Tom Oomen

Nonparametric System Identification of Motion Systems

Until a few years ago, standard practice in motion control was to identify frequency response functions (FRFs) using so-called noise excitation. Here, noise refers to a realization of a stochastic process, so just a random sequence of numbers, possibly with some coloring. These FRFs are used for many different tasks, including manually tune feedback controllers, closed-loop controller validation, and as a basis for parametric modeling. Intuitively, a frequency response function is a response to sinusoidal inputs, so using such a noise excitation may not be the most intuitive solution. And indeed, the use of multisine experiments, i.e., using sums-of-sinusoids, has important advantages. In 2006, we started exploratory studies towards this, revealing that many of the FRFs we had obtained actually contained bias errors (systematic errors). In addition, multisine experiments allowed us to construct accurate quality certificates in terms of variance. Initial results are reported in

  • Accuracy Assessment in Frequency Response-based Identification of a Flexible Mechatronic Stage
    D.S.M. Denie
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2008

We have further developed this towards the use of multisine experiments, which is reported at several locations, including

  • Experimental Modeling and Validation for Robust Motion Control of Next-Generation Wafer Stages
    R.M.A. van Herpen
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2009

  • Improving Wafer Stage Motion Performance through Robust-Control-Relevant Model Set Identification and Multivariable Control
    Sander Quist
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2010

  • Connecting System Identification and Robust Control for Next-Generation Motion Control of a Wafer Stage [pdf|link]
    Tom Oomen, Robbert van Herpen, Sander Quist, Marc van de Wal, Okko Bosgra, and Maarten Steinbuch
    Appendix A of IEEE Transactions on Control Systems Technology, 22(1): 102-118, 2014

Interestingly, by exploiting the freedom of choice in the phases of the multisines, one can actually obtain a quantification of nonlinear effects by randomly changing these, leading to a so-called best linear approximation (BLA) and a nonlinear variance term. This is investigated, e.g., in

  • Experimental analysis of the influence of structural deformations on a new lightweight industrial motion system on its positioning accuracy using a systematic identification-and-robust-control design framework
    Joris Termaat
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2011

Finally, ongoing research focuses on using advanced nonparametric local parameteric modeling techniques. The basic motivation is that these enable decreased experiment time and/or increased accuracy. For instance, in its basic form these methods require only a single multisine experiment for a multivariable system. Also, transient effects are explicitly modeled, i.e., one does not need to have to wait until transients die out. Initial results are reported in

  • Enhancing Motion Control Practice Through Modern Non-Parametric Identification Techniques
    M.M. Poot'n B.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2014

  • Non-Parametric Identification for High-Precision Motion Systems
    A. van der Maas - Van Rietschoten
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2015

At present, we are continuing research for next-generation motion systems, which we envision to have a high number of inputs and outputs, as well as position-dependent behavior. To achieve this, we are developing MIMO local parametric modeling techniques, as well as local parametric modeling techniques for LPV systems, e.g., to exploit the smooth position-dependent behavior. For some recent results, see, e.g.,

This leads to an enhanced estimation accuracy. This is shown in the following figure, where on the left hand side, state-of-the-art LPM methods are applied, while on the right hand side, the proposed approach leads to a much smaller estimation error:

Ongoing applications include a range of motion systems, from positioning stages to active vibration isolation tables, printers, and wafer stages, as well as the identification of diesel engines with Thijs van Keulen (DAF). To profile various of such nonparametric identification techniques, we have recently developed a benchmark problem, including a very large data set, see our benchmark system page.


The above results are in collaboration with many co-workers, including

  • Active researchers at TU/e-ME-CST: Robbert Voorhoeve, Maarten Steinbuch, Thijs van Keulen

  • Previous reseachers at TU/e-ME-CST: Okko Bosgra, Robbert van Herpen, Sander Quist, Duncan Denie, Joris Termaat, Annemiek van der Maas, Rick van der Maas, Lars Huijben

  • Industrial collaborators from Philips/ASML: Marc van de Wal, Wouter Aangenent
    and many others

Note that all figures shown on this page can be found in the mentioned papers. Please follow the guidelines regarding copyright and references when citing these.