Tom Oomen


Research on Advanced and Iterative Feedforward Control

From our prespective, traditional feedforward control design techniques involve a trade-off between performance and flexibility. Flexibility is here meant as performance robustness with respect to e.g. setpoint changes. Our vision is that new research is necessary to obtain a breakthrough that does not suffer from this trade-off. This is summarized in the following figure and in the publication:

We investigate two aspects:

  • ILC for ultra-high performance: see our dedicated Iterative Learning Control page

  • advanced feedforward control by combining high flexibility of traditional controllers with high performance obtained through iterative learning control

As a continuation of the pioneering work of Jeroen van de Wijdeven and Stan van der Meulen in the early 2000s in the CST group, we have made significant progress in developing a framework for advanced feedforward control. We are developing the following two alternative approaches: on based on Iterative Learning Control (ILC) and one based on System Identification. Both approaches are outlined below. Their differences are also clearly illustrated in the following movie:

ILC with basis functions

On the one hand, a research line based on ILC is pursued. The basic idea is to introduce basis functions in ILC to parameterize the feedforward signal. Initial steps using polynomial basis functions are presented in

All of the above results have been developed in the so-called lifted ILC framework with typically a quadratic criterion. To facilitate the implementation in various industries, we have also developed an approach based on frequency domain ILC design principles. The results are documented in

  • Frequency-domain ILC approach for repeating and varying tasks: With application to semiconductor bonding equipment [preprint]
    Frank Boeren, Abhishek Bareja, Tom Kok, and Tom Oomen
    IEEE/ASME Transactions on Mechatronics, To appear

  • Unified ILC Framework for Repeating and Varying Tasks: A Frequency Domain Approach with Application to Semiconductor Bonding Equipment
    Frank Boeren, Abhishek Bareja, Tom Kok, and Tom Oomen
    In 54th IEEE Conference on Decision and Control, Invited paper, Osaka, Japan, 2015

Interesting applications of these ILC-based approaches are reported in various places, including

  • Using iterative learning control with basis functions to compensate medium deformation in a wide-format inkjet printer [preprint|link]
    Joost Bolder, Tom Oomen, Sjirk Koekebakker, and Maarten Steinbuch
    IFAC Mechatronics, Invited paper, 24(8): 944-953, 2014

  • Rational basis functions and Norm Optimal ILC: Application to industrial setups
    B. Moris
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2013

  • Unified ILC Design Framework for Repeating and Almost Repeating Tasks
    Abhishek Bareja
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2014

  • Iterative Learning Control with a Rational Feedforward Basis: a new Solution Algorithm
    Jurgen van Zundert
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2014

System identification based approach: instrumental variables

On the other hand, we have been developing an approach based on Instrumental Variable System Identification. Initial steps towards this approach have been taken already in 2008, after we realised that pre-existing data-based feedforward tuning approaches suffered from a closed-loop identification problem. Initial steps towards IV-based feedforward tuning are reported in

Soon after developing these techniques, we realised that we had indeed solved the bias problems due to closed-loop operation, but the accuracy of our approach in terms of variance had not yet been investigated. In fact, initial applications suffered from a very poor performance due to a large variance error. This lead to the development of optimal instumental variable based methods, which are reported in

  • Accuracy aspects in motion feedforward tuning [pdf]
    Frank Boeren, Tom Oomen, and Maarten Steinbuch
    In Proceedings of the 2014 American Control Conference, 2178-2183, Portland, Oregon, United States, 2014

  • Enhanced motion feedforward tuning exploiting IV-identification: with extension to input shaping
    Leon van Breugel
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2013 Further extensions towards input shaping are reported in

  • Joint input shaping and feedforward for point-to-point motion: Automated tuning for an industrial nanopositioning system [preprint|link|errata]
    Frank Boeren, Dennis Bruijnen, Niels van Dijk, and Tom Oomen
    IFAC Mechatronics, Invited paper, 24(6): 572-581, 2014 Whereas extensions to rational feedforward compensators are reported in

  • Rational feedforward tuning: Approaches, stable inversion, and experimental Comparison [pdf]
    Lennart Blanken, Frank Boeren, Dennis Bruijnen, and Tom Oomen
    In 2016 IEEE American Control Conference, Invited paper, Boston, Massachusetts, United States, 2016

Several successful applications of the Instrumental Variable approach have been obtained and are reported in, e.g.,

  • Iterative feedforward tuning approach and experimental verification for nano-precision motion systems [pdf]
    Frank Boeren, Dennis Bruijnen, Tom Oomen
    In ASME 2014 Dynamic Systems and Control, San Antonio, Texas, 2014

  • Enhanced motion feedforward tuning exploiting IV-identification: with extension to input shaping
    Leon van Breugel
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2013

  • Rational Feedforward: Optimal IV Approach and Experimental Comparison on a Wafer Stage
    Lennart Blanken
    M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2015

  • Rational feedforward tuning: Approaches, stable inversion, and experimental Comparison [pdf]
    Lennart Blanken, Frank Boeren, Dennis Bruijnen, and Tom Oomen
    In 2016 IEEE American Control Conference, Invited paper, Boston, Massachusetts, United States, 2016

Rational basis functions: tuning and non-causality

As an extension of polynomial basis functions, we have been extensively investigating the use of rational basis functions in feedforward and learning control. In particular, the use of rational learning filters is quite common in ILC (think about L-filters), which are often implemented using ZPETC. In our ILC course (see Teaching), we have been promoting the use of stable inversion for quite some time already.

In this respect, the steps one has to take with rational feedforward are very similar to an ILC design. Especially in the first iteration, this is basically just inverting the system, either being open-loop or closed-loop, but this does not lead to a fundamental difference.

The inverse of a system can be directly computed

where the key observation is that the inverse has a certain system matrix that depends on all matrices of the original state-space realization. As a result, stability is not straightforward, and in the LTI case this requires non-minimum phase behavior of the original system. See, e.g.,

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

The main idea behind implementing these ZPETC and stable inversion algorithms is to try to invert a nonminimum-phase system. Of course, these inverses are unstable if one uses the standard unilateral Laplace or z-transform. By using the bilateral Laplace or z-transform, a bounded yet noncausal inverse can be obtained, which is exact. In an ILC setting, this of course is not an issue since learning is done off-line. Interestingly, this is also not an issue for motion feedforward design, since the reference signal is often known beforehand. As a result of these non-causal inverses, the feedforward controller can anticipate on the reference to come through pre-actuation. The following figure reveals the typical benefit on a motion system.



The details of these results are described in

  • Lennart Blanken, Frank Boeren, Dennis Bruijnen, Tom Oomen
    Submitted for publication, 2015

  • Rational feedforward tuning: Approaches, stable inversion, and experimental Comparison [pdf]
    Lennart Blanken, Frank Boeren, Dennis Bruijnen, and Tom Oomen
    In 2016 IEEE American Control Conference, Invited paper, Boston, Massachusetts, United States, 2016

Further developments of rational basis functions in ILC are presented in

Similarly, the use of rational basis functions in instrumental variable-based feedforward tuning are presented in

  • Rational Iterative Feedforward Control: Optimal Instrumental Variable Approach for Enhanced Performance
    Frank Boeren, Lennart Blanken, Dennis Bruijnen, and Tom Oomen
    In 54th IEEE Conference on Decision and Control, Invited paper, Osaka, Japan, 2015

State-space computations for stable inversion are described in Appendix A of

Extensions: beyond SISO LTI

The results described above involve the basic steps we have taken in recent years. At present, the research on these topics gained quite some momentum, at present (2016) four Ph.D. projects are working on this in our team. Some recent extensions include the following.

Extension to LTV systems. Clearly, the equations above already give the inverse for an LTV system. Although it becomes a complex equation (the inverse's system matrix depends on all original system matrices), these inverses can directly be computed. We have developed a whole variety of algorithms to address this, some of them are reported in

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

Extension to position-dependent motion systems. The fact that motion systems move over time typically introduces position-dependent and thus time-dependent dynamics, see also the position-dependent control page. This is addresses in an ILC and model-inversion context, e.g., leading to the following result

some details may be found in

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

as well as a rational feedforward tuning approach, e.g., initial results are documented in

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

Extension to address implementation aspects, including multirate and non-equidistant sampling. An important aspect of the mentioned approaches above is that these use sampled signals for optimising the performance with a single sampling frequency. In many high-tech systems, multivariable feedforward controllers are implemented. In the near future, we expect that

  • non-equidistant sampling may enhance reliable and fast (on average) sampling frequencies. Some initial results are described in

    • On the potential of lifted domain feedforward controllers with a periodic sampling sequence [pdf]
      Jurgen van Zundert, Tom Oomen, Dip Goswami, and Maurice Heemels
      In 2016 IEEE American Control Conference, Invited paper, Boston, Massachusetts, United States, 2016

  • sampling frequencies may be significantly increased in control loops that are critical for high performance. To avoid excessive hardware cost, we believe it may be attractive to implement other loops at a low sampling frequency. Therefore, we are developing a multirate feedforward approach to deal with this scenario. The results are in line with the sampled-data/multirate ILC approaches in the research page on iterative learning control but then using basis functions as explained above and multirate controllers. The results are documented in

  • Extension to multivariable systems. If the system is multivariable, additional complications may be encountered. Small parts of the interesting research that is done here are described in

    • Design techniques for multivariable ILC: Application to an industrial flatbed printer
      Lennart Blanken, Jeroen Willems, Sjirk Koekebakker, and Tom Oomen
      In 7th IFAC Symposium on Mechatronic Systems & 15th Mechatronics Forum International Conference, Loughborough, UK, 2016

  • Further extensions. The above list is just a glimpse on what is being developed at the moment. Please check again soon, as we will gradually expand this page (usually with some delay, unfortunately, so don't forget to check the publications page, which is usually a bit more up to date.

Learn more?

If you want to learn how to improve the performance of your system, check out the teaching page for information on M.Sc., Ph.D., and post-academic/industrial courses!

Acknowledgement

The success of all the above work is due to the hard and excellent work of many people involved in this research, including

  • Active researchers at TU/e-ME-CST: Frank Boeren, Jurgen van Zundert, Lennart Blanken, Robin de Rozario, Maarten Steinbuch, Maurice Heemels

  • Previous reseachers at TU/e-ME-CST: Joost Bolder, Okko Bosgra, Bart Moris, Leon van Breugel, Abhishek Bareja, Robin de Rozario, Janno Lunenburg, Jan Verhaegh, Jeroen van de Wijdeven, Stan van der Meulen, Pepijn Smits, Duarte Antunes

  • Industrial collaborators from NXP, Oce, Philips: Sjirk Koekebakker, Dennis Bruijnen, Tom Kok, Niels van Dijk, 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.