Regular Papers

International Journal of Control, Automation and Systems 2021; 19(4): 1588-1596

Published online February 18, 2021

https://doi.org/10.1007/s12555-019-0295-y

© The International Journal of Control, Automation, and Systems

Iterative Learning Control for Fractional Order Linear Systems with Time Delay Based on Frequency Analysis

Yugang Wang, Fengyu Zhou*, Lei Yin, and Fang Wan

Shandong University

Abstract

To overcome the deficiencies of time delay in the repetitive control of fractional-order linear systems, Pdα -type iterative learning control (ILC) law and P & convolution-type ILC law are designed for input and state time delay, respectively. Convergence conditions are derived in frequency domain via contraction mapping principle. Besides, the convergence frequency domain of proposed feedback controllers is obtained over a finite frequency range to design the controllers effectively. Then, the effectiveness of the proposed theoretical schemes is demonstrated using two numerical examples. The influence of time delay is eliminated, and output trajectory convergence to the desired one is guaranteed. Moreover, the Nyquist diagram of transfer function G(s) and time delay variation are analyzed in frequency domain to reveal the influence of convergence on the system.

Keywords Fractional order linear system, frequency domain analysis, iterative learning control, time delay.

Article

Regular Papers

International Journal of Control, Automation and Systems 2021; 19(4): 1588-1596

Published online April 1, 2021 https://doi.org/10.1007/s12555-019-0295-y

Copyright © The International Journal of Control, Automation, and Systems.

Iterative Learning Control for Fractional Order Linear Systems with Time Delay Based on Frequency Analysis

Yugang Wang, Fengyu Zhou*, Lei Yin, and Fang Wan

Shandong University

Abstract

To overcome the deficiencies of time delay in the repetitive control of fractional-order linear systems, Pdα -type iterative learning control (ILC) law and P & convolution-type ILC law are designed for input and state time delay, respectively. Convergence conditions are derived in frequency domain via contraction mapping principle. Besides, the convergence frequency domain of proposed feedback controllers is obtained over a finite frequency range to design the controllers effectively. Then, the effectiveness of the proposed theoretical schemes is demonstrated using two numerical examples. The influence of time delay is eliminated, and output trajectory convergence to the desired one is guaranteed. Moreover, the Nyquist diagram of transfer function G(s) and time delay variation are analyzed in frequency domain to reveal the influence of convergence on the system.

Keywords: Fractional order linear system, frequency domain analysis, iterative learning control, time delay.

IJCAS
May 2024

Vol. 22, No. 5, pp. 1461~1759

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