Rational Basis Functions in Iterative Learning Control—With Experimental Verification on a Motion System

Abstract

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Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems

“…1(a), see (102) . The theoretical framework is further extended towards input shaping (103) and rational feedforward structures in (104)- (106) , which have as key advantage that these can exactly compensate non-minimum phase dynamics, see (107) for a detailed exposition, and also (95) (108) (109) for further details and applications. Finally, a strongly related approach that further connects to system identification in Sec.…”

Using iterative learning control with basis functions to compensate medium deformation in a wide-format inkjet printer

“…Norm-optimal ILC is an important class of ILC algorithms, e.g., [1,21,15,2,19], where f jþ1 is determined from the solution of an optimization problem. Norm-optimal ILC with basis functions [4,5,34,33] is an extension of the norm-optimal ILC framework, where the feed forward is generated using a set of basis functions. The optimization criterion for the present paper defined as follows.…”

“…In the present paper, Fðh j Þ is chosen linearly in h j , such that e z jþ1 is linear in h j . Consequently, the performance criterion (7) is quadratic in h jþ1 and hence an analytic solution to (8) exists [5,34]. The structure of Fðh j Þ is part of the controller design and presented in Section 5.…”

“…Although ILC is known to achieve very good tracking performance, the learned command signal is optimal for a specific task only [5], extrapolation to other tasks can lead to significant performance degradation [34,18].…”

“…The earlier approach in [4] cannot be applied directly since the controller structure is not suitable for the additional non-real-time measurements, moreover, the extrapolation capabilities are not investigated. The results in [5] employ a more complex set of basis functions than considered here, to further increase performance and extrapolation capabilities. These results however, only include experimental results on a simple laboratory-scale motion system, and are more suited for a different class of systems than considered in this paper.…”