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2012 | OriginalPaper | Chapter

3. One-Shot Optimization—The VRFT Method

Authors : Alexandre Sanfelice Bazanella, Lucíola Campestrini, Diego Eckhard

Published in: Data-Driven Controller Design

Publisher: Springer Netherlands

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Abstract

Once the designer has chosen the performance criterion, it must be minimized, which in a data-driven control design will be done using only input-output data collected from the system. It is possible in many situations to perform this minimization in only “one-shot”, that is, with only one batch of data collected in only one operating condition. These “one-shot” solutions, which are the most convenient, are the subject of Chap. 3. The virtual reference feedback tuning method (VRFT, for short) is presented and its statistical properties—consistency, variance—are demonstrated. Its extension to nonminimum phase processes is also presented. A number of simulation studies illustrate the properties of VRFT.

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previous chapter H 2 Performance Criteria

next chapter Iterative Optimization

Again, we leave to the reader to check the details in the literature.

Since we are estimating a PI controller, which is formed by a parameter vector of size two, and we are dealing with a noise-free case, we can use the minimum amount of data.

The introduction of the filter causes the cost function J ^VR(ρ) to become flatter, so we have plotted 200J ^VR(ρ) to make the visual comparison to the other costs easier.

Pseudo Random Binary Signal.

The ellipses were computed from the data, so this is the sample covariance.

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Title: One-Shot Optimization—The VRFT Method
Authors: Alexandre Sanfelice Bazanella
Lucíola Campestrini
Diego Eckhard
Publisher: Springer Netherlands
Book: Data-Driven Controller Design
Print ISBN: 978-94-007-2299-6

Electronic ISBN: 978-94-007-2300-9

Copyright Year: 2012
DOI: https://doi.org/10.1007/978-94-007-2300-9_3