Discrete-frequency convergence of iterative learning control for linear time-invariant systems with higher-order relative degree

Ruan, Xiaoe; Li, Zhaozhen; Bien, Zeungnam

doi:10.1007/s11633-015-0884-z

Cited by 10 publications

(5 citation statements)

References 12 publications

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“…e control design problem is to determine a new ILC law based on the model inversion such that the trial-to-trial error convergence occurs in j; that is, lim j→∞ ‖e j ‖ � 0 [41].…”

Section: Convergence Analysis Of the Proposed Learning Gainmentioning

confidence: 99%

New Iterative Learning Control Algorithm Using Learning Gain Based on σ Inversion for Nonsquare Multi-Input Multi-Output Systems

Noueili

Chagra

Ksouri

2018

Modelling and Simulation in Engineering

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Model inversion Iterative Learning Control (ILC) for a class of nonsquare linear time variant/invariant multi-input multi-output (MIMO) systems is considered in this paper. A new ILC algorithm is developed based on σ-right inversion of nonsquare learning gain matrices to resolve the matrix inversion problems appeared in the direct model inversion of nonsquare MIMO systems. Furthermore, a sufficient and necessary monotonic convergence condition is established. With rigorous analysis, the proposed ILC scheme guarantees the convergence of the tracking error. To prove the effectiveness and to illustrate the performance of the proposed approach for linear time-invariant (LTI) and time-varying nonsquare systems, two illustrative examples are simulated.

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“…e control design problem is to determine a new ILC law based on the model inversion such that the trial-to-trial error convergence occurs in j; that is, lim j→∞ ‖e j ‖ � 0 [41].…”

Section: Convergence Analysis Of the Proposed Learning Gainmentioning

confidence: 99%

New Iterative Learning Control Algorithm Using Learning Gain Based on σ Inversion for Nonsquare Multi-Input Multi-Output Systems

Noueili

Chagra

Ksouri

2018

Modelling and Simulation in Engineering

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“…Under an arbitrary initial error condition, this algorithm only made the system converge to a bounded range. For high relative degree SISO continuous systems, the presented ILC algorithm in [34] is based on the high relative degree, which utilized a form of multi-pulse compensation to suppress arbitrary initial shifts. For high relative degree linear discrete-time MIMO systems, [35] presented three ILC algorithms based on average operator to achieve complete tracking under the condition that the initial state vibrate slightly near a fixed point.…”

Section: Introductionmentioning

confidence: 99%

Iterative Learning Control for High Relative Degree Discrete-Time Systems with Random Initial Shifts

Chen,

Lu,

Yin

2023

IJACSA

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In this paper, an iterative learning control (ILC) strategy under compression mapping framework is presented for high relative degree discrete-time systems with random initial shifts. Firstly, utilizing the high relative degree of the system and difference term, a control law is designed and a p-order non-homogeneous linear difference equation is established. The appropriate control gain is selected according to the characteristics of solution of the difference equation and the initial shifts, so as to ensure that the high relative degree discrete-time system can reach a steady-state deviation output at a fixed time. Subsequently, a PD-type control law is employed to correct the fixed deviation of the system. Theoretical analysis indicates that this ILC strategy can ensure that the high relative degree systems achieve accurate tracking after the predefined time. Finally, the simulation experiments are conducted on a linear discretetime Multiple-Input Multiple-Output(MIMO) system with relative degree 1 and a Multiple-Input Single-Output(MISO) system with relative degree 2, respectively, and the results verify the effectiveness of the algorithm.

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“…The conventional learning compensators are of a proportional-type and/or a derivative-type feed-forward tracking error form and the principal exploitations are of sufficient conditions for guaranteeing either an asymptotical or a monotonic convergence in terms of the tracking error measured in kinds of norms such as lambda-norm, sup-norm, Lebesgue-p norm. [6][7][8][9] The outstretched studies are ranging from a higher-iteration-order compensator, 10 a higher-time-order compensator 11 to an iteration-varying length issue 12 and so on. The extensional focuses are including the robustness to a variety of uncertainties such as the initial state shifting, 13,14 the iteration-varying desired References 15,16 or the system parameters uncertainties, 17,18 and so forth.…”

Section: Introductionmentioning

confidence: 99%

Input–output‐driven gain‐adaptive iterative learning control for linear discrete‐time‐invariant systems

Liu

Ruan

2021

Intl J Robust & Nonlinear

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For a class of linear discrete-time-invariant systems repetitively operated in a finite time length, an iterative correction algorithm is exploited to identify the system Markov parameters with multi-operation inputs and outputs in obeying a criterion, of which the time order of the corrector is adaptive to the time order of the controller. Interactively, an adaptive iterative learning control is architected which composes the compensator with the approximated Markov parameters and the tracking error in sequentially minimizing a quadratic objective function of the tracking error and the compensation. Algebraic manipulation achieves that the Markov parameters correction error is monotonically declining without any step parameter selection. Further, a rigorous derivation clarifies that the time order of the learning compensator must agree to the relative degree of the system and the tracking error is linearly monotonously convergent if the Markov parameters correction error falls into an allowable range. Inspiringly, the methods and results release the confinement to both the correction and the learning ratios. In addition, a smaller learning ratio factor tolerates a larger Markov parameters correction error. Numerical experiments support the significance and the validity.

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Discrete-frequency convergence of iterative learning control for linear time-invariant systems with higher-order relative degree

Cited by 10 publications

References 12 publications

New Iterative Learning Control Algorithm Using Learning Gain Based on σ Inversion for Nonsquare Multi-Input Multi-Output Systems

New Iterative Learning Control Algorithm Using Learning Gain Based on σ Inversion for Nonsquare Multi-Input Multi-Output Systems

Iterative Learning Control for High Relative Degree Discrete-Time Systems with Random Initial Shifts

Input–output‐driven gain‐adaptive iterative learning control for linear discrete‐time‐invariant systems

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