Combined $H _{\infty}$-Feedback Control and Iterative Learning Control Design With Application to Nanopositioning Systems

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 ≫ 0 dB). To illustrate the design approach, two case studies using different nano-positioning devices are given.