Combined H∞-feedback Control and Iterative Learning Control Design with Application to Nanopositioning Systems

Brian E. Helfrich
Chibum Lee
Douglas A. Bristow, Missouri University of Science and Technology
Jingyan Dong
Srinivasa M. Salapaka
Placid M. Ferreira
X. H. Xiao
Andrew G. Alleyne

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This paper examines a coordinated feedback and feedforward control design strategy for precision motion control (PMC) systems. It is assumed that the primary exogenous signals are repeated; including disturbances and references. Therefore, an iterative learning control (ILC) feedforward strategy can be used. The introduction of additional non-repeating exogenous signals, including disturbances, noise, and reset errors, necessitates the proper coordination between feedback and feedforward controllers to achieve high performance. A novel ratio of repeated versus non-repeated signal power in the frequency domain is introduced and defined as the repetitive-to-non-repetitive (RNR) ratio. This frequency specific ratio allows for a new approach to delegating feedback and feedforward control efforts based on RNR value. A systematic procedure for control design is given whereby the feedback addresses the non-repeating exogenous signal content ( RNR < 0 dB}) and the feedforward ILC addresses the repeating signal content ( RNR > dB). To illustrate the design approach, two case studies using different nano-positioning devices are given.