Tom Oomen


Sampled-data Control

Nowadays, most controllers are implemented in a digital environment, i.e., using analog-digital and digital-analog convertors to interact with our physical system, which operates in a continuous time domain. Most of our design techniques involve approximations. Indeed, either first a continuous time model is used, for which a continuous time controller is designed. This controller is then subsequently discretized, typically involving approximations. On the other hand, from a system identification point of view, one often makes a discrete time model directly from data, and then directly a discrete time controller is designed. However, this is also an approximation: it ignores the intersample behavior!

In our research, we have looked at various ways of optimally dealing with this situation, i.e., doing a sampled-data control design, which involves the direct design of a discrete time controller for a continuous time system with continuous time performance specifications.

Feedback

When attempting to design a feedback controller for a sampled-data system, one will quickly realize that such a system is inherently linear periodically time varying (LPTV). As a consequence, the standard notion of frequency domain is lost. It turns out that generalizations of typical norms can be made, like the cal{H}_infty-norm, but this loses its connection to typical loop-shaping designs (it is not the usual frequency domain anymore) and uncertainty also becomes LPTV - so it does not correspond to the nice well-known circles in a Nyquist diagram anymore.

We have developed an iterative approach that alternates between discrete time controller design and sampled-data performance analysis. We developed this in a multirate context to enable the use of system identification for obtaining the models, which is fast, accurate, and inexpensive (for motion systems, a continuous time model does not seem to make much sense: there will be infinitely many flexible modes at higher frequencies!). The results are reported in

where also an interesting case study on aliased disturbances is reported. Aliasing of resonance phenomena is investigated in

ILC for sampled-data systems

Iterative Learning Control (ILC) is traditionally implemented in a digital computer environment, i.e., in discrete time. In contrast to standard feedback control where disturbance attenuation is limited due to the Bode sensitivity integral, ILC can attenuate disturbances up to the Nyquist frequency. As a result, it achieves almost perfect performance… at the sampling instants. Our research hypothesis was that pushing the performance at the sampling instants this far might go at the expense of the intersample behavior (actually, the main reason that led to this reason was a disagreement on the notion of lifted system between Jeroen van de Wijdeven and myself: the notion of lifted system in ILC seemed fairly different from the usual definition in LPTV and sampled-data systems - this has also been settled, see my lecture notes!). To investigate this, we developed a sampled-data/multirate ILC framework, which is documented 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.