Tae Tom Oomen

Connecting System Identification and Robust Control for Next-Generation Motion Control of a Wafer Stage

Next-generation precision motion systems are lightweight to meet stringent requirements regarding throughput and accuracy. Such lightweight systems typically exhibit lightly damped flexible dynamics in the controller cross-over region. State-of-the-art modeling and motion control design procedures do not deliver the required model complexity and fidelity to control the flexible dynamical behavior. The aim of this paper is to develop a combined system identification and robust control design procedure for high performance motion control and apply it to a wafer stage. Hereto, new connections between system identification and robust control are employed. The experimental results confirm that the proposed procedure significantly extends existing results and enables next-generation motion control design.

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

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.

Design framework for high-performance optimal sampled-data control with application to a wafer stage

Control design for high-performance sampled-data systems with continuous time performance specifications is investigated. Direct optimal sampled-data control design explicitly addresses both the digital controller implementation and the intersample behaviour. The model that is required for direct optimal sampled-data control should evolve in continuous time. Accurate models for control design, however, generally evolve in discrete time since they are obtained by means of system identification techniques. The purpose of this paper is the development of a control design framework that enables the usage of models delivered by system identification techniques, while explicitly addressing both the digital controller implementation and the intersample behaviour aspects. Thereto, the incompatibility of the models delivered by system identification techniques and the models used in sampled-data control is analysed. To use models delivered by system identification techniques in conjunction with optimal sampled-data control, tools are employed that stem from multirate system theory. For the actual control design, key theoretical issues in sampled-data control, which include the linear periodically time-varying nature of sampled-data systems, are addressed. The control design approach is applied to the -optimal feedback control design of an industrial high-performance wafer scanner. Experimental results illustrate the necessity of addressing the intersample behaviour in high-performance control design.

Optimality and flexibility in Iterative Learning Control for varying tasks

Iterative Learning Control (ILC) can significantly enhance the performance of systems that perform repeating tasks. However, small variations in the performed task may lead to a large performance deterioration. The aim of this paper is to develop a novel ILC approach, by exploiting rational basis functions, that enables performance enhancement through iterative learning while providing flexibility with respect to task variations. The proposed approach involves an iterative optimization procedure after each task, that exploits recent developments in instrumental variable-based system identification. Enhanced performance compared to pre-existing results is proven theoretically and illustrated through simulation examples.

Brief paper: Suppressing intersample behavior in iterative learning control

Iterative Learning Control (ILC) is a control strategy to improve the performance of digital batch repetitive processes. Due to its digital implementation, discrete time ILC approaches do not guarantee good intersample behavior. In fact, common discrete time ILC approaches may deteriorate the intersample behavior, thereby reducing the performance of the sampled-data system. In this paper, a generally applicable multirate ILC approach is presented that enables to balance the at-sample performance and the intersample behavior. Furthermore, key theoretical issues regarding multirate systems are addressed, including the time-varying nature of the multirate ILC setup. The proposed multirate ILC approach is shown to outperform discrete time ILC in realistic simulation examples.

Optimally conditioned instrumental variable approach for frequency-domain system identification

Accurate frequency-domain system identification demands for reliable computational algorithms. The aim of this paper is to develop a new algorithm for parametric system identification with favorable convergence properties and optimal numerical conditioning. Recent results in frequency-domain instrumental variable identification are exploited, which lead to enhanced convergence properties compared to classical identification algorithms. In addition, bi-orthonormal polynomials with respect to a data-dependent bi-linear form are introduced for system identification. Hereby, optimal numerical conditioning of the relevant system of equations is achieved. This is shown to be particularly important for the class of instrumental variable algorithms, for which numerical conditioning is typically quadratic compared to alternative frequency-domain identification algorithms. Superiority of the proposed algorithm is demonstrated by means of both simulation and experimental results.

System Identification and Low-Order Optimal Control of Intersample Behavior in ILC

Although iterative learning control (ILC) algorithms enable performance improvement for batch repetitive systems using limited system knowledge, at least an approximate model is essential. The aim of the present technical note is to develop an ILC framework for sampled-data systems, i.e., by incorporating the intersample response. Hereto, a novel parametric system identification procedure and a low-order optimal ILC controller synthesis procedure are presented that both incorporate the intersample behavior in a multirate framework. The results include i) improved computational properties compared to prior optimization-based ILC algorithms, and ii) improved performance of sampled-data systems compared to common discrete time ILC. These results are confirmed in a simulation example.

Estimating disturbances and model uncertainty in model validation for robust control

Deterministic approaches to model validation for robust control are investigated. In common deterministic model validation approaches, a trade-off between disturbances and model uncertainty is present, resulting in an ill-posed problem. In this paper, an approach to model validation is presented that attempts to remedy the ill-posedness. By employing accurate, non-parametric, deterministic disturbance models in conjunction with enforcing averaging properties of deterministic disturbances, a novel framework enabling model validation for robust control is obtained. The approach results in a realistically estimated model uncertainty and a disturbance model, and is illustrated in a simulation example.

Robust-Control-Relevant Coprime Factor Identification with Application to Model Validation of a Wafer Stage

Abstract The performance of robust controllers depends on the set of candidate plants, but at present this intimate connection is untransparent. The aim of this paper is to construct a model set to improve the performance in a subsequent robust control design. Analysis of uncertainty structures reveals that there is an unexploited freedom in the realization of coprime factorizations in the dual-Youla uncertainty structure. The main result of this paper is a specific coprime factorization that results in model sets that are tuned for robust control. The presented coprime factorization can be identified directly from data. Application of the proposed methodology to an industrial wafer stage reveals improved model validation results.

Robust-control-relevant coprime factor identification: A numerically reliable frequency domain approach

In approximate identification, the goal of the model should be taken into account when evaluating model quality. The purpose of this paper is the development of a system identification procedure, resulting in model sets that are suitable for subsequent robust control design. Incorporation of control relevance in the procedure results in a closed-loop frequency response-based multivariable system identification procedure. The model is represented as a coprime factorization, enabling the usage of stable model perturbations. The main result is the direct estimation of control-relevant coprime factors, exploiting knowledge of a stabilizing controller during the identification experiment. A numerically reliable iterative algorithm is devised, which is illustrated by means of experimental results.