Synthesis and implementation of non-integer integrators using RLC devices

Daou, Roy Abi Zeid; Francis, Clovis; Moreau, Xavier

doi:10.1080/00207210903061980

Cited by 26 publications

(7 citation statements)

References 10 publications

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“…. We note that for η > 1, > 1, and η κ > 1, the influence of K k for the fractional order α is minimal [43,74,75]. Nonetheless, the recursive dependence revealed problems for small α, with arg {G N (jω)} oscillating.…”

Section: Fractional-order Sensormentioning

confidence: 84%

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Fractional-Order Sensing and Control: Embedding the Nonlinear Dynamics of Robot Manipulators into the Multidimensional Scaling Method

Lopes

Machado

2021

Sensors

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This paper studies the use of multidimensional scaling (MDS) to assess the performance of fractional-order variable structure controllers (VSCs). The test bed consisted of a revolute planar robotic manipulator. The fractional derivatives required by the VSC can be obtained either by adopting numerical real-time signal processing or by using adequate sensors exhibiting fractional dynamics. Integer (fractional) VCS and fractional (integer) sliding mode combinations with different design parameters were tested. Two performance indices based in the time and frequency domains were adopted to compare the system states. The MDS generated the loci of objects corresponding to the tested cases, and the patterns were interpreted as signatures of the system behavior. Numerical experiments illustrated the feasibility and effectiveness of the approach for assessing and visualizing VSC systems.

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Section: Fractional-order Sensormentioning

confidence: 84%

“…For the case of selecting the parameters recursively, M k+1 = η M k , B k+1 = B k and K k+1 = κK k , η, , κ ∈ R + , we obtain [43,[73][74][75]:…”

Section: Fractional-order Sensormentioning

confidence: 99%

Fractional-Order Sensing and Control: Embedding the Nonlinear Dynamics of Robot Manipulators into the Multidimensional Scaling Method

Lopes

Machado

2021

Sensors

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“…If we choose the parameters recursively, that is, Mi+1=ηMi,Bi+1=εBi and Ki+1=κKi,η,ε,κ∈R+, then we obtain (Daou et al., 2009; Ionescu et al., 2010; Oustaloup et al., 2000; Petráš, 2009): …”

Section: Fundamental Conceptsmentioning

confidence: 99%

“…The domain of GN(jω) characterized by FO behavior is defined by the conditions |jω|<B1M1 and |jω| << K1B1. Moreover, for η>1,ε>1 and ηκ>1, the contribution of K i for α is negligible (Daou et al., 2009; Ionescu et al., 2010; Oustaloup et al., 2000).…”

Section: Fundamental Conceptsmentioning

confidence: 99%

Towards fractional sensors

Lopes

Machado

Galhano

2018

Journal of Vibration and Control

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This paper proposes a new sensor architecture inspired on the classical accelerometer and the fractional calculus. The fractional sensor (FS) adopts a modular construction with [Formula: see text] stages, where each stage consists of an association of mass–spring–damper elements. A proper selection of the elements in the global mechanical structure yields fractional-order characteristics. The frequency and time responses of the proposed apparatus are studied and compared with those exhibited by an ideal fractional order device. The FS can be implemented by means of modern fabrication techniques used with micro electro-mechanical systems.

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“…Through the analysis of the storage and memory characteristics of the actual capacitance, the fractional-order of the capacitance-voltage equation in different dielectric materials was tested, and the inductors were also pointed to have fractional-order characteristics in 1994 [21]. By studying the charge and discharge memory properties of the resistor, capacitor, and inductor in the actual working process, the RLC circuit presented non-integer order characteristics in a certain range of parameters or certain operating conditions [22], and the fractional calculus theory was used to describe the memory characteristics of RLC circuit [23]. Through the experimental data and identification algorithms, the modeling method of the timedomain fractional-order model of permanent magnet synchronous motor (PMSM) was proposed [24].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Chaos Control of Fractional Order D-PMSG for Wind Turbine with Uncertain Parameters by State Feedback Design

Yang

Sheng

et al. 2021

Energies

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To research the chaotic motion problem of the direct-drive permanent magnet synchronous generator (D-PMSG) for a wind turbine with uncertain parameters and fractional order characteristics, a control strategy established upon fuzzy state feedback is proposed. Firstly, according to the working mechanism of D-PMSG, the Lorenz nonlinear mathematical model is established by affine transformation and time transformation. Secondly, fractional order nonlinear systems (FONSs) are transformed into linear sub-model by Takagi–Sugeno (T-S) fuzzy model. Then, the fuzzy state feedback controller is designed through Parallel Distributed Compensation (PDC) control principle to suppress the chaotic motion. By applying the fractional Lyapunov stability theory (FLST), the sufficient conditions for Mittag–Leffler stability are formulated in the format of linear matrix inequalities (LMIs). Finally, the control performance and effectiveness of the proposed controller are demonstrated through numerical simulations, and the chaotic motions in D-PMSG can be eliminated quickly.

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Synthesis and implementation of non-integer integrators using RLC devices

Cited by 26 publications

References 10 publications

Fractional-Order Sensing and Control: Embedding the Nonlinear Dynamics of Robot Manipulators into the Multidimensional Scaling Method

Fractional-Order Sensing and Control: Embedding the Nonlinear Dynamics of Robot Manipulators into the Multidimensional Scaling Method

Towards fractional sensors

Fuzzy Chaos Control of Fractional Order D-PMSG for Wind Turbine with Uncertain Parameters by State Feedback Design

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