Parameter-Varying Feedforward Control: A Kernel-Based Learning Approach

TL;DR

The paper tackles high-precision tracking in mechatronic systems with parameter variations by learning parameter-varying feedforward controls directly from data. It combines iterative learning with kernel-regularized estimation in an RKHS to model arbitrary dependence on the LPV scheduling variable, enabling incorporation of physical insights via kernel design. The approach is validated experimentally on a belt-driven carriage, showing substantial reductions in RMS and peak tracking errors and diminished harmonic content compared to conventional LTI feedforward. This nonparametric, data-driven framework enhances robustness and task flexibility for LPV systems and has clear practical implications for industrial motion control.

Abstract

The increasing demands for high accuracy in mechatronic systems necessitate the incorporation of parameter variations in feedforward control. The aim of this paper is to develop a data-driven approach for direct learning of parameter-varying feedforward control to increase tracking performance. The developed approach is based on kernel-regularized function estimation in conjunction with iterative learning to directly learn parameter-varying feedforward control from data. This approach enables high tracking performance for feedforward control of linear parameter-varying dynamics, providing flexibility to varying reference tasks. The developed framework is validated on a benchmark industrial experimental setup featuring a belt-driven carriage.

Figures (16)

• Figure 1: Experimental setup considered, where the position of the belt-driven carriage $y$ is to be controlled using the input to the motor $u$.
• Figure 2: Control structure considered.
• Figure 3: Reference $r$ (), scaled reference velocity $\dot{r}$ (), and scaled reference acceleration ()applied to the experimental setup.
• Figure 4: During constant velocity (), the experimental tracking error for 5 repetitions of the reference in Figure \ref{['LPVILC:fig:ExperimentalReference']} with zero feedforward $f_j=0$ ()and their sample mean ()show highly repeatable position-dependent effects.
• Figure 5: Power spectrum of the tracking error during constant velocity for 5 times tracking the reference in Figure \ref{['LPVILC:fig:ExperimentalReference']} with zero feedforward $f_j=0$ ()and their sample mean ()shows highly repetitive behavior in spatial domain.

Theorems & Definitions (7)

• Example 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5
• Remark 6
• Remark 8