An Integral and MRAC–Based Approach to the Adaptive Stabilisation of a Class of Linear Time–Delay Systems with Unknown Parameters

The design of a novel strategy based on the model reference adaptive control method for the stabilisation of a second-order linear time-delay system with unknown parameters is presented. The proposed approach is developed under the assumption that only one state of the system is available, and the s...

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Bibliographic Details
Published in:International journal of applied mathematics and computer science 2024-03, Vol.34 (1), p.81-91
Main Authors: Ramírez Jerónimo, Luis Felipe, Saldivar, Belem, Aguilar-Ibañez, Carlos, Acosta, José Ángel
Format: Article
Language:English
Subjects:
Adaptation
Adaptive control
backstepping
Chemical reactors
Control methods
Controllers
Design parameters
integral operator
Mathematical models
Model reference adaptive control
MRAC
Time delay systems
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Summary:The design of a novel strategy based on the model reference adaptive control method for the stabilisation of a second-order linear time-delay system with unknown parameters is presented. The proposed approach is developed under the assumption that only one state of the system is available, and the sign of the control gain is known. First, the integral operator is applied to obtain a new representation of the original system, where the whole state is known. The use of the integral operator decomposes the control problem into two subproblems that are solved by using the model reference adaptive control method and the backstepping procedure. The effectiveness of the proposed approach is illustrated through an academic example and a practical application case regarding a chemical reactor recycle system.
ISSN:1641-876X
2083-8492
DOI:10.61822/amcs-2024-0006