Abstract
We present a system identification method based on recursive least-squares (RLS) and coprime collaborative sensing, which can recover system dynamics from non-uniform temporal data. Focusing on systems with fast input sampling and slow output sampling, we use a polynomial transformation to reparameterize the system model and create an auxiliary model that can be identified from the non-uniform data. We show the identifiability of the auxiliary model using a Diophantine equation approach. Numerical examples demonstrate successful system reconstruction and the ability to capture fast system response with limited temporal feedback.
References
1.
Isermann
, R.
, 1989
, Digital Control Systems
, Springer Science & Business Media
, Heidelberg
.2.
Gambier
, A.
, 2004
, “Real-Time Control Systems: A Tutorial
,” 5th Asian Control Conference (IEEE Cat. No. 04EX904)
, Melbourne, Australia
, July 20–23
, Vol. 2, IEEE, pp. 1024
–1031
.3.
Khan
, S.
, Goodall
, R. M.
, and Dixon
, R.
, 2013
, “Non-Uniform Sampling Strategies for Digital Control
,” Int. J. Syst. Sci.
, 44
(12
), pp. 2234
–2254
. 4.
Ding
, F.
, Qiu
, L.
, and Chen
, T.
, 2009
, “Reconstruction of Continuous-Time Systems From Their Non-uniformly Sampled Discrete-Time Systems
,” Automatica
, 45
(2
), pp. 324
–332
. 5.
Albertos
, P.
, and Crespo
, A.
, 1999
, “Real-Time Control of Non-uniformly Sampled Systems
,” Control Eng. Pract.
, 7
(4
), pp. 445
–458
. 6.
Landau
, I. D.
, Lozano
, R.
, M’Saad
, M.
, and Karimi
, A.
, 2011
, Adaptive Control: Algorithms, Analysis and Applications
, Springer Science & Business Media
, London
.7.
Powell
, M. J. D.
, 1981
, Approximation Theory and Methods
, Cambridge University Press
, Cambridge
.8.
Raghavan
, H.
, Gopaluni
, R. B.
, Shah
, S.
, Pakpahan
, J.
, Patwardhan
, R.
, and Robson
, C.
, 2005
, “Gray-Box Identification of Dynamic Models for the Bleaching Operation in a Pulp Mill
,” J. Process Control
, 15
(4
), pp. 451
–468
. 9.
Amirthalingam
, R.
, Sung
, S. W.
, and Lee
, J. H.
, 2000
, “Two-Step Procedure for Data-Based Modeling for Inferential Control Applications
,” AIChE J.
, 46
(10
), pp. 1974
–1988
. 10.
Sircar
, P.
, and Sarkar
, T. K.
, 1988
, “System Identification From Nonuniformly Spaced Signal Measurements
,” Signal Process.
, 14
(3
), pp. 253
–268
. 11.
Gillberg
, J.
, and Ljung
, L.
, 2010
, “Frequency Domain Identification of Continuous-Time Output Error Models, Part II: Non-uniformly Sampled Data and B-Spline Output Approximation
,” Automatica
, 46
(1
), pp. 11
–18
. 12.
Dempster
, A. P.
, Laird
, N. M.
, and Rubin
, D. B.
, 1977
, “Maximum Likelihood From Incomplete Data Via the EM Algorithm
,” J. R. Stat. Soc.: Ser. B (Methodol.)
, 39
(1
), pp. 1
–22
.13.
Shumway
, R. H.
, and Stoffer
, D. S.
, 1982
, “An Approach to Time Series Smoothing and Forecasting Using the EM Algorithm
,” J. Time Series Anal.
, 3
(4
), pp. 253
–264
. 14.
Isaksson
, A. J.
, 1993
, “Identification of ARX-Models Subject to Missing Data
,” IEEE Trans. Automat. Contr.
, 38
(5
), pp. 813
–819
. 15.
Jones
, R. H.
, 1980
, “Maximum Likelihood Fitting of ARMA Models to Time Series With Missing Observations
,” Technometrics
, 22
(3
), pp. 389
–395
. 16.
Li
, D.
, Shah
, S. L.
, and Chen
, T.
, 2001
, “Identification of Fast-Rate Models From Multirate Data
,” Int. J. Control
, 74
(7
), pp. 680
–689
. 17.
Li
, D.
, Shah
, S. L.
, and Chen
, T.
, 2002
, “Analysis of Dual-Rate Inferential Control Systems
,” Automatica
, 38
(6
), pp. 1053
–1059
. 18.
Zhu
, Y.
, Telkamp
, H.
, Wang
, J.
, and Fu
, Q.
, 2009
, “System Identification Using Slow and Irregular Output Samples
,” J. Process. Control
, 19
(1
), pp. 58
–67
. 19.
Lu
, W.
, and Grant Fisher
, D.
, 1988
, “Output Estimation With Multi-Rate Sampling
,” Int. J. Control
, 48
(1
), pp. 149
–160
. 20.
Atsumi
, T.
, 2023
, “Magnetic-Head Positioning Control System in HDDs
,” https://www.mathworks.com/matlabcentral/fileexchange/111515-magnetic-head-positioning-control-system-in-hdds, MATLAB Central File Exchange, Retrieved July 20, 2023.Copyright © 2023 by ASME
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