Data-driven frequency-domain iterative learning control with transfer learning

Data-driven iterative learning control (ILC) can achieve improved tracking performance over model-based ILC by eliminating the fitting error from parametric system representations. Existing data-driven approaches in frequency domain take advantage of the affordability and speed associated with acquiring non-parametric frequency response function data for effective learning. However, the quality of data significantly influences the achievable performance. Additionally, a notable drawback is that learning is reset whenever the tracked trajectory changes, despite having learned similar frequency contents before. Extending these approaches to multivariate systems with non-negligible coupling is also not straightforward. This paper aims to address the aforementioned challenges in data-driven ILC by employing spectral analysis (SA), which improves the learned data-driven inversion by mitigating the measurement noise. Fast and robust convergence is made possible through an iteration-varying learning gain. Also proposed is a transfer learning strategy in the frequency domain, wherein the inversion learned in specific frequency bin(s) will be preserved and utilized to expedite convergence in subsequent tasks. The presented ILC algorithm based on SA naturally extends to the multi-input multi-output (MIMO) framework, and the convergence can be ensured by complex-valued matrix analysis. The methodology is experimentally validated on a galvanometer for the SISO case and an H-type dual-drive gantry system for the MIMO case, demonstrating enhanced performance, transfer learning capabilities, and applicability to MIMO systems.