A PD-type Iterative Learning Control Algorithm for One-dimension Linear Wave Equation

Hamidaoui, Meryem; Shao, Cheng; Haouassi, Samia

doi:10.1007/s12555-019-0094-5

Cited by 18 publications

(8 citation statements)

References 25 publications

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“…Step 1. Obtain the model parameters of the controlled object and transform them into a discrete time-invariant system as shown in equation (1). If there is a solution, then go to the next process and adopt gain and learning laws applied.…”

Section: Control Algorithmmentioning

confidence: 99%

“…Step 2. Design iterative learning fault-tolerant control law in the form of formula (11), and apply LMI toolbox in MATLAB to solve eorems 2 or 3 according to the parameters given in formula (1), and obtain the parameters K1 and K2 of the system with and without uncertainty in formula (1), respectively. If there is a feasible solution, proceed to the next step; otherwise, redesign.…”

Section: Control Algorithmmentioning

confidence: 99%

“…e study in [1] designed a PD-type iterative learning control algorithm for a linear continuous repetition system based on the 2D method and obtained the system with accurate tracking control; the authors of [2,3] combined with the stability theory discrete process designed an iterative learning controller. e output error of the system converges monotonically, and the performance in the direction of the batch axis gradually improves with the repeated process.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Design and Implementation of Novel LMI‐Based Iterative Learning Robust Nonlinear Controller

et al. 2021

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An iterative learning robust fault-tolerant control algorithm is proposed for a class of uncertain discrete systems with repeated action with nonlinear and actuator faults. First, by defining an actuator fault coefficient matrix, we convert the iterative learning control system into an equivalent unknown nonlinear repetitive process model. Then, based on the mixed Lyapunov function approach, we describe the stability of the nonlinear repetitive mechanism on time and trial indices and have appropriate conditions for the repeated control system’s stability in terms of linear matrix inequality theory. Through LMI techniques, we have obtained satisfactory results and controller stability, and robustness against fault tolerance is also discussed in detail. Finally, the simulation results of the output tracking control of the two exemplary models verify the effectiveness of the proposed algorithm.

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Section: Control Algorithmmentioning

confidence: 99%

Section: Control Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design and Implementation of Novel LMI‐Based Iterative Learning Robust Nonlinear Controller

et al. 2021

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“…e paper [39] found that even though the learning algorithm is theoretically convergent when it gets an enormous parameter value, the upper bound of the error during the initial stage of system operation often exceeds the allowable error range of practical engineering. To avoid the above defects of the λ norm, the papers [40,41] presented the convergence of PD iterative learning control algorithm in the sense of PD measurement in the definite upper norm [42,43]. It is found that the learning algorithm is convergent only in a subinterval of the system running time interval.…”

Section: Introductionmentioning

confidence: 99%

An Accelerated Error Convergence Design Criterion and Implementation of Lebesgue-p Norm ILC Control Topology for Linear Position Control Systems

Riaz

Hui

Waqas

et al. 2021

Mathematical Problems in Engineering

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Traditional and typical iterative learning control algorithm shows that the convergence rate of error is very low for a class of regular linear systems. A fast iterative learning control algorithm is designed to deal with this problem in this paper. The algorithm is based on the traditional P-type iterative learning control law, which increases the composition of adjacent two overlapping quantities, the tracking error of previous cycle difference signals, and the current error difference. Using convolution to promote Young inequalities proved strictly that, in terms of Lebesgue-p norm, when the number of iterations tends to infinity, the tracking error converges to zero in the system and presents the convergence condition of the algorithm. Compared with the traditional P-type iterative learning control algorithm, the proposed algorithm improves convergence speed and evades the defect using the norm metric’s tracking error. Finally, the validation of the effectiveness of the proposed algorithm is further proved by simulation results.

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“…The ILC has become an alternative method to solve the control problem, since it is simple, quick, efficient, and has perfect tracking performance. ILC has been used to track a settled target in many systems, such as fractional systems [13], ordinary difference systems [14,15], and distributed parameter systems or partial differential systems [16,17]. However, there are a few subjects on ILC for partial difference systems [18,19], where the authors consider the parabolic PDS.…”

Section: Introductionmentioning

confidence: 99%

ILC for Non-Linear Hyperbolic Partial Difference Systems

Hamidaoui

Shao

2021

Mathematics

Self Cite

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This paper discusses the iterative learning control problem for a class of non-linear partial difference system hyperbolic types. The proposed algorithm is the PD-type iterative learning control algorithm with initial state learning. Initially, we introduced the hyperbolic system and the control law used. Subsequently, we presented some dilemmas. Then, sufficient conditions for monotone convergence of the tracking error are established under the convenient assumption. Furthermore, we give a detailed convergence analysis based on previously given lemmas and the discrete Gronwall’s inequality for the system. Finally, we illustrate the effectiveness of the method using a numerical example.

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A PD-type Iterative Learning Control Algorithm for One-dimension Linear Wave Equation

Cited by 18 publications

References 25 publications

Design and Implementation of Novel LMI‐Based Iterative Learning Robust Nonlinear Controller

Design and Implementation of Novel LMI‐Based Iterative Learning Robust Nonlinear Controller

An Accelerated Error Convergence Design Criterion and Implementation of Lebesgue-p Norm ILC Control Topology for Linear Position Control Systems

ILC for Non-Linear Hyperbolic Partial Difference Systems

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