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Algorithms
Special Issues
Fractional Order Systems and Signals: Modelling, Identification and Control Applications
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Fractional Order Systems and Signals: Modelling, Identification and Control Applications

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (15 May 2018) | Viewed by 33921

Special Issue Editors

Prof. Dr. Manuel Duarte-Mermoud

E-Mail Website
Guest Editor
Department of Electrical Engineering at the University of Chile, in Santiago, Chile
Interests: robust adaptive control (linear and nonlinear; fractional and integer order) system identification and parameter estimation intelligent; control and applications technology for automation; applied control to mining, energy, electric power, electro-medicine and wine industry
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Rafael Castro-Linares

E-Mail Website
Guest Editor
Department of Electrical Engineering, Section of Mechatronics, Center of Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV), México City, Mexico
Interests: analysis and design of controllers for nonlinear systems and applications; control of servomechanisms; computer-controlled systems; robot control; unmanned aerial and ground autonomous vehicle control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In the past, several results involving fractional order operators have been reported both in theory and applications, covering different fields such as modelling, identification, estimation, control and signal processing, among others. The interest in using fractional order tools has increased rapidly over the last few decades, with solid results being obtained for the study of fractional order systems and signals from transient behavior, stability, convergence and boundedness viewpoints, allowing a comparison of these techniques with those based on integer order derivative and integral operators, expanding the horizons on these topics.

The present Special Issue is devoted to new theories and applications, making use of fractional order operators and comparisons with their integer order counterparts. The topics of interest include, but are not limited to, the following areas:

  • ­  Fractional order control (adaptive and non-adaptive). Theory and practice.
  • ­  Fractional order sliding mode control and applications.
  • ­  Stability of fractional order differential equations and systems.
  • ­  Fractional order observers and estimators.
  • ­  Back-stepping fractional order control (adaptive and non-adaptive systems).
  • ­  Fractional integrals and derivatives and their applications.
  • ­  Fractional order signal processing.
  • ­  Fractional order passivity and applications.
  • ­  Conformable fractional calculus.
  • ­  New definitions of fractional derivatives.
  • ­  Applications of fractional calculus.
  • ­  Fractional order stochastic systems and controls.
  • ­  Fractional order modelling of physical systems.

Prof. Dr. Manuel Duarte-Mermoud
Prof. Dr. Rafael Castro-Linares
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fractional Calculus
  • Fractional Systems
  • Fractional Operators
  • Fractional Control
  • Fractional Observers
  • Fractional Differential Equations
  • Fractional Difference Equations
  • Fractional Integral Equations

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Published Papers (8 papers)

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24 pages, 2881 KiB  
Article
Fractional Order Sliding Mode Control of a Class of Second Order Perturbed Nonlinear Systems: Application to the Trajectory Tracking of a Quadrotor
by Arturo Govea-Vargas, Rafael Castro-Linares, Manuel A. Duarte-Mermoud, Norelys Aguila-Camacho and Gustavo E. Ceballos-Benavides
Algorithms 2018, 11(11), 168; https://doi.org/10.3390/a11110168 - 26 Oct 2018
Cited by 12 | Viewed by 3830
Abstract
A Fractional Order Sliding Mode Control (FOSMC) is proposed in this paper for an integer second order nonlinear system with an unknown additive perturbation term. A sufficient condition is given to assure the attractiveness to a given sliding surface where trajectory tracking is [...] Read more.
A Fractional Order Sliding Mode Control (FOSMC) is proposed in this paper for an integer second order nonlinear system with an unknown additive perturbation term. A sufficient condition is given to assure the attractiveness to a given sliding surface where trajectory tracking is assured, despite the presence of the perturbation term. The control scheme is applied to the model of a quadrotor vehicle in order to have trajectory tracking in the space. Simulation results are presented to evaluate the performance of the control scheme. Full article
(This article belongs to the Special Issue Fractional Order Systems and Signals: Modelling, Identification and Control Applications)
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18 pages, 633 KiB  
Article
Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems
by Manuel A. Duarte-Mermoud, Javier A. Gallegos, Norelys Aguila-Camacho and Rafael Castro-Linares
Algorithms 2018, 11(9), 136; https://doi.org/10.3390/a11090136 - 9 Sep 2018
Viewed by 3255
Abstract
Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which [...] Read more.
Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers. Full article
(This article belongs to the Special Issue Fractional Order Systems and Signals: Modelling, Identification and Control Applications)
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35 pages, 21799 KiB  
Article
Fractional-Order Closed-Loop Model Reference Adaptive Control for Anesthesia
by Gerardo Navarro-Guerrero and Yu Tang
Algorithms 2018, 11(7), 106; https://doi.org/10.3390/a11070106 - 14 Jul 2018
Cited by 10 | Viewed by 4557
Abstract
The design of a fractional-order closed-loop model reference adaptive control (FOCMRAC) for anesthesia based on a fractional-order model (FOM) is proposed in the paper. This proposed model gets around many difficulties, namely, unknown parameters, lack of state measurement, inter and intra-patient variability, and [...] Read more.
The design of a fractional-order closed-loop model reference adaptive control (FOCMRAC) for anesthesia based on a fractional-order model (FOM) is proposed in the paper. This proposed model gets around many difficulties, namely, unknown parameters, lack of state measurement, inter and intra-patient variability, and variable time-delay, encountered in controller designs based on the PK/PD model commonly used for control of anesthesia, and allows to design a simple adaptive controller based on the Lyapunov analysis. Simulations illustrate the effectiveness and robustness of the proposed control. Full article
(This article belongs to the Special Issue Fractional Order Systems and Signals: Modelling, Identification and Control Applications)
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15 pages, 6160 KiB  
Article
Solutions to the Sub-Optimality and Stability Issues of Recursive Pole and Zero Distribution Algorithms for the Approximation of Fractional Order Models
by Jocelyn Sabatier
Algorithms 2018, 11(7), 103; https://doi.org/10.3390/a11070103 - 12 Jul 2018
Cited by 6 | Viewed by 3490
Abstract
This paper analyses algorithms currently found in the literature for the approximation of fractional order models and based on recursive pole and zero distributions. The analysis focuses on the sub-optimality of the approximations obtained and stability issues that may appear after approximation depending [...] Read more.
This paper analyses algorithms currently found in the literature for the approximation of fractional order models and based on recursive pole and zero distributions. The analysis focuses on the sub-optimality of the approximations obtained and stability issues that may appear after approximation depending on the pole location of the initial fractional order model. Solutions are proposed to reduce this sub-optimality and to avoid stability issues. Full article
(This article belongs to the Special Issue Fractional Order Systems and Signals: Modelling, Identification and Control Applications)
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17 pages, 1827 KiB  
Article
Robust Fuzzy Adaptive Sliding Mode Stabilization for Fractional-Order Chaos
by Bachir Bourouba and Samir Ladaci
Algorithms 2018, 11(7), 101; https://doi.org/10.3390/a11070101 - 7 Jul 2018
Cited by 17 | Viewed by 4448
Abstract
In this paper, a new adaptive fuzzy sliding mode control (AFSMC) design strategy is proposed for the control of a special class of three-dimensional fractional order chaotic systems with uncertainties and external disturbance. The design methodology is developed in two stages: first, an [...] Read more.
In this paper, a new adaptive fuzzy sliding mode control (AFSMC) design strategy is proposed for the control of a special class of three-dimensional fractional order chaotic systems with uncertainties and external disturbance. The design methodology is developed in two stages: first, an adaptive sliding mode control law is proposed for the class of fractional order chaotic systems without uncertainties, and then a fuzzy logic system is used to estimate the control compensation effort to be added in the case of uncertainties on the system’s model. Based on the Lyapunov theory, the stability analysis of both control laws is provided with elimination of the chattering action in the control signal. The developed control scheme is simple to implement and the overall control scheme guarantees the global asymptotic stability in the Lyapunov sense if all the involved signals are uniformly bounded. In the present work, simulation studies on fractional-order Chen chaotic systems are carried out to show the efficiency of the proposed fractional adaptive controllers. Full article
(This article belongs to the Special Issue Fractional Order Systems and Signals: Modelling, Identification and Control Applications)
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13 pages, 3951 KiB  
Article
Experimental Validation of a Novel Auto-Tuning Method for a Fractional Order PI Controller on an UR10 Robot
by Cristina I. Muresan, Cosmin Copot, Isabela Birs, Robin De Keyser, Steve Vanlanduit and Clara M. Ionescu
Algorithms 2018, 11(7), 95; https://doi.org/10.3390/a11070095 - 30 Jun 2018
Cited by 13 | Viewed by 4463
Abstract
Classical fractional order controller tuning techniques usually consider the frequency domain specifications (phase margin, gain crossover frequency, iso-damping) and are based on knowledge of a process model, as well as solving a system of nonlinear equations to determine the controller parameters. In this [...] Read more.
Classical fractional order controller tuning techniques usually consider the frequency domain specifications (phase margin, gain crossover frequency, iso-damping) and are based on knowledge of a process model, as well as solving a system of nonlinear equations to determine the controller parameters. In this paper, a novel auto-tuning method is used to tune a fractional order PI controller. The advantages of the proposed auto-tuning method are two-fold: There is no need for a process model, neither to solve the system of nonlinear equations. The tuning is based on defining a forbidden region in the Nyquist plane using the phase margin requirement and determining the parameters of the fractional order controller such that the loop frequency response remains out of the forbidden region. Additionally, the final controller parameters are those that minimize the difference between the slope of the loop frequency response and the slope of the forbidden region border, to ensure the iso-damping property. To validate the proposed method, a case study has been used consisting of a pick and place movement of an UR10 robot. The experimental results, considering two different robot configurations, demonstrate that the designed fractional order PI controller is indeed robust. Full article
(This article belongs to the Special Issue Fractional Order Systems and Signals: Modelling, Identification and Control Applications)
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15 pages, 1263 KiB  
Article
A Novel Method for Control Performance Assessment with Fractional Order Signal Processing and Its Application to Semiconductor Manufacturing
by Kai Liu, YangQuan Chen, Paweł D. Domański and Xi Zhang
Algorithms 2018, 11(7), 90; https://doi.org/10.3390/a11070090 - 26 Jun 2018
Cited by 15 | Viewed by 4417
Abstract
The significant task for control performance assessment (CPA) is to review and evaluate the performance of the control system. The control system in the semiconductor industry exhibits a complex dynamic behavior, which is hard to analyze. This paper investigates the interesting crossover properties [...] Read more.
The significant task for control performance assessment (CPA) is to review and evaluate the performance of the control system. The control system in the semiconductor industry exhibits a complex dynamic behavior, which is hard to analyze. This paper investigates the interesting crossover properties of Hurst exponent estimations and proposes a novel method for feature extraction of the nonlinear multi-input multi-output (MIMO) systems. At first, coupled data from real industry are analyzed by multifractal detrended fluctuation analysis (MFDFA) and the resultant multifractal spectrum is obtained. Secondly, the crossover points with spline fit in the scale-law curve are located and then employed to segment the entire scale-law curve into several different scaling regions, in which a single Hurst exponent can be estimated. Thirdly, to further ascertain the origin of the multifractality of control signals, the generalized Hurst exponents of the original series are compared with shuffled data. At last, non-Gaussian statistical properties, multifractal properties and Hurst exponents of the process control variables are derived and compared with different sets of tuning parameters. The results have shown that CPA of the MIMO system can be better employed with the help of fractional order signal processing (FOSP). Full article
(This article belongs to the Special Issue Fractional Order Systems and Signals: Modelling, Identification and Control Applications)
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20 pages, 2157 KiB  
Article
ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems
by Yong-Hong Lan and Zhe-Min Cui
Algorithms 2018, 11(6), 85; https://doi.org/10.3390/a11060085 - 14 Jun 2018
Cited by 2 | Viewed by 4601
Abstract
This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and [...] Read more.
This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by introducing a new norm and using the generalized Gronwall inequality, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example. Full article
(This article belongs to the Special Issue Fractional Order Systems and Signals: Modelling, Identification and Control Applications)
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