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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Notes
- 1.
Again, we leave to the reader to check the details in the literature.
- 2.
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.
- 3.
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.
- 4.
Pseudo Random Binary Signal.
- 5.
The ellipses were computed from the data, so this is the sample covariance.
References
K.J. Åström, B. Wittenmark, Adaptive Control, 2nd edn. (Addison-Wesley, Reading, 1995)
R.R. Bitmead, S. Cheong, System identification based instability detection of noisy ARMA systems, in Proc. 15th IFAC Symposium on System Identification, Saint-Malo, France (IFAC, 2009), pp. 290–295
L. Campestrini, D. Eckhard, M. Gevers, A.S. Bazanella, Virtual reference feedback tuning for non-minimum phase plants. Automatica 47, 1778–1784 (2011)
M.C. Campi, A. Lecchini, S. Savaresi, An application of the virtual reference feedback tuning method to a benchmark problem. Eur. J. Control 9, 66–76 (2003)
M.C. Campi, A. Lecchini, S.M. Savaresi, Virtual reference feedback tuning: A direct method for the design of feedback controllers. Automatica 38, 1337–1346 (2002)
M.C. Campi, S.M. Savaresi, Direct nonlinear control design: The virtual reference feedback tuning (VRFT) approach. Automatica 51, 14–27 (2006)
M. Gevers, A.S. Bazanella, X. Bombois, L. Mišković, Identification and the information matrix: How to get just sufficiently rich? IEEE Trans. Autom. Control 54(12), 2828–2840 (2009)
G. Goodwin, K.S. Sin, Adaptive Filtering, Prediction and Control (Prentice Hall International, Englewood Cliffs, 2009)
H. Hjalmarsson, M. Gevers, S. Gunnarsson, O. Lequin, Iterative feedback tuning: Theory and applications. IEEE Control Syst. Mag. 18(4), 26–41 (1998)
A. Karimi, K. van Heusden, D. Bonvin, Non-iterative data-driven controller tuning using the correlation approach, in Proc. European Control Conference, Kos, Greece, 2007
A. Lecchini, M. Gevers, On iterative feedback tuning for non-minimum phase plants, in 41st IEEE Conference on Decision and Control, 2002, pp. 4658–4663
L. Ljung, System Identification—Theory for the User, 2nd edn. (Prentice Hall, New York, 1999)
J. Mårtensson, Geometric Analysis of Stochastic Model Errors in System Identification, PhD thesis, Royal Institute of Technology (KTH), October 2007
J. Mårtensson, H. Hjalmarsson, Variance error quantifications for identified poles and zeros. Automatica 45(11), 2512–2525 (2009)
M. Nakamoto, An application of the virtual reference feedback tuning for an MIMO process, in Proc. SICE Annual Conference, Sapporo, Japan, vol. 3 (IEEE Press, New York, 2005), pp. 2208–2213
A. Sala, A. Esparza, Extensions to “virtual reference feedback tuning: A direct method for the design of feedback controllers”. Automatica 41, 1473–1476 (2005)
T. Söderström, P. Stoica, System Identification (Prentice Hall, New York, 1989)
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Sanfelice Bazanella, A., Campestrini, L., Eckhard, D. (2012). One-Shot Optimization—The VRFT Method. In: Data-Driven Controller Design. Communications and Control Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2300-9_3
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