Transcript ESC 2003 - University of Sheffield

Parity equations-based unknown input
reconstruction for Hammerstein-Wiener
systems in errors-in-variables framework
Malgorzata Sumislawska
Prof Keith J Burnham
Coventry University
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Motivation
 Errors-in-variables (EIV) framework
 Input and output signals are subjected to white, Gaussian, zeromean, mutually uncorrelated measurement noise sequences
 Long history of research on EIV framework in Control Theory and
Applications Centre
 Aim: reconstruct unknown input while minimising impact
----of measurement noise on unknown input estimate
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Slide 2
Motivation
 Hammerstein-Wiener (HW) system representation considered
 Relatively simple model structure
 Can approximate large class of nonlinear systems
 Limited attention paid to HW systems in EIV framework
N1(.) , N2(.) – static nonlinear functions
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Slide 3
Problem solution
 Knowing N1(.) and N2(.) calculate input and output to linear
dynamic block
 Input and output estimates to linear block affected by noise
signals to
be calculated
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Slide 4
Problem solution
 Knowing N1(.) and N2(.) calculate input and output to linear
dynamic block
 Input and output estimates to linear block affected by noise
 Linear EIV setup with heteroscedastic noise, whose variance
depends on operating point
 Need for adaptive scheme
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Slide 5
Problem solution
 Influence of noise minimised using Lagrange multipliers
optimisation method
 Time-varying noise variances estimated from N1(.) and N2(.)
using Taylor expansion
 Experimental (Monte-Carlo simulation) results match
theoretical calculations
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Slide 6
Summary and future work
 Summary
 Novel approach for unknown input reconstruction developed
 Effect of measurement noise minimised in adaptive manner
 The work published in
Sumislawska M., Larkowski, T., Burnham, K. J., ‘Unknown input
reconstruction observer for Hammerstein-Wiener systems in the
errors-in-variables', Proceedings of 16st IFAC Symposium on
System Identification, Brussels, Belgium, 11-13 July 2012
 Future work
 Coloured output noise
 Multivariable case
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Slide 7