Iterative learning control with discrete-time nonlinear nonminimum phase models via stable inversion

TL;DR

This paper introduces ILILC, a novel iterative learning control framework combining Newton's method with stable inversion, enabling effective reference tracking in nonlinear, non-minimum phase discrete-time systems such as piezoactuators and robotic manipulators.

Contribution

The paper develops a new ILC synthesis method that integrates stable inversion with Newton's root finding, improving convergence in challenging nonlinear systems with unstable inverses.

Findings

ILILC converges where Newton-based ILC diverges.

ILILC reduces the number of trials needed for convergence by over 66%.

Validated in simulation with model errors and noise.

Abstract

Output reference tracking can be improved by iteratively learning from past data to inform the design of feedforward control inputs for subsequent tracking attempts. This process is called iterative learning control (ILC). This article develops a method to apply ILC to systems with nonlinear discrete-time dynamical models with unstable inverses (i.e. discrete-time nonlinear non-minimum phase models). This class of systems includes piezoactuators, electric power converters, and manipulators with flexible links, which may be found in nanopositioning stages, rolling mills, and robotic arms, respectively. As these devices may be required to execute fine transient reference tracking tasks repetitively in contexts such as manufacturing, they may benefit from ILC. Specifically, this article facilitates ILC of such systems by presenting a new ILC synthesis framework that allows combination of the principles of Newton's root finding algorithm with stable inversion, a technique for generating stable trajectories from unstable models. The new framework, called Invert-Linearize ILC (ILILC), is validated in simulation on a cart-and-pendulum system with model error, process noise, and measurement noise. Where preexisting Newton-based ILC diverges, ILILC with stable inversion converges, and does so in less than one third the number of trials necessary for the convergence of a gradient-descent-based ILC technique used as a benchmark.