Design Fractional-order PID Controllers for Single-Joint Robot Arm Model

Batiha, Iqbal M.; Njadat, Suhaib A.; Batyha, Radwan M.; Zraiqat, Amjed; Dababneh, Amer; Momani, Shaher

doi:10.15849/ijasca.220720.07

Cited by 21 publications

(8 citation statements)

References 18 publications

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“…In what follow, we will endeavor to propose a new result that examines the existence and uniqueness of a weak solution for the fractional-order diffusion problem (8). For this purpose, it is sufficient to prove that problem (9) has a unique solution u, which has been previously proposed in Proposition 1.…”

Section: Existence and Uniqueness Resultsmentioning

confidence: 96%

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On a Weak Solution of a Fractional-order Temporal Equation

Batiha¹,

Chebana²,

Oussaeif³

et al. 2022

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Several real-world phenomena emerging in engineering and science fields can be described successfully by developing certain models using fractional-order partial differential equations. The exact, analytical, semi-analytical or even numerical solutions for these models should be examined and investigated by distinguishing between their solvablities and non-solvabilities. In this paper, we aim to establish some sufficient conditions for exploring the existence and uniqueness of solution for a class of initial-boundary value problems with Dirichlet condition. The gained results from this research paper are established for the class of fractional-order partial differential equations by a method based on Lax Milgram theorem, which relies in its construction on properties of the symmetric part of the bilinear form. Lax Milgram theorem is deemed as a mathematical scheme that can be used to examine the existence and uniqueness of weak solutions for fractional-order partial differential equations. These equations are formulated here in view of the Caputo fractional-order derivative operator, which its inverse operator is the Riemann-Louville fractional-order integral one. The results of this paper will be supportive for mathematical analyzers and researchers when a fractional-order partial differential equation is handled in terms of finding its exact, analytical, semi-analytical or numerical solution.

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Section: Existence and Uniqueness Resultsmentioning

confidence: 96%

“…Fractional-order differential equations, which can be obtained by generalizing ordinary differential equations to an arbitrary order, play a crucial role in engineering, physics, and applied mathematics [7,8,9]. Several complex phenomena can be modeled with the help of using these equations [10,11].…”

Section: Introductionmentioning

confidence: 99%

On a Weak Solution of a Fractional-order Temporal Equation

Batiha¹,

Chebana²,

Oussaeif³

et al. 2022

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“…Podlubny et al are credited with creating the fractional-order PID controller in 1977 by adding two extra parameters (γ and ρ) to the basic parameters (K p , K i , K d ) of the PID controller, which clearly shows the high response speed of this construction compared to the classical version [15][16][17]. Generally, the PID controller is obtained by using the following fractional-order integro-differential equation [18]:…”

Section: The Fractional-order Pid Controllermentioning

confidence: 99%

A Numerical Implementation of Fractional-Order PID Controllers for Autonomous Vehicles

Batiha

Ababneh

Al-Nana

et al. 2023

Axioms

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In the context of reaching the best way to control the movement of autonomous cars linearly and angularly, making them more stable and balanced on different roads and ensuring that they avoid road obstacles, this manuscript chiefly aims to reach the optimal approach for a fractional-order PID controller (or PIγDρ-controller) instead of the already classical one used to provide smooth automatic parking for electrical autonomous cars. The fractional-order PIγDρ-controller is based on the particle swarm optimization (PSO) algorithm for its design, with two different approximations: Oustaloup’s approximation and the continued fractional expansion (CFE) approximation. Our approaches to the fractional-order PID using the results of the PSO algorithm are compared with the classical PID that was designed using the results of the Cohen–Coon, Ziegler–Nichols and bacteria foraging algorithms. The scheme represented by the proposed PIγDρ-controller can provide the system of the autonomous vehicle with more stable results than that of the PID controller.

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“…Converting a real-world problem into ordinary or partial differential equations is the essential task for mathematical modeling [4,5,7]. Differential equations, ordinary or partial, are equations relating unknown functions and some of their derivatives.…”

Section: Introductionmentioning

confidence: 99%

Solutions of linear and non-linear partial differential equations by means of tensor product theory of Banach space

Alshanti

2024

ejde

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In this article, we introduce an analytical method for solving both non-separable linear and non-linear partial differential equations, for which separation of variables method does not work. This method is based on the theory of tensor product in Banach spaces coupled with some properties of atoms operators. We provide some illustrative examples. For more information see https://ejde.math.txstate.edu/Volumes/2024/28/abstr.html

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Design Fractional-order PID Controllers for Single-Joint Robot Arm Model

Cited by 21 publications

References 18 publications

On a Weak Solution of a Fractional-order Temporal Equation

On a Weak Solution of a Fractional-order Temporal Equation

A Numerical Implementation of Fractional-Order PID Controllers for Autonomous Vehicles

Solutions of linear and non-linear partial differential equations by means of tensor product theory of Banach space

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