Phase-aligned spatial iterative learning control with constrained Hermite reconstruction for position-periodic disturbance compensation

This paper addresses position-periodic disturbance compensation in high-precision rotary motion systems under variable-speed operation. Such disturbances are repeatable in angular position, but the cycle-to-cycle time–position mapping changes when the speed varies. When this mapping repeats, conventional time-domain iterative learning control (ILC) can in principle learn the corresponding temporal signal. The present work targets variable-speed operation with a cycle-varying time–position mapping, where a fixed elapsed-time index no longer corresponds consistently to angular position, while sampled-memory spatial ILC additionally requires reconstruction from nonuniform or sparse angular samples. To address these issues, a phase-aligned sampled-memory SILC framework with constrained Hermite reconstruction (CHR-SILC) is proposed. A spatial-bandwidth-scheduled robustness filter maintains an approximately constant learning bandwidth with respect to spatial order, and its equivalent delay is converted into an angular phase advance for memory querying. The learned feedforward signal is stored in sampled angular memory and reconstructed online by a local CHR operator with periodic neighbor selection, outer-interval slope estimation, and slope-magnitude limiting. A contraction-based robustness analysis gives a sufficient condition for nominal convergence and characterizes practical uniform ultimate boundedness under bounded implementation residuals and cycle-varying uncertainty. Reconstruction-layer evaluations show reduced reconstruction errors under the tested sparse and nonuniform sampling conditions. Experiments on a turntable system demonstrate reduced tracking errors under nominal- and variable-speed operation, with low measured online computational cost and retained relative error-suppression capability under the tested load variation.