Fractional-Order Adaptive Sliding Mode Control for Fractional-Order Buck-Boost Converters

Xie Lingling,Liu Zhipei,Ning Kangzhi,Qin Rui 대한전기학회 2022 Journal of Electrical Engineering & Technology Vol.17 No.3

In previous studies, the combination of fractional calculus (FC) and sliding-mode control (SMC) has been gaining more and more interest due to fusion characteristics of SMC and FC. But most study integer-order buck converters, and few study control strategies of fractional-order converters. In this paper, the sliding mode controller and fractional adaptive sliding mode controller for fractional-order buck-boost converters are proposed. An affi ne nonlinear system model of the fractionalorder buck-boost converter is built. Based on the diff erential geometry theory, the exact feedback linearization is performed on the affi ne nonlinear model of the fractional-order buck-boost converter. On this basis, a fractional adaptive sliding mode controller is designed by selecting a linear sliding surface and adaptive control law. The stability of the fractional controller is proved by the Mittag–Leffl er stability theorem. The simulation results show that the fractional adaptive sliding mode control has good dynamic response performance and small steady-stage error regulating characteristics. Compared with traditional sliding mode control and PI λ control, the control method demonstrates stronger robustness under various disturbances.

분수-체계 외란 관측기와 분수-체계 슬라이딩 모드 제어기를 적용한 Euler-Lagrange 시스템에 대한 위치 제어

한성익 제어·로봇·시스템학회 2020 제어·로봇·시스템학회 논문지 Vol.26 No.9

. A fractional-order based sliding mode controller and disturbance observer were developed for enhanced positioning performance of Euler Lagrange systems. First, an issue of a fractional-order sliding control was addressed to obtain rapid convergence compared to the conventional standard and terminal sliding mode controls. Next, a fractional-order disturbance observer based on the fractional-order sliding surface was developed to obtain more enhanced estimation performance over the integer-order based disturbance observer. In order to demonstrate the superior properties of the proposed strategies, simulations were performed for a three-link articulated manipulator.

Extended Kalman Filters for Continuous-time Nonlinear Fractionalorder Systems Involving Correlated and Uncorrelated Process and Measurement Noises

Fanghui Liu,Zhe Gao,Chao Yang,Ruicheng Ma 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.9

In order to improve the estimation accuracy of the state information and save the computing time for fractional-order systems containing correlated and uncorrelated process and measurement noises, this paper investigates fractional-order extended Kalman filters for continuous-time nonlinear fractional-order systems using the method of fractional-order average derivative. Compared with Grünwald-Letnikov difference, the estimation accuracy is improved via the fractional-order average derivative method. Meanwhile, the computing time in the stateestimation is saved. To deal with the correlated and uncorrelated process and measurement noises, two kinds of extended Kalman filters for nonlinear fractional-order systems are given. Finally, the effectiveness of the proposed fractional-order extended Kalman filters based on fractional-order average derivative is validated by two examples.

A Modeling and Analysis Method for CCM Fractional Order Buck‑Boost Converter by Using R–L Fractional Defnition

Lingling Xie,Zhipei Liu,Bo Zhang 대한전기학회 2020 Journal of Electrical Engineering & Technology Vol.15 No.4

Fractional defnition is important for the application of fractional-order theory in electrical engineering, and fractional-order theory directly afects the accuracy of the model and the operating characteristics of the power converter. Most researchers used the fractional defnition of Caputo to study fractional order power converter. However, it is found that the model based on Caputo fractional defnition is inconsistent with the actual situation. A novel modeling and analysis method for the fractional buck–boost converter is proposed in this paper. Firstly, the fractional converter model operating in continuous conduction mode (CCM) is established and the DC analysis is completed by using Riemann–Liouville (R–L) fractional defnition. The R–L fractional defnition is nearly 1.1% more accurate than the Caputo defnition in the DC analysis. Secondly, the infuence of the capacitor and inductor orders on the converter is performed. The results show that the capacitor and inductor orders have great efect on the DC components of the state variable and the steady-state characteristics of the fractional order buckboost converter. Finally, simulation and experiment results are provided that the validity of theoretical analysis.

A Novel Stability Criteria of a Class Nonlinear Fractional-order HIV-1 System with Multiple Delay

Zhe Zhang,Jing Zhang,Fanyong Cheng,Feng Liu 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.9

This paper mainly deduces a new stability criteria of the fractional-order HIV-1 system with delay on the basis of Wirtinger inequality, fractional-order Lyapunov method and integral mean value theorem. The Wirtinger inequality is rarely applied to stability analysis of fractional-order system. Nevertheless, this paper extends thegeneral form of the Lyapunov-krasovskii function to a novel fractional expression form by applying definitionof Caputo fractional derivative. Via the the integral mean value theorem, fractional-order Lyapunov method and Wirtinger inequality, the novel stability criteria is deduced. It is the integral mean value theorem that reduces the conservatism of the stability criteria. The simulation results show that the proposed criteria can satisfy different fractional-order operators.In addition, it can not only solve the stability problem of fractional-order HIV-1 system with the constant time delay, but also of the fractional-order HIV-1 system with time-varying time delay. Thus, the new stability criteria has generality and universality. So as to verify our theoretical results, many numerical simulations are provided.

Laguerre based design of fractional-order PD controller

Mohammad. Tabatabaei,Romina. Salehi 제어로봇시스템학회 2016 제어로봇시스템학회 국제학술대회 논문집 Vol.2016 No.10

In this paper, a fractional-order PD controller based on Laguerre orthonormal functions is constructed for commensurate fractional order systems. The main idea is to expand the transfer functions of the fractional order plant, the desired open loop gain, and the fractional order PD controller in terms of their Laguerre basis functions. The fractional order PD controller coefficients are obtained by matching the first two coefficients of the open loop gain Laguerre series with the desired one. The optimum value of the Laguerre basis function pole is appropriately selected to minimize an integral square error performance index. The numerical simulations demonstrate the performance of the proposed Laguerre based fractional order PD controller, as well.

Adaptive Fractional-order Unscented Kalman Filters for Nonlinear Fractional-order Systems

Yue Miao,Zhe Gao,Chuang Yang 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.4

In this paper, the Gruwald-Letnikov method is used to discretize a continuous-time nonlinear fractional-order system with unknown parameters and fractional-order, and an adaptive fractional-order unscented Kalman filter is proposed. Taking the unknown fractional-order and parameters as the augmented states, the augmented state equation is established to solve the problem on the unknown fractional-order and parameters. In order to improve the accuracy of state estimation, an adaptive fractional-order unscented Kalman filter is designed to deal with the nonlinear functions by using the unscented transformation. Meanwhile, the problem on state estimation for the estimated system with a non-differentiable nonlinear functions is also solved. Finally, the effectiveness of the proposed algorithm is verified by two simulation examples.

Kalman Filters for Continuous-time Fractional-order Systems Involving Fractional-order Colored Noises Using Tustin Generating Function

Zhe Gao 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.3

This study presents fractional-order Kalman filers for linear fractional-order systems with colored noises using Tustin generating function. A continuous-time fractional-order system with the fractional-order colored process noise is discretized by Tustin generating function. The augmented vector consists of the state and the colored noise is offered to construct an augmented system based on the discretized state equation of a fractional-order system and the colored process noise. The Tustin fractional-order Kalman filter is designed based on the augmented system to obtain the state estimation, effectively. Besides, the colored noise involved in the measurement of a continuous-time fractional-order system is also discussed, and the corresponding Tustin fractional-order Kalman filter is provided in this study. Two illustrative examples are given to verify the effectiveness of Tustin fractionalorder Kalman filters for the colored process and measurement noises.

Mechanical Resonance Suppression in Servo System Based on The Fractional Order Low-pass Filter

Ming Yang,Yongjian Fu,Xin Lv,Dianguo Xu 전력전자학회 2015 ICPE(ISPE)논문집 Vol.2015 No.6

The conventional filter method could effectively suppress resonance in servo system without backlash. But when the system contains backlash, the methods may fail. In this paper, a fractional order low-pass filter substitutes the integer order low-pass in a dual-inertia servo system with backlash to solve the problem. Fractional algorithm provides greater flexibility for robust control design, because it makes the order of the low-pass filter from integer domain to real-number domain. Fractional order low-pass filter can achieve a better tradeoff between robustness and resonance suppression by selecting the appropriate order. For implementation of the fractional order, Oustaloup recursive approximation method is introduced. Experimental results show that fractional-order low-pass filter can improve robustness while suppressing system resonance.

Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments

Srivastava, Hari Mohan Department of Mathematics 2020 Kyungpook mathematical journal Vol.60 No.1

The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional "differintegral" equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind.