Fractional modelling and identification of thermal systems

Gabano, Jean-Denis; Poinot, Thierry

doi:10.1016/j.sigpro.2010.02.005

Cited by 182 publications

(96 citation statements)

References 17 publications

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“…In [12], the control of viscoelastic damped structure is presented. Control applications to a flexible transmission [13], an active suspension [14], a buck converter [15], a robotic manipulator [16], and a thermal system [17] are also found in the literature. For AMB system applications, there have also been a few works that make use of the fractional calculus concept.…”

Section: Fractional Order Calculus Definition and Applicationsmentioning

confidence: 99%

Fractional Order PID Control of Rotor Suspension by Active Magnetic Bearings

Anantachaisilp¹,

Lin

2017

Actuators

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Abstract:One of the key issues in control design for Active Magnetic Bearing (AMB) systems is the tradeoff between the simplicity of the controller structure and the performance of the closed-loop system. To achieve this tradeoff, this paper proposes the design of a fractional order Proportional-Integral-Derivative (FOPID) controller. The FOPID controller consists of only two additional parameters in comparison with a conventional PID controller. The feasibility of FOPID for AMB systems is investigated for rotor suspension in both the radial and axial directions. Tuning methods are developed based on the evolutionary algorithms for searching the optimal values of the controller parameters. The resulting FOPID controllers are then tested and compared with a conventional PID controller, as well as with some advanced controllers such as Linear Quadratic Gausian (LQG) and H ∞ controllers. The comparison is made in terms of various stability and robustness specifications, as well as the dimensions of the controllers as implemented. Lastly, to validate the proposed method, experimental testing is carried out on a single-stage centrifugal compressor test rig equipped with magnetic bearings. The results show that, with a proper selection of gains and fractional orders, the performance of the resulting FOPID is similar to those of the advanced controllers.

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Section: Fractional Order Calculus Definition and Applicationsmentioning

confidence: 99%

Fractional Order PID Control of Rotor Suspension by Active Magnetic Bearings

Anantachaisilp¹,

Lin

2017

Actuators

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“…This area has been attractive by many researches [41,42] and many kind of observer strategies have been evolved especially for several classes of chemical systems to estimate their internal states [43,44]. In addition, the use of observers becomes a challenge in front of many requirements of accuracy and suitable estimation performances.…”

Section: Soc Optimization Using Fractional Observermentioning

confidence: 99%

Kalman filter Observer for SoC prediction of Lithium cells

Ayadi¹,

Lahiani²,

Derbel³

2017

Adv. sci. technol. eng. syst. j.

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“…Recently, there is a large increase in interest of fractional calculus application as well theoretical and practical points of view, see for example [1][2][3][4][5][6][7][8][9][10][11][12]. Basic information, ideas and some applications of fractional calculus can be found for example in [5,13,14].…”

Section: Introductionmentioning

confidence: 99%

Full-order observers for linear fractional multi-order difference systems

Wyrwas

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The paper is devoted to the construction of observers for linear fractional multi-order difference systems with Riemann-Liouvilleand Grünwald-Letnikov-type operators. Basing on the Z-transform method the sufficient condition for the existence of the presented observers is established. The behaviour of the constructed observer is demonstrated in numerical examples.Key words: difference operators, fractional order difference system, observer. Full-order observers for linear fractional multi-order difference systemsM. WYRWAS * Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A St., 15-351 Białystok, Poland h = 1 has been studied in [24,25]. The aim of the present paper is to study the construction of the full-order observers for linear fractional muti-order discrete-time systems with the RiemannLiouville-and Grünwald-Letnikov-type difference operators with the step h > 0. We restrict the design of the observers for the systems whose fractional orders are from the interval (0, 1], because the systems with fractional orders higher than one can be always transform to systems with orders less than or equal to one, see for instance [26].The paper is organized in the following way. Section 2 gathers preliminary notations, facts and definitions needed in the sequel. In Section 3 the initial value problems for fractional multi-order systems are presented. The main results of the paper, namely the construction of the fractional observer, that estimates the unknown state vector, is presented in Section 5. Since the fractional order system corresponding to the error vector should be asymptotically stable in order to guarantee the estimation of the unknown state of the system by the observer, the condition for asymptotic stability of fractional order systems is given in Section 4. Additionally, two examples that illustrate our results are presented. Finally, the conclusions are drawn. [19,20] and [21]. ing a numerical solution of ystem in a state-space form iant as well as time-variant lts are also valid for system rent types of variable orders ch the fractional variable order state-space system was physically build and the experimental results were compared with numerical implementations. PreliminariesThe paper is organized as follows. At the beginning, in Sect. 2, the few types of fractional variable order derivatives are recalled, together with their discrete approximations and matrix forms. In Sect. 3 the solution of linear control system in state-space form for time-variant and time-invariant noncommensurate fractional variable order system is presented. An analog model of particular type of fractional variable order state-space system is introduced in Sect. 4. The experimental and numerical results are collected in Sect. 5. Finally, Sect. 6 summarizes the main results. Fractional variable order operatorsBelow, we recall the already known different types of fractional constant and variable order derivatives and differences. Definitions of variable order operatorsThe following fractiona...

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Fractional modelling and identification of thermal systems

Cited by 182 publications

References 17 publications

Fractional Order PID Control of Rotor Suspension by Active Magnetic Bearings

Fractional Order PID Control of Rotor Suspension by Active Magnetic Bearings

Kalman filter Observer for SoC prediction of Lithium cells

Full-order observers for linear fractional multi-order difference systems

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