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A comparative analysis of electromechanical model of piezoelectric actuator through Caputo–Fabrizio and Atangana–Baleanu fractional derivatives
Author(s) -
Abro Kashif Ali,
Atangana Abdon
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6638
Subject(s) - mathematics , laplace transform , displacement (psychology) , fractional calculus , operator (biology) , partial differential equation , actuator , mathematical analysis , control theory (sociology) , series (stratigraphy) , engineering , computer science , control (management) , psychology , paleontology , biochemistry , chemistry , repressor , biology , transcription factor , electrical engineering , psychotherapist , gene , artificial intelligence
The dynamical characteristics of the electrical and mechanical domains are usually detected by means of electromechanical model of piezoelectric actuator; this is because it manages extremely small displacements in the range from 10 pm (1 pm = 10 −12 m) to 100 μm . This manuscript is dedicatedly written on the fractional modeling of electromechanical model of piezoelectric actuator through modern fractional definitions, namely, Atangan–Baleanu and Caputo–Fabrizio fractional operators, which are based on capturing the full memory effects with and without Markovian and non‐Markovian properties. The modeled governing partial differential equation of displacement is solved by means of Laplace transform method. The investigated solutions of displacement have been expressed in terms of Fox‐ H function and series format for avoiding the involvement of gamma functions. A comparative analysis is performed graphically between solutions obtained from Atangan–Baleanu fractional operator and Caputo–Fabrizio fractional operator. Our results suggest that displacement via Atangan–Baleanu fractional operator dominates than displacement via Caputo–Fabrizio fractional operator for controller design even to bypass the hysteresis effect. Additionally, comparison of both fractional techniques on displacement suggests that the utilization of the frequency domain is much more effective than the displacement via classical approaches.