) the existence and uniqueness of the System time--domain response; and ii) the dynamic behavior of the zero input response. Finally, one numerical example is provided to show the validity of the theoretical results.
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Stability for nonlinear Fractional Order Systems: an indirect approach
Nonlinear Dynamics, 2017Co-Authors: Yuquan Chen, Yiheng Wei, Xi Zhou, Yong WangAbstract:In this paper, we first verify that Fractional Order Systems using Caputo’s or Riemann–Liouville’s derivative can be represented by the continuous frequency distributed model with initial value carefully allocated. Then, the relation of the stability between the Fractional Order System and its corresponding integer Order System is discussed and it is proven that stability of integer Order System implies the stability of its corresponding Fractional Order System under some mild conditions. Moreover, we extend the stability theorems to the finite-dimensional case since Fractional Order Systems are always implemented by approximation. Some illustrative examples are finally provided to show the usage and effectiveness of the proposed stability theorems.
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Robust analysis and synthesis for a class of Fractional Order Systems with coupling uncertainties
International Journal of Control Automation and Systems, 2015Co-Authors: Shu Liang, Cheng Peng, Zeng Liao, Yong WangAbstract:A class of uncertain Fractional Order Systems is concerned where intervals of System matrices parameters are affected by the Fractional Order. Moreover, the Order is also uncertain and belongs to an interval containing the integer one. This kind of System models are reasonable results of Fractional Order System identifications. In this note, we derive the robust stability analysis and synthesis of such uncertain Fractional Order Systems. Two numerical examples are presented to illustrate the effectiveness and potential of the developed theoretical results.
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CDC - Positive real lemmas for Fractional Order Systems
53rd IEEE Conference on Decision and Control, 2014Co-Authors: Xi Zhou, Yiheng Wei, Shu Liang, Yong WangAbstract:This paper is concerned with the positive realness of Fractional Order linear time-invariant Systems with the commensurate Order 0 < α < 2. Sufficient and necessary condition for a Fractional Order System to be positive real is derived in terms of linear matrix inequalities. Furthermore, the sufficient condition for positive real Fractional Order Systems with pseudo state feedback is investigated. Numerical examples are given to illustrate the effectiveness of the method proposed in this paper.
Xue Dingy - One of the best experts on this subject based on the ideXlab platform.
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Fractional Order pid controller design for Fractional Order System
Control theory & applications, 2007Co-Authors: Xue DingyAbstract:Fractional Order calculus model could model various real materials more adequately than integer Order ones and provides an excellent tool for the description of dynamical processes.These Fractional Order models need the corre-sponding Fractional Order controllers to be proposed.A Fractional Order PID controller design method is proposed for the Fractional Order System model in this paper.An example is also given to demonstrate the better response of Fractional Order PID controller in comparison with the classical PID controller.
