Recent Results in Fractional-Order Modeling in Multi-Agent Systems and Linear Friction Welding

Leyden, Kevin

doi:10.1016/j.ifacol.2015.05.180

Cited by 10 publications

(5 citation statements)

References 8 publications

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“…We will now introduce the fractional generalization of these components of friction, and derive the corresponding generalized dissipative force. Even though this contribution can be implicitly connected with the previous results in the literature describing dissipative forces of fractional order [34][35][36] to the best of the authors' knowledge, there is no model of friction in robotic joints similar to the one proposed here. Hence, in this paper we propose the following modification for F…”

Section: Generalized Fractional Order Friction Forcesmentioning

confidence: 58%

Further results on advanced robust iterative learning control and modeling of robotic systems

Lazarević

Mandić

Ostojić

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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Recently, calculus of general order [Formula: see text] has attracted attention in scientific literature, where fractional operators are often used for control issues and the modeling of the dynamics of complex systems. In this work, some attention will be devoted to the problem of viscous friction in robotic joints. The calculus of general order and the calculus of variations are utilized for the modeling of viscous friction which is extended to the fractional derivative of the angular displacement. In addition, to solve the output tracking problem of a robotic manipulator with three DOFs with revolute joints in the presence of model uncertainties, robust advanced iterative learning control (AILC) is introduced. First, a feedback linearization procedure of a nonlinear robotic system is applied. Then, the proposed intelligent feedforward-feedback AILC algorithm is introduced. The convergence of the proposed AILC scheme is established in the time domain in detail. Finally, simulations on the given robotic arm system confirm the effectiveness of the robust AILC method.

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Section: Generalized Fractional Order Friction Forcesmentioning

confidence: 58%

Further results on advanced robust iterative learning control and modeling of robotic systems

Lazarević

Mandić

Ostojić

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Therefore, there is a strong need for generalized operators that should have abilities to demonstrate the generic behavior of the physical phenomena, see ( [51], Chap. 5,7, and [15,52,53]). The most commonly used fractional derivative operators are the Riemann-Liouville and Caputo expressed in the following way [26]:…”

Section: Fractional Calculusmentioning

confidence: 99%

Orthogonal Polynomials Based Operational Matrices with Applications to Bagley-Torvik Fractional Derivative Differential Equations

Talib¹,

Özger²

2023

Recent Research in Polynomials [Working Title]

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Orthogonal polynomials are the natural way to express the elements of the inner product spaces as an infinite sum of orthonormal basis sets. The construction and development of the many important numerical algorithms are based on the operational matrices of orthogonal polynomials including spectral tau, spectral collocation, and operational matrices approach are few of them. The widely used orthogonal polynomials are Legendre, Jacobi, and Chebyshev. However, only a few papers are available where the Hermite polynomials (HPs) were exploited to solve numerically the differential equations. The notable characteristic of the HPs is its ability to approximate the square-integrable functions on the entire real line. The prime objective of this chapter is to introduce the two new generalized operational matrices of HPs which are developed in the sense of the Riemann-Liouville fractional-order integral operator and Hilfer fractional-order derivative operator. The newly derived operational matrices are further used to construct a numerical algorithm for solving the Bagley--Trovik types fractional derivative differential equations (FDDE). Moreover, the results obtained by using the proposed algorithm are compared with the results obtained otherwise to demonstrate the efficiency and accuracy of the proposed numerical algorithm. Some examples are solved for application purposes.

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“…Other related studies include [26] (walking robots), [27], [28] (flexible manipulators), [29] (time delays) and control using fractional-order PID control [28], [30]. Our other prior papers on fractional calculus in engineering are [31], [32].…”

Section: A Literature Review and Research Contextmentioning

confidence: 99%

Using fractional-order differential equations for health monitoring of a system of cooperating robots

Leyden

2016

2016 IEEE International Conference on Robotics and Automation (ICRA)

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The dynamics of many large-scale robotic formation systems, including structured systems as well as some random scale-free networks of agents, can be accurately described using fractional-order differential equations. A fractional-order differential equation can contain derivative terms with noninteger order, e.g., the one-half derivative. This paper demonstrates that the fractional order of the dynamics of a system may be a potentially powerful new way to monitor the operational status of such systems. When the order of the system changes, it can indicate an important change in the status of the system. Integer-order models will never exhibit a change in order because the order is dictated by a natural first principle and the structure of the system. For this reason, traditional health monitoring tools essentially focus on identifying parameter variations in a mathematical description of the system, but not changes in order. When fractional-order models are considered, the infinite number of possible real-valued orders between any two integer orders may capture essential changes in the system's dynamics. This paper provides an example of such changes, provides a theoretical justification for the approach, and explores possible limitations to the approach.

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Recent Results in Fractional-Order Modeling in Multi-Agent Systems and Linear Friction Welding

Cited by 10 publications

References 8 publications

Further results on advanced robust iterative learning control and modeling of robotic systems

Further results on advanced robust iterative learning control and modeling of robotic systems

Orthogonal Polynomials Based Operational Matrices with Applications to Bagley-Torvik Fractional Derivative Differential Equations

Using fractional-order differential equations for health monitoring of a system of cooperating robots

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