In active noise control, it is desired to generate destructive interference by model-independent control. This is possible for single-channel systems to which a recently proposed method, called orthogonal adaptation, is applicable. In this study, the new method is extended to multichannel systems. An important issue is how to optimize a feedforward controller in the minimum H2 norm sense. In practice, secondary paths of some multichannel systems may be nonminimum phase. It is a difficult problem to design H2 feedforward controllers for multichannel systems with nonminimum phase secondary paths. The problem is solved analytically here with the best achievable, a practical and an economical solution. A recursive least squares algorithm is presented for online identification of multiple paths without persistent excitations. These solutions make it possible to implement noninvasive mode-independent controllers for multichannel systems. Experiment results are presented to verify the analytical results.

1.
C. H.
Hansen
and
S. D.
Snyder
,
Active Control of Noise and Vibration
(
E and FN Spon
, London,
1997
).
2.
P. A.
Nelson
and
S. J.
Elliott
,
Active Control of Sound
(
Academic
, London,
1992
).
3.
D. E.
Hall
,
Basic Acoustics
(
Wiley
, New York,
1987
).
4.
M. A.
Vaudrey
,
W. T.
Baumann
, and
W. R.
Saunders
, “
Stability and operation constraints of adaptive LMS-based feedback control
,”
Automatica
39
,
595
605
(
2003
).
5.
E.
Bjarnason
, “
Analysis of the filtered-x LMS algorithm
,”
IEEE Trans. Speech Audio Process.
3
(
3
),
504
514
(
1995
).
6.
S. D.
Snyder
and
C. H.
Hansen
, “
The influence of transducer transfer functions and acoustic time delay on the LMS algorithm in active noise control systems
,”
J. Sound Vib.
140
(
3
),
409
424
(
1990
).
7.
G. C.
Goodwin
and
K. S.
Sin
,
Adaptive Filtering, Prediction and Control
(
Prentice-Hall
, Englewood Cliffs, NJ,
l984
).
8.
L. J.
Eriksson
and
M. C.
Allie
, “
Use of random noise for on-line transducer modeling in an adaptive active attenuation system
,”
J. Acoust. Soc. Am.
85
,
797
802
(
1989
).
9.
M.
Zhang
,
H.
Lan
, and
W.
Ser
, “
Cross-updated active noise control system with online secondary path modeling
,”
IEEE Trans. Speech Audio Process.
9
,
598
602
(
2000
).
10.
M.
Zhang
,
H.
Lan
, and
W.
Ser
, “
A robust online secondary path modeling method with auxiliary noise power scheduling strategy and norm constraint manipulation
,”
IEEE Trans. Speech Audio Process.
11
(
1
),
45
53
(
2003
).
11.
W. C.
Nowlin
,
G. S.
Guthart
, and
G. K.
Toth
, “
Noninvasive system identification for multichannel broadband active noise control
,”
J. Acoust. Soc. Am.
107
,
2049
2060
(
2000
).
12.
X.
Qiu
and
C. H.
Hansen
, “
An algorithm for active control of transformer noise with online cancellation path modelling based on the perturbation method
,”
J. Sound Vib.
240
(
4
),
647
665
(
2001
).
13.
B. J.
Kim
and
D. C.
Swanson
, “
Linear independence method for system identification/secondary path modeling for active control
,”
J. Acoust. Soc. Am.
118
(
3
),
1452
1468
(
2005
).
14.
J.
Yuan
, “
Orthogonal adaptation for active noise control
,”
J. Acoust. Soc. Am.
120
(
1
),
204
210
(
2006
).
15.
P. A.
Regalia
,
Adaptive IIR Filtering in Signal Processing and Control
(
Dekker
, New York,
1995
).
16.
J.
Yuan
, “
Improving an adaptive controller for non-minimum phase plants
,”
Automatica
38
,
869
8735
(
2002
).
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