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Entropy
Volume 22
Issue 3
10.3390/e22030300
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Article

Commensurate and Non-Commensurate Fractional-Order Discrete Models of an Electric Individual-Wheel Drive on an Autonomous Platform

by
Marcin Bąkała
1,
Piotr Duch
1,
J. A. Tenreiro Machado
2,*,
Piotr Ostalczyk
1 and
Dominik Sankowski
1
1
Institute of Applied Computer Science, ódź University of Technology, ul. Stefanowskiego 18/22, 90-537 Lodz, Poland
2
Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(3), 300; https://doi.org/10.3390/e22030300
Submission received: 24 January 2020 / Revised: 20 February 2020 / Accepted: 2 March 2020 / Published: 5 March 2020
(This article belongs to the Special Issue Complex and Fractional Dynamical Systems)
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Abstract

This paper presents integer and linear time-invariant fractional order (FO) models of a closed-loop electric individual-wheel drive implemented on an autonomous platform. Two discrete-time FO models are tested: non-commensurate and commensurate. A classical model described by the second-order linear difference equation is used as the reference. According to the sum of the squared error criterion (SSE), we compare a two-parameter integer order model with four-parameter non-commensurate and three-parameter commensurate FO descriptions. The computer simulation results are compared with the measured velocity of a real autonomous platform powered by a closed-loop electric individual-wheel drive.
Keywords: fractional-order backward-difference; difference equation; identification fractional-order backward-difference; difference equation; identification

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MDPI and ACS Style

Bąkała, M.; Duch, P.; Tenreiro Machado, J.A.; Ostalczyk, P.; Sankowski, D. Commensurate and Non-Commensurate Fractional-Order Discrete Models of an Electric Individual-Wheel Drive on an Autonomous Platform. Entropy 2020, 22, 300. https://doi.org/10.3390/e22030300

AMA Style

Bąkała M, Duch P, Tenreiro Machado JA, Ostalczyk P, Sankowski D. Commensurate and Non-Commensurate Fractional-Order Discrete Models of an Electric Individual-Wheel Drive on an Autonomous Platform. Entropy. 2020; 22(3):300. https://doi.org/10.3390/e22030300

Chicago/Turabian Style

Bąkała, Marcin, Piotr Duch, J. A. Tenreiro Machado, Piotr Ostalczyk, and Dominik Sankowski. 2020. "Commensurate and Non-Commensurate Fractional-Order Discrete Models of an Electric Individual-Wheel Drive on an Autonomous Platform" Entropy 22, no. 3: 300. https://doi.org/10.3390/e22030300

APA Style

Bąkała, M., Duch, P., Tenreiro Machado, J. A., Ostalczyk, P., & Sankowski, D. (2020). Commensurate and Non-Commensurate Fractional-Order Discrete Models of an Electric Individual-Wheel Drive on an Autonomous Platform. Entropy, 22(3), 300. https://doi.org/10.3390/e22030300

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