A robust-control-relevant perspective on model order selection

Abstract onl

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

A robust-control-relevance 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

Bi-orthonormal basis functions for improved frequency-domain system identification

Frequency-domain identification algorithms are considered. The aim of this paper is to develop a new algorithm that i) converges to a minimum of the objective function, and ii) possesses optimal numerical properties. Hereto, recent results in instrumental variable system identification are exploited. In addition, a new bilinear form is proposed that leads to the novel introduction of bi-orthonormal polynomials in system identification. The combination of these aspects leads to the desired convergence properties in conjunction with optimal numerical conditioning. The results are supported by means of a simulation example

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

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 coprimefactorizations in the dual-Youla uncertainty structure. The main result of this paper is aspecific coprime factorization that results in model sets that are tuned for robust control. Thepresented coprime factorization can be identified directly from data. Application of the proposedmethodology to an industrial wafer stage reveals improved model validation results

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

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

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 coprimefactorizations in the dual-Youla uncertainty structure. The main result of this paper is aspecific coprime factorization that results in model sets that are tuned for robust control. Thepresented coprime factorization can be identified directly from data. Application of the proposedmethodology to an industrial wafer stage reveals improved model validation results

SISO-Closed-Loop Identifikation: eine Toolbox für den Einsatz in der industriellen Praxis

In process control, retuning of controllers is necessary from time to time due to changes of plant dynamics. Thereby, opening of the control loop is often not desired. In order to proceed in a model-based manner, a toolbox for closed-loop identification is developed in the present contribution in view of application in industrial practice. First, the theoretical foundations of closed-loop identification are reviewed, second the structure of a ready-to-use toolbox is described, and third the succesful application of the method to a real process is shown. Finally, open questions for further development are presented