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Data-driven Controller Certification through Vinnicombe Test and Local Rational Models

This paper proposes an algorithm to certify a monovariable controller based on the well-known Vinnicombe metric. That metric is known to be too conservative; however, by using a frequency-wise approach and scaling the measured signals the metric may be made less conservative, as already shown in the literature. The calculations depend on the estimation of some frequency response functions (FRF), for which we suggest the use of the Local Rational Models (LRM). Finally, we show that under certain circumstances the controller certification task may be reduced to computing the intersection of a finite number of intervals representing the scaling factors that certify the controller at each frequency.