Tom Oomen


Identification for Robust Control

Evaluating the quality of models depends on the purpose of it. Often, the model goal is control design, in which case the only purpose of the model is to deliver a robust and high performance controller. When identifying models for robust control, this particular goal has to be taken into account in the identification criterion. Since the optimal controller is unknown, this typically reads to iterative procedures, many of which have been developed since the 1990s.

In our research, we have recently improved the connection between system identification and robust control design. A key ingredient in robust control theory is the use of coprime factorizations. Spurred by developments in robust control theory, where normalized coprime factorizations have gained increased popularity due to their inherent connection to distance metrics, system identification algorithms have been developed that deliver these normalized coprime factorizations. Interestingly, in

a new coprime factorization has been presented that connects directly with earlier control-relevant identification criteria that have been developed in the early 1990s. These coprime factorizations have been further developed in

In addition, in the latter paper, the key benefit of these non-normalized factorizations is obtained. In particular, by employing these robust-control-relevant coprime factorizations in the dual-Youla uncertainty structure, we have been able to connect the size of uncertainty and the control criterion. This enables the use of any uncertainty modeling technique in a control-relevant fashion, including model validation and iterative cal{H}_infty-norm estimation, which are documented in the following papers, respectively.

The result of the uncertainty structure is an unstructured perturbation block (which helps a lot when you want to do mu-synthesis via DK-iterations!), which essentially scales the uncertainty channels towards the control criterion, both in a multivariable manner, and in a frequency-dependent manner. The main idea is that the model set will be very accurate in the controller cross-over region, while a large uncertainty is tolerated at low and high frequencies (since the controller will have integral action and roll-off, respectively!). A wafer stage application is reported in

whereas a CVT system is investigated in the following paper, which also includes an experimental comparison with classical additive uncertainty structures.

The developed techniques are applied to a range of applications, including wafer stage position control in

overactuation/oversensing in

inferential control in

and a CVT application in

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.