Polynomial Iterative Learning Control (ILC) Tracking Control Design for Uncertain Repetitive Continuous-Time Linear Systems Applied to an Active Suspension of a Car Seat

Selma Ben Attia, Sultan Alzahrani (), Saad Alhuwaimel, Salah Salhi and Houssem Eddine Ouerfelli
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Selma Ben Attia: National Engineering School of Tunis, LR11ES20 Analysis, Conception and Control of Systems Laboratory, University Tunis El Manar, Tunis 1002, Tunisia
Sultan Alzahrani: King Abdulaziz City for Sciences and Technology (KACST), Riyadh 11442, Saudi Arabia
Saad Alhuwaimel: King Abdulaziz City for Sciences and Technology (KACST), Riyadh 11442, Saudi Arabia
Salah Salhi: National Engineering School of Tunis, LR11ES20 Analysis, Conception and Control of Systems Laboratory, University Tunis El Manar, Tunis 1002, Tunisia
Houssem Eddine Ouerfelli: National Engineering School of Tunis, LR11ES20 Analysis, Conception and Control of Systems Laboratory, University Tunis El Manar, Tunis 1002, Tunisia

Mathematics, 2024, vol. 12, issue 16, 1-22

Abstract: This paper addresses the issue of polynomial iterative learning tracking control (Poly-ILC) for continuous-time linear systems (LTI) operating repetitively. It explores the design of an iterative learning control law by examining the stability along the pass theory of 2D repetitive systems. The obtained result is a generalization of the notion of stability along passages, taking into account transient performances. To strike a balance between stability along passages and transient performance, we extend our developed result in the discrete case, relying on some numerical tools. Specifically, in this work we investigate the convergence of tracking error with given learning controller gains. The key contribution of this structure of control lies in establishing an LMI (linear matrix inequality) condition that ensures both pole placement according to desired specifications and the convergence of output error between iterations. Furthermore, new sufficient conditions for stability regions along the pass addressing the tracking problem of differential linear repetitive processes are developed. Numerical results are provided to demonstrate the effectiveness of the proposed approaches.

Keywords: continuous-time linear repetitive system; iterative learning control (ILC); stability along the pass (SAP); D-stability regions; polynomial-type ILC; tracking control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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