Rma Robbert van Herpen

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.

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.

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.

Inferential motion control: Identification and robust control with unmeasured performance variables

Next-generation motion systems are expected to exhibit dominant flexible dynamical behavior. As a result, a dynamic relation between the measured variables and the performance variables is inevitable. The aim of the present paper is i) to develop a control framework to deal with unmeasured performance variables and ii) to implement the proposed methodology on a prototype experimental setup. A system identification for robust inferential control approach is pursued. Indeed, in the case that the performance variables cannot be measured directly, then these can be inferred from the measurements by means of a model. Experimental results i) confirm that prior approaches that aim at an improved response in terms of the measured variables can result in a deteriorated performance and ii) reveal that the proposed framework enables high performance robust inferential control.

Identification and visualization of robust-control-relevant model sets with application to an industrial wafer stage

The performance of robust controllers hinges on the underlying model set. However, at present it is unclear which properties of the physical system should be accurately identified to enable high performance robust control. The aim of this paper is to clarify the intimate relation between quality of certain physical system properties and the resulting control performance. Hereto, an extended robust-control-relevant system identification methodology and a new visualisation approach is developed that is applicable to multivariable systems. The developed methodology is applied to an industrial wafer stage system. Experimental results indeed confirm that the developed techniques contribute to clarifying the complex relation between system identification and robust control.

A robust-control-relevant perspective on model order selection

High-performance robust control hinges on explicit compensation of performance-limiting system phenomena. Hereto, such phenomena need to be described with high fidelity by the model set. Clearly, this demands for a delicate mutual selection of the nominal model and the uncertainty bound. Both should have a limited complexity to enable successful controller synthesis and implementation. The aim of this paper is to investigate model order selection for robust-control-relevant identification. Therefore, it is investigated how the worst-case performance that is associated with a model set is influenced by the complexity of the nominal model and the uncertainty bound. It turns out that, using a judiciously selected uncertainty coordinate frame, worst-case performance can be made invariant for the order of the uncertainty bound. Nevertheless, dynamic uncertainty modeling may still be worthwhile when accounting for approximations that are commonly made in robust-control relevant identification, as is analyzed in this paper as well.

On numerically reliable frequency-domain system identification: new connections and a comparison of methods

Frequency domain identification of complex systems imposes important challenges with respect to numerically reliable algorithms. This is evidenced by the use of different rational and data-dependent basis functions in the literature. The aim of this paper is to compare these different methods and to establish new connections. This leads to two new identification algorithms. The conditioning and convergence properties of the considered methods are investigated on simulated and experimental data. The results reveal interesting convergence differences between (nonlinear) least squares and instrumental variable methods. In addition, the results shed light on the conditioning associated with so-called frequency localising basis functions, vector fitting algorithms, and (bi)-orthonormal basis functions.

Numerically Reliable Frequency-Domain Estimation of Transfer Functions: A Computationally Efficient Methodology

Abstract Parametric identification of lightweight motion systems requires solving large weighted least-squares problems. The numerical conditioning of such problems, which determines the solution accuracy, crucially depends on the polynomial basis that is used to formulate the problem. The aim of this paper is to optimize numerical conditioning by constructing a polynomial basis that is orthonormal with respect to a data-dependent inner product. This basis is constructed in a computationally efficient way by exploiting underlying structure of the problem, related to polynomial recurrence relations. Through a confrontation with an industrial system with large dynamical complexity, numerical accuracy and efficiency of the method are confirmed.

Experimental evaluation of robust-control-relevance: A confrontation with a next-generation wafer stage

Control-relevance is a paradigm that interconnects identification with successive model-based control design. Hereby, the current controller, used to conduct identification experiments, is an important factor to success in the design of a new, improved controller. The aim of this paper is to investigate the role of the experimental controller in robust-control-relevant modeling. Such a study is sensible only when unnecessary conservatism is prevented in the construction of perturbed model sets. Hereto, this paper establishes a model uncertainty description that transparently connects to the imposed robust performance criterion. By confronting the developed approach with a next-generation industrial wafer stage, the important role of the experimental controller during modeling for robust control is clarified indeed. It turns out that only after an increase of performance in successive control design iterations, construction of higher order model sets becomes both feasible and significant. As such, in pursuit of performance optimization up to fundamental limits, the experimental controller ensures a gradual extrapolation of the current experimental conditions.

Enhancing performance through multivariable weighting function design in ℋ − loop-shaping: with application to a motion system

The quality of model-based controllers hinges on a careful specification of performance and robustness requirements. In typical norm-based control designs, these performance and robustness requirements are specified in a scalar optimization criterion, even for complex multivariable systems. This paper aims to develop a novel and systematic approach for the formulation of this optimization criterion for complex multivariable systems. Hereto, characteristics of the underlying system are exploited. In contrast to pre-existing approaches that typically lead to multiloop SISO weighting functions, the proposed approach enables the design of multivariable weighting functions. Experimental results confirm that the proposed procedure significantly improves the performance of an industrial motion system compared to earlier approaches.