A new frequency domain system identification method based on a multi-frequency input signal is proposed. Frequency contents of the oscillating signal are estimated using a modified Kaczmarz algorithm proposed in this paper. Lyapunov stability analysis is performed for this new Kaczmarz algorithm and transient bounds for estimation error are established. Moreover, a new method for estimation of the variance of the measurement noise in Kaczmarz algorithms is also described. A comparison of a transient performance of modified Kaczmarz algorithm and a recursive least-squares algorithm is presented. The results are applied to a frequency domain identification of a DC motor.
AvedyanE. D.Modified Kaczmarz algorithms for estimating the parameters of linear plants. Autom. Remote Control, 1978, 39(5), 674–680.
5.
VandoornT.De BelieF.VynckeT.MelkebeekJ.LataireP.Generation of multisinusoidal test signals for the identification of synchronous-machine parameters by using a voltage-source inverter. IEEE Trans. Industr. Electron., 2010, 57(1), 430–439.
6.
AndersonB. D. O.BitmeadR. R.JonsonC. R.KokotovichP. V.KosutR.MarelesI. M. J.PralyL.RiedleB. D.Stability of adaptive systems: passivity and averaging analysis, 1986 (MIT Press, Cambridge, Massachusetts).
7.
GoodwinG.SinK.Adaptive filtering, prediction and control, 1984 (Prentice-Hall, Englewood Cliffs, New Jersey).
8.
FominV. N.FradkovA. L.YakubovichV. A.Adaptive control of the dynamic plants, 1981 (Nauka, Moscow) (in Russian).
9.
IsermanR.Digital control systems, 1981 (Springer, Berlin).
10.
LandauI.ZitoG.Digital control systems: design, identification and implementation, 2006 (Springer, London).
11.
SastryS.BodsonM.Adaptive control: stability, convergence, and robustness, Prentice-Hall Advanced Reference Series (Engineering), 1994 (Prentice-Hall, Englewood Cliffs, New Jersey).
12.
HornR.JohnsonC.Matrix analysis, 1985 (Cambridge University Press, Cambridge).
13.
StotskyA.Recursive trigonometric interpolation algorithms. Proc. IMechE, Part I: J. Systems and Control Engineering, 2010, 224(1), 65–77. DOI 10.1243/09596518JSCE82310.1243/09596518JSCE823.
