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

Author(s):  
WANG Hongwei ◽  
ZHANG Qian ◽  
ZHA Qin ◽  
Mutalifu Ahemaide

Abstract 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.

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Xikui Hu ◽  
Ping Zhou

Based on the integer-order memristive system that can generate two-scroll, three-scroll, and four-scroll chaotic attractors, in this paper, we found other phenomena that two kinds of three-scroll chaotic attractors coexist in this system with different initial conditions. Furthermore, we proposed a coexisting fractional-order system based on the three-scroll chaotic attractors system, in which the three-scroll or four-scroll chaotic attractors emerged with different fractional-orders q. Meanwhile, with fractional-order q=0.965 and different initial conditions, coexistence of two kinds of three-scroll and four-scroll chaotic attractors is found simultaneously. Finally, we discussed controlling chaos for the fractional-order memristive chaotic system.


2021 ◽  
Author(s):  
Martin Hecht ◽  
Robert Seifert ◽  
Wilfried Hofmann

The electromagnetic dynamics of nonlaminated magnetic actuators are highly influenced by eddy currents and minor perturbations like core saturation, hysteresis as well as fringing and leakage fluxes. In the literature, analytical high-fidelity models describing these phenomena are known, which lead to complex reluctance networks or transcendental system descriptions with fractional-order characteristics. Therefore, they are not suitable for a direct implementation within the actuator control. Previously, we provided appropriate analytical rational approximations that allow a digital real-time implementation of these models on a microcontroller. However, the inclusion of the minor perturbations, if possible, leads to impractical model orders requiring simplifications, which compromise the model accuracy. This article studies numerical methods to reduce high model orders or directly approximate the transcendental systems or empirical measurement data. The greater degree of freedom allows for a possible higher model accuracy with sufficiently low orders. We review and improve existing approaches like Levy's method and Vector Fitting and apply them to the frequency response of the underlying fractional-order system. Furthermore we propose an order reduction algorithm based on a pole-zero-cancellation with tracking error compensation. Using measurement data, a comparison shows that the numerical approaches match or excel our previously studied analytical approximation.


2021 ◽  
Author(s):  
Martin Hecht ◽  
Robert Seifert ◽  
Wilfried Hofmann

The electromagnetic dynamics of nonlaminated magnetic actuators are highly influenced by eddy currents and minor perturbations like core saturation, hysteresis as well as fringing and leakage fluxes. In the literature, analytical high-fidelity models describing these phenomena are known, which lead to complex reluctance networks or transcendental system descriptions with fractional-order characteristics. Therefore, they are not suitable for a direct implementation within the actuator control. Previously, we provided appropriate analytical rational approximations that allow a digital real-time implementation of these models on a microcontroller. However, the inclusion of the minor perturbations, if possible, leads to impractical model orders requiring simplifications, which compromise the model accuracy. This article studies numerical methods to reduce high model orders or directly approximate the transcendental systems or empirical measurement data. The greater degree of freedom allows for a possible higher model accuracy with sufficiently low orders. We review and improve existing approaches like Levy's method and Vector Fitting and apply them to the frequency response of the underlying fractional-order system. Furthermore we propose an order reduction algorithm based on a pole-zero-cancellation with tracking error compensation. Using measurement data, a comparison shows that the numerical approaches match or excel our previously studied analytical approximation.


Author(s):  
Linyun Huang ◽  
Youngchul Bae

Based on the fractional order of nonlinear system for love model with a periodic function as an external force, analyzed the characteristics of the chaotic dynamic in this study. The relationship between the chaotic dynamic of the fractional-love model with the external force and the fractional-order system was analyzed when the parameters are fixed. Further, we also studied the relationship between the chaotic systemic dynamic and the parameters when the fractional-order system is fixed. The results show that when the parameters are fixed, the fractional-order system exhibited segmented chaotic states for the different fractional orders of the system. When fixed the fractional-order system, the system exhibited the periodic and chaotic states as parameter changes.


2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.


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