Suppressing Position-Dependent Disturbances in Repetitive Control: With Application to a Substrate Carrier System

Abstract

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Gaussian Process Repetitive Control With Application to an Industrial Substrate Carrier System With Spatial Disturbances

“…Remark 3: In contrast to existing spatial RC approaches, the nonequidistant data are used to estimate a distribution over (periodic) function, whereas traditional approaches either require interpolation in a discrete buffer [17]- [19] or require to reformulate the systems in the spatial domain resulting in time-varying dynamics [2], [4]. This article presents a systematic design approach for continuous buffers without interpolation while also removing the need for complex timevarying models.…”

“…What remains is to select a suitable kernel function that represents the spatial disturbance prior knowledge for GP regression. The kernel function imposes prior knowledge on the disturbance function d, as shown in (15) and (17).…”

“…Spatial disturbance models have been developed for RC [1], [16], where the disturbance is modeled as a nonlinear potentially time-varying parametric model. Alternatively, in [17]- [19], a discrete buffer is presented, which contains position information to model the spatial disturbance. These discrete buffers require additional interpolation to deal with the inherently nonequidistant data points in the spatial domain.…”

Gaussian Process Repetitive Control for Suppressing Spatial Disturbances

“…The main challenge arising in the spatial domain, is that observations are inherently nonequidistantly distributed due to speed variations. Hence, a fixed memory loop as in traditional RC is not suitable, see Mooren et al (2020). Therefore, an alternative solution using a GP, essentially estimating a continuous memory loop, is presented here.…”

A Gaussian Process Approach to Multiple Internal Models in Repetitive Control

“…Engineered systems become increasingly complex, leading to disturbances that originate from different domains, e.g., time, position, or commutation angle [4], [5], referred to as multi-dimensional disturbances. Examples include an industrial printer where a rotating belt generates a disturbance that is periodic in the belt-position domain [6], where at the same time the print head generates a disturbance that is periodic in time due to its repeating motion [7]. Thermo-mechanical problems also appear, e.g., in wafer-stages with non-perfect This research has received funding from the European Union H2020 program ECSEL-2016-1 under grant n. 737453 (I-MECH), and the ECSEL Joint Undertaking under grant agreement n. 101007311 (IMOCO4.E) commutations functions that induce spatial disturbances, while at the same time illumination of the wafer induces a thermal deformation [8], [9].…”