Tom Oomen


LPV

One of the main applications that we are investigating are motion systems. Due to their inherent movements, such systems typically exhibit position-dependent dynamics. Our aim is to address such position-dependent dynamics in various aspects, including dependencies in the measured variables due to these inherent movements and in the performance variables in inferential control (since the performance variable is sometimes position varying, e.g., in lithographic exposure of a sequence of ICs on a wafer). As such, we are developing position-dependent models with the aim to develop position-dependent feedback, feedforward, observers, learning control, etc.

One framework to handle such position-dependent effects is through so-called linear parameter-varying (LPV) systems. Recently, we have addressed several aspects, including the following

Enhanced accuracy in non-parametric identification of LPV systems

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.,

In the latter paper, an nD-LPM/LRM technique is proposed, as is graphically illustrated in the following picture:

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:

Parametric identification of position-dependent mechanical systems

To efficiently design position-dependent observers, position-dependent feedback controllers, etc., parametric models are of essential importance. In the last two decades, many black-box algorithms have been developed for the identification of LPV systems. Recently, we have developed a combined experimental/physics-based, i.e., grey-box identification technique for mechanical/motion systems. The initial results are very promising and are reported in

  • Identifying position-dependent mechanical systems: A physics-based LPV approach, with application to a wafer stage
    R. de Rozario
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2015 (confidential)

Position-dependent feedforward

Achieving performance in motion systems typically requires feedforward. If the performance involves position-dependent dynamics, which can be either measured directly, or in an inferential situation (imagine that the performance in e.g. a wafer scanner depends on the actual spot on the wafer where it is being exposed, as is schematically illustrated, above), then the feedforward controller has to be position-dependent. Recently, we have extended our advanced feedforward control framework to a position-dependent situation. Initial results are promising and will be published soon

  • P. Smits
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2016 (to appear)

Also, applications to an industrial motion system have been obtained, including an ILC and model-inversion context, e.g., leading to the following result

some more details may be found in

  • Jurgen van Zundert, Joost Bolder, Sjirk Koekebakker, and Tom Oomen
    Manuscript under review, 2016

LPV-IFT

Iterative Feedback Tuning (IFT) is an iterative algorithm for tuning controllers without requiring a model. Instead, dedicated experiments are performed on the true system, which provide the gradient of the criterion w.r.t. the controller parameters. Initial results are reported in the following publication.

Acknowledgement

The above results are in collaboration with many co-workers, both from TU/e-ME and industry.

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.