Tracking control of non-minimum phase systems: a kernel-based approach

Abstract

Feedforward control with model inversion is a widely-used solution for high-precision output tracking. However, because inverting a non-minimum phase model generates unbounded control input, model-inversion only applies to limited types of systems. This paper presents a new non-parametric pseudo-inversion approach to design bounded optimal control input with desirable properties for arbitrary types of systems. Closed-form equations are presented for the batch (full preview) and recursive (limited preview) implementations of this approach, and its performance is compared against existing pseudo-inversion methods in benchmark numerical examples. Furthermore, the practical implementation of the proposed method is demonstrated by designing a feedforward controller for a commercial 3-Dimensional (3D) printer. The results show that the proposed approach effectively compensates for the structural vibrations of the printer, preventing layer-shifting errors that usually happen during high-speed printing.

Keywords:

• Feedforward control
• nonminimum phase system
• Bayesian estimation
• model inversion
• kernel estimation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability

All the codes and data that support the findings of this study are openly available in DDM UVIC repository at https://github.com/DDM-UVIC/Tracking-Control-of-Non-minimum-Phase-Systems-A-Kernel-based-Approach.

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under the Discovery Grant Program.