Tom Oomen

Iterative Data-Driven H-infinity Norm Estimation of Multivariable Systems With Application to Robust Active Vibration Isolation

This paper aims to develop a new data-driven H∞ norm estimation algorithm for model-error modeling of multivariable systems. An iterative approach is presented that requires significantly a fewer prior assumptions on the true system, hence it provides stronger guarantees in a robust control design. The iterative estimation algorithm is embedded in a robust control design framework with a judiciously selected uncertainty structure to facilitate high control performance. The approach is experimentally implemented on an industrial active vibration isolation system.

Well-Posed Model Uncertainty Estimation by Design of Validation Experiments

Abstract In deterministic model validation approaches, model errors can be attributed to both disturbances and model uncertainty, leading to an ill-posed problem formulation. The aim of this paper is to remedy the ill-posedness in model validation for robust control. A two-stage procedure is developed, where first an accurate, nonparametric, deterministic disturbance model is estimated from data, followed by the enforcement of averaging properties through an appropriate periodic experiment design. The proposed deterministic approach results in an asymptotically correctly estimated model uncertainty and is illustrated in a simulation example.

Constrained Iterative Feedback Tuning for Robust Control of a Wafer Stage System

Iterative feedback tuning (IFT) enables the data-driven tuning of controller parameters without the explicit need for a parametric model. It is known, however, that IFT can lead to nonrobust solutions. The aim of this paper is to develop an IFT approach with robustness constraints. A constrained IFT problem is formulated that is solved by introducing a penalty function. Essentially, the gradient estimates decompose into: 1) the well-known IFT gradients and 2) the gradients with respect to this penalty function. The latter are obtained through a nonparametric model of the controlled system. This guarantees robust stability while only requiring a nonparametric model. The experimental results obtained from the motion control systems of an industrial wafer scanner confirm enhanced performance with guaranteed robustness estimates.

Frequency-Domain ILC Approach for Repeating and Varying Tasks: With Application to Semiconductor Bonding Equipment

Iterative learning control (ILC) enables high performance for exactly repeating tasks in motion systems. Besides such tasks, many motion systems also exhibit varying tasks. In such cases, ILC algorithms are known to deteriorate performance. An example is given by bonding equipment in semiconductor assembly processes, which contains motion axes with tasks that can vary slightly. The aim of this paper is to develop an ILC approach that obtains high machine performance for possibly varying tasks, while enabling straightforward and effective industrial design rules. In particular, a frequency-domain-based design of ILC filters is pursued, which is combined with basis functions to cope with variations in tasks. Application to a high-speed axis of an industrial wire bonder shows that high servo performance is obtained for both repeating and varying tasks.

Enhancing feedforward controller tuning via instrumental variables: with application to nanopositioning

ABSTRACT Feedforward control enables high performance of a motion system. Recently, algorithms have been proposed that eliminate bias errors in tuning the parameters of a feedforward controller. The aim of this paper is to develop a new algorithm that combines unbiased parameter estimates with optimal accuracy in terms of variance. A simulation study is presented to illustrate the poor accuracy properties of pre-existing algorithms compared to the proposed approach. Experimental results obtained on an industrial nanopositioning system confirm the practical relevance of the proposed method.

Constrained Iterative Feedback Tuning for Robust High-Precision Motion Control

The aim of this paper is to extend iterative feedback tuning (IFT), which is a data- based approach for controller tuning, with robustness constraints. Hereto a constrained IFT problem is formulated that is solved by introducing a penalty function. Essentially, the gradient estimates decompose into (a) the well-known IFT gradients and (b) the gradients with respect to this penalty function. Experimental results obtained from the motion control systems of an industrial wafer scanner confirm enhanced performance with guaranteed robustness properties.

Analyzing iterations in identification with application to nonparametric H ∞ -norm estimation

Many iterative approaches in the field of system identification for control have been developed. Although successful implementations have been reported, a solid analysis with respect to the convergence of these iterations has not been established. The aim of this paper is to present a thorough analysis of a specific iterative algorithm that involves nonparametric H ∞ -norm estimation. The pursued methodology involves a novel frequency domain approach that addresses both additive stochastic disturbances and input normalization. The results of the convergence analysis are twofold: (1) the presence of additive disturbances introduces a bias in the estimation procedure, and (2) the iterative procedure can be interpreted as experiment design for H ∞ -norm estimation, revealing the value of iterations and limits of accuracy in terms of the Fisher information matrix. The results are confirmed by means of a simulation example.

Enhancing ℋ∞ Norm Estimation using Local LPM/LRM Modeling: Applied to an AVIS

Abstract Accurate uncertainty modeling is of key importance in high performance robust control design. The aim of this paper is to develop a new uncertainty modeling procedure that enhances the accuracy of the ℋ ∞ norm. A frequency response based approach is adopted. The key novelty of this paper is a new method to address the intergrid error using local parametric modeling methods. These local polynomial and rational models enhance the estimates at the discrete frequency grid. Moreover, the presented methods are shown to enhance the intergrid error estimate. This is illustrated using simulations and experiments on an industrial active vibration isolation system. Compared to the local polynomial models, local rational models are able to handle lightly-damped resonances using far fewer data points.

Batch-to-Batch Rational Feedforward Control: From Iterative Learning to Identification Approaches, With Application to a Wafer Stage

Feedforward control enables high performance for industrial motion systems that perform nonrepeating motion tasks. Recently, learning techniques have been proposed that improve both performance and flexibility to nonrepeating tasks in a batch-to-batch fashion by using a rational parameterization in feedforward control. This paper aims to unify these approaches through a single framework that provides transparent connections and clear differences between the alternatives. Experimental results on an industrial motion system confirm the theoretical findings and illustrate benefits of rational feedforward tuning in motion systems, including preactuation and postactuation.

ITERATIVE FEEDFORWARD TUNING APPROACH AND EXPERIMENTAL VERIFICATION FOR NANO-PRECISION MOTION SYSTEMS

Feedforward control can significantly improve the performance of industrial motion systems through compensation of the servo error induced by the reference signal. Recently, new feedforward tuning algorithms have been proposed that exploit measured data from previous tasks and a suitable feedforward parametrization to attain high servo performance. The aim of this paper is to formulate a design procedure for motion feedforward tuning. Experimental results on an industrial motion system illustrate the improvement in servo performance obtained by means of the proposed tuning procedure.