research @ wolfgang-reinelt.de
identification for control

Identification for control is an area which has received a renewed interest since the beginning of the 1990s - several special journal issues appeared on that subject. A major motivation of this research is to achieve robust stabilisation of the real plant. Thus it is customary to identify not only a nominal model, but also an uncertainty set, i.e. a set of models to be considered in the control design process. For example, if non-parametric design methods are adopted, it is natural to look for uncertainty regions/bands in the Bode plot.
A further consequence of the control objective is that it might be sufficient to estimate the real plant well up to a certain frequency (somewhere in the region of the cross over) and to tolerate a larger uncertainty for higher frequencies. These aspects move the emphasis from the classical residual analysis to the computation and visualisation of the nominal model and the associated uncertainty in the frequency domain. Starting off with this, the key question is: in which frequency range can we rely on model and its uncertainty?

In preliminary studies we looked at Stochastic Embedding (G.C. Goodwin), the unknown-but-bounded approach in Set Membership Identification (the "Italian" way of identification), Prediction error methods and Model Error Modelling (L. Ljung) and compared nominal models and uncertainty region, as fa(i)r as possible in these different frameworks. A somewhat related line of research, the validation concept of nominal models for H and µ-techniques (R.S. Smith, K. Poola) has been reviewed as well. These efforts are documented in the following reports and papers, not necessarily presenting new theory, but being of review character, additionally testing some software:

As a spin-off product, the concept of an explicit dynamical error (or bias error) to UBB/Set Membership Techniques, was introduced in order to improve the quality of the uncertainty region, associated with a central set membership estimate. This concept was then compared to the ones studied before, a simulation example with a nonlinear plant gives an idea, how all these methods behave. This can be found in:
Ongoing works, however, establish the link to an actual controller design, directly based on the "result" of an identification procedure as described above. Hence, this line of research is "control for identification" instead of "identification for control". Techniques used are the nu-gap metric (Vinnicombe, 1993) for analysis of the identified model set from a closed loop perspective and robust controller design techniques for rank one uncertainties (Rantzer & Megretski, 1994). Here, a scheme for robust controller design that accounts for parametric as well as dynamic uncertainties has been proposed; robust performance requirements in terms of the shape of the sensitivity function can be easily incorporated. This is described in:
An area closely related to the research described above, is modelling, identification and control of spatially distributed systems, such as piezoelectric laminate beams. Semi-physical modelling is combined with standard identification techniques to deliver a model; model uncertainty of the physical parameters is derived using bootstrapping methods for bilinear systems. The methods studied above are used for this area of applications. A first result is given in:
Future works are concerned with nonlinear error models and applications.

Funding and Cooperations

This work is supported by the European Commission through the EU TMR Project System Identification. People, closely involved in these activities are the control groups at Universita' di Siena, Italy (A. Garulli, A. Vicino), Universidad Nacional de Quilmes, Bernal, Argentina (J.H. Braslavsky), and of course in Linköping (L. Ljung).

Software: i4c

A software concerned with identification for control, called i4c - Identification for Control Package , is under construction. It contains the stochastic embedding technique (implemented by Julio H. Braslavsky), the set membership techniques (implemented by Andrea Garulli) and the prediction error methods in the model error modelling setup, suited for version 5 of the Matlab Identification toolbox by Lennart Ljung. Interface is the transfer function data structure used in Matlab's Control Systems toolbox, which is compatible with the structure in the new Matlab Identification toolbox.

Research Seminars

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Last update: Tue May 8 20:34:25 2007 by Wolfgang Reinelt . Legal Disclaimer