Iterative learning control (ILC) approaches often exhibit poor extrapolation properties with respect to exogenous signals, such as setpoint variations. This brief introduces rational basis functions in ILC. Such rational basis functions have the potential to both increase performance and enhance the extrapolation properties. The key difficulty that is associated with these rational basis functions lies in a significantly more complex optimization problem when compared with using preexisting polynomial basis functions. In this brief, a new iterative optimization algorithm is proposed that enables the use of rational basis functions in ILC for single-input single-output systems. An experimental case study confirms the advantages of rational basis functions compared with preexisting results, as well as the effectiveness of the proposed iterative algorithm.

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Rational Basis Functions in Iterative Learning Control—With Experimental Verification on a Motion System

In this article, we discuss iterative learning control (ILC) for systems with input/output (i/o) basis functions. First, we show that various different ILC formulations in the literature can be cap...

Using basis functions in iterative learning control : analysis and design theory

https://pure.tue.nl/ws/files/77792274/Mech2017_v7.pdf

On inversion-based approaches for feedforward and ILC

We consider the problem of synthesis of iterative learning control (ILC) schemes for constrained linear systems executing a repetitive task. The ILC problem with affine constraints and quadratic objective functions is formulated as a convex quadratic program, for which there exist computationally efficient solvers. The key difference between standard convex optimization and the corresponding constrained ILC problem is that each iteration in the latter requires an experiment run. We implement an interior-point-type method to reduce the number of iterations (and hence the number of experiment runs). We discuss the system-theoretic interpretations of the resulting optimization problem that lead to reductions in computational complexity and compare the performance of the implementation based on the interior-point method to another approach based on the active set method on a simulation example. We demonstrate the technique on a prototype wafer stage system with actuator saturation constraints and l2 norm of the tracking error as the objective function. The key contribution of this paper is the systematic use of numerical tools from constrained convex optimization in the ILC design.

Optimization-Based Constrained Iterative Learning Control

http://www.mate.tue.nl/mate/pdfs/11373.pdf

MIMO feed-forward design in wafer scanners using a gradient approximation-based algorithm

In this paper, the feedforward controller design problem for high-precision electromechanical servo systems that execute finite time tasks is addressed. The presented procedure combines the selection of the fixed structure of the feedforward controller and the optimization of the controller parameters by iterative trials. A linear parametrization of the feedforward controller in a two-degree-of-freedom control architecture is chosen, which results in a feedforward controller that is applicable to a class of motion profiles as well as in a convex optimization problem, with the objective function being a quadratic function of the tracking error. Optimization by iterative trials avoids the need for detailed knowledge of the plant, achieves the controller parameter values that are optimal with respect to the actual plant, and allows for the adaptation to possible variations that occur in the plant dynamics. Experimental results on a high-precision wafer stage and a desktop printer illustrate the procedure.

http://www.mate.tue.nl/mate/pdfs/9097.pdf

RL Rob Tousain

Papers

Fixed Structure Feedforward Controller Design Exploiting Iterative Trials: Application to a Wafer Stage and a Desktop Printer