Fractional order modeling and control for under-actuated inverted pendulum

Shalaby, Raafat; El-Hossainy, Mohammad; Abozalam, Belal

doi:10.1016/j.cnsns.2019.02.023

Cited by 46 publications

(20 citation statements)

References 32 publications

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“…Fractional calculus expands the conventional integral order calculus from integer to non-integer values. A more accurate mathematical model could be accomplished by fractional calculus since the overall system degrees of freedom are increased [19]- [20]. It is fair to say that in the utmost realistic applications, dynamics of most mechanical and electrical systems are inherently characterized to have non-integer integral and differential orders [19].…”

Section: Introductionmentioning

confidence: 99%

Improved Mathematical Modeling of Six Phase Induction Machines Based on Fractional Calculus

et al. 2021

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Multiphase induction machine modelling represents a crucial research topic for both machine control and performance evaluation purposes. Generally, multiphase induction machines are preferably modelled using the vector space decomposition technique with some assumptions to simplify the mathematical model. However, different sources of non-linearities, including low order harmonics mapped to secondary subspaces, cross-coupling saturation and iron losses result in a notable deviation from the experimentally measured waveforms. Furthermore, considering full symmetry amongst motors phases seems to be a rather idealistic assumption. Fractional order modelling has recently emerged as a promising mathematical technique to model highly nonlinear electrical and mechanical systems. This paper proposes an improved vector space decomposition (VSD)-based fractional order model of an asymmetrical six-phase induction machine under both healthy and open phase fault conditions with different neutral arrangements. The appropriate differentiation orders have been obtained by optimizing the error function between simulated and experimental waveforms. The results are compared with the conventional integral order-based model. Experimental validation has been carried out using a 1.5Hp prototype induction machine.

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Section: Introductionmentioning

confidence: 99%

Improved Mathematical Modeling of Six Phase Induction Machines Based on Fractional Calculus

et al. 2021

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“…Fractional order systems (FOSs) is more common than the traditional integer order systems, especially for the application with long memory characteristics, such as supercapacitors [1], thermal diffusion processes [2,3], and viscoelastic structures [4], etc. More and more researchers began to pay attention to fractional models, and found that fractional model has more accurate description method for many physical processes [5,6]. In order to deal with the modeling problems of fractional order system, some modeling methods are presented to deal with parameters identification and fractional orders estimation, including poisson moment functions (PMF) [7,8], modulation functions [9,10], auxiliary variable method [11], orthogonal basis functions [12], and block pulse functions [13], etc.…”

Section: Introductionmentioning

confidence: 99%

Identification of Fractional Order System with Scarce Measurement Data Based on Multi Innovation Estimation Algorithm

Wang¹,

Qian²,

Qin³

et al. 2021

Preprint

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Aiming at the modeling issues of fractional order Hammerstein system with scarce measurements, a novel multi-innovation hybrid identification algorithm is proposed to deal with them. Firstly, a multi-innovation estimation algorithm based on auxiliary model is presented to estimate the parameters of the nonlinear fractional order system, and a multi-innovation Levenberg-Marquardt algorithm are derived to confirm the fractional orders. Secondly, the convergence properties of the proposed algorithm are analyzed using the lemmas and theorems. Finally, in order to illustrate the effectiveness of the proposed algorithm, two fractional order nonlinear systems with scarce measurements are studied to prove the validity.

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“…Distinct from integral calculus, fractional calculus exhibits global relevance and historical memory characteristics. Moreover, it is more accurate in describing complex systems with historical dependence or distributed parameters (Aslipour and Yazdizadeh, 2019;Shalaby et al, 2019). Therefore, fractional calculus has wide system modelling applications, such as for modelling the thermal diffusion problem of boilers (Zhang et al, 2017), the elasticplastic behaviour of metals (Mendiguren et al, 2012), the electrical characteristic of fuel cells (Cao et al, 2010) and the viscoelastic behaviour of polymer materials (Nerantzaki and Babouskos, 2011).…”

Section: Introductionmentioning

confidence: 99%

Fractional order system modelling with Legendre wavelet multi-resolution analysis

Wang

Liang

et al. 2021

Transactions of the Institute of Measurement and Control

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This paper proposes a method of fractional order system (FOS) modelling with Legendre wavelet multi-resolution analysis. The proposed method expands the input and output signals of the system in the form of a Legendre wavelet, and constructs the Legendre wavelet integration operational matrix by use of a block-pulse function. To address the problem of the considerable volume of system identification data and system noise in practical engineering applications, the multi-resolution characteristics of the wavelet are combined to build a wavelet integration operational matrix from the multi-scale space. By continuously discarding the high-frequency information to reduce the length of the identification data, the identification speed of the system is accelerated and the influence of noise on the identification accuracy is reduced. In addition, the least squares method is used to find the optimal order in the identification interval and further accelerate the FOS modelling process. The proposed method rapidly identifies the FOS parameters with high accuracy, and is thus feasible for engineering applications. Its effectiveness is verified by simulation and photoelectric stabilized sighting platform experiment.

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Fractional order modeling and control for under-actuated inverted pendulum

Cited by 46 publications

References 32 publications

Improved Mathematical Modeling of Six Phase Induction Machines Based on Fractional Calculus

Improved Mathematical Modeling of Six Phase Induction Machines Based on Fractional Calculus

Identification of Fractional Order System with Scarce Measurement Data Based on Multi Innovation Estimation Algorithm

Fractional order system modelling with Legendre wavelet multi-resolution analysis

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