Abstract
In this chapter, the basic principles of identification of dynamic systems from input–output data are reviewed. The various steps of the system identification procedure are emphasized. Algorithms which were successfully used for identification of active vibration control systems are presented.
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Notes
- 1.
Linear feedback regulator design will require also the model of the disturbance. Linear feedforward compensator design will require in addition a model of the primary path. Design of adaptive regulators or of feedforward compensators require only the model of the secondary path.
- 2.
The parameter estimation error induced by the measurement noise is called “bias”.
- 3.
Routines for generating PRBS can be downloaded from the websites: http://www.landau-adaptivecontrol.org and http://www.gipsa-lab.grenoble-inp.fr/~ioandore.landau/identificationandcontrol/.
- 4.
Functions prbs.m and prbs.c available on the websites: http://www.landau-adaptivecontrol.org and http://www.gipsa-lab.grenoble-inp.fr/ ioandore.landau/identificationandcontrol/ allow to generate PRBS of various lengths and magnitudes.
- 5.
Routines corresponding to this method in MATLAB (estorderiv.m) and Scilab (estorderiv.sci) can be downloaded from the websites: http://www.landau-adaptivecontrol.org and http://www.gipsa-lab.grenoble-inp.fr/ ioandore.landau/identificationandcontrol/.
- 6.
Routines for these algorithms can be downloaded from the websites: http://www.landau-adaptivecontrol.org and http://www.gipsa-lab.grenoble-inp.fr/~ioandore.landau/identificationandcontrol/.
- 7.
The interactive stand alone software iReg (http://tudor-bogdan.airimitoaie.name/ireg.html) provides parameter estimations algorithms for all the mentioned “plant \(+\) noise” structures as well as an automated identification procedure covering all the stages of system identification. It has been extensively used for identification of active vibration control systems.
- 8.
Routines corresponding to this validation method in MATLAB and Scilab can be downloaded from the websites: http://www.landau-adaptivecontrol.org and http://www.gipsa-lab.grenoble-inp.fr/ ioandore.landau/identificationandcontrol/.
- 9.
Conversely, for Gaussian data, uncorrelation implies independence. In this case, \(RN(i)=0, i \ge 1\) implies independence between \(\varepsilon (t), \varepsilon (t-1) \ldots ,\) i.e., the sequence of residuals \(\{ \varepsilon (t) \}\) is a Gaussian white noise.
References
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Landau, I.D., Airimitoaie, TB., Castellanos-Silva, A., Constantinescu, A. (2017). Identification of the Active Vibration Control Systems—The Bases. In: Adaptive and Robust Active Vibration Control. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-41450-8_5
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DOI: https://doi.org/10.1007/978-3-319-41450-8_5
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