Fractional-order controller design for oscillatory fractional time-delay systems based on the numerical inverse Laplace transform algorithms
type: Item
instance of: scholarly article
title: Fractional-order controller design for oscillatory fractional time-delay systems based on the numerical inverse Laplace transform algorithms
zbMATH Open document ID: 1394.93114
DOI: 10.1155/2015/917382
author: Lu Liu
author: Feng Pan
author: Dingyu Xue
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: Fractional-order time-delay system is thought to be a kind of oscillatory complex system which could not be controlled efficaciously so far because it does not have an analytical solution when using inverse Laplace transform. In this paper, a type of fractional-order controller based on numerical inverse Laplace transform algorithm INVLAP was proposed for the mentioned systems by searching for the optimal controller parameters with the objective function of ITAE index due to the verified nature that fractional-order controllers were the best means of controlling fractional-order systems. Simulations of step unit tracking and load-disturbance responses of the proposed fractional-order optimal \(P I^\lambda D^\mu\) controller (FOPID) and corresponding conventional optimal PID (OPID) controller have been done on three typical kinds of fractional time-delay system with different ratio between time delay (\(L\)) and time constant (\(T\)) and a complex high-order fractional time delay system to verify the availability of the presented control method.
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 93C80
zbMATH DE Number: 6927555
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/917382
OpenAlex ID: W2077941203
Wikidata QID: Q59120267
cites work: The CRONE control of resonant plants: application to a flexible transmission
cites work: Q4250595
cites work: Fractional-order systems and controls. Fundamentals and applications
cites work: Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review
cites work: FARIMA with stable innovations model of Great Salt Lake elevation time series
cites work: Tuning of fractional PID controllers with Ziegler-Nichols-type rules
cites work: On fractional \(PI^{\lambda }\) controllers: Some tuning rules for robustness to plant uncertainties
cites work: Application of numerical inverse Laplace transform algorithms in fractional calculus
cites work: A numerical algorithm for stability testing of fractional delay systems
cites work: Advances in Fractional Calculus
cites work: Approximate formulae for numerical inversion of Laplace transforms
cites work: Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers
cites work: Nelder-Mead Simplex Modifications for Simulation Optimization
description: scientific article; zbMATH DE number 6927555