A robust active controller using spatially feedforward structure is proposed for broadband attenuation of noise in ducts. To meet the requirements of performance and robust stability in the presence of plant uncertainties, an H2 cost function and an H constrain are employed in the synthesis of the controller. The design is then converted into a convex programming problem using Q-parametrization and frequency discretization. An optimal controller that satisfies the quadratic cost functions and linear inequality constraints can be found by sequential quadratic programming. The optimal controller was implemented via a digital signal processor (DSP) and verified by experiments. Experiment results showed that the system attained 16.5 dB maximal attenuation and 5.9 dB total attenuation in the frequency band 200–600 Hz.

1.
J.
Hong
,
J. C.
Akers
,
R.
Venugopal
,
M. N.
Lee
,
A. G.
Sparks
,
P. D.
Washabaugh
, and
D. S.
Bernstein
, “
Modeling, identification, and feedback control of noise in an acoustic duct
,”
IEEE Trans. Control Syst. Technol.
4
,
283
291
(
1996
).
2.
Z.
Wu
,
V. K.
Varadan
, and
V. V.
Varadan
, “
Time-domain analysis and synthesis of active noise control systems in ducts
,”
J. Acoust. Soc. Am.
101
,
1502
1511
(
1997
).
3.
J. C.
Carmona
and
V. M.
Alvarado
, “
Active noise control of a duct using robust control theory
,”
IEEE Trans. Control Syst. Technol.
8
,
930
938
(
2000
).
4.
M. R.
Bai
and
T. Y.
Wu
, “
Study of the acoustic feedback problem of active noise control by using the l1 and l2 vector space optimization approaches
,”
J. Acoust. Soc. Am.
102
,
1004
1012
(
1997
).
5.
M. R.
Bai
and
H. P.
Chen
, “
Development of a feedforward active noise control system by using the H2 and H model matching principle
,”
J. Sound Vib.
201
,
189
204
(
1997
).
6.
M. R.
Bai
and
T. Y.
Wu
, “
Simulation of an internal model-based active noise control system for suppressing periodic disturbances
,”
ASME J. Vibr. Acoust.
120
,
111
116
(
1998
).
7.
M. R.
Bai
and
H. H.
Lin
, “
Comparison of active noise control structures in the presence of acoustical feedback by using the H synthesis technique
,”
J. Sound Vib.
206
,
453
471
(
1997
).
8.
J.
Hong
and
D. S.
Bernstein
, “
Bode Integral Constraints, Colocation, and Spillover in Active Noise and Vibration Control
,”
IEEE Trans. Control Syst. Technol.
6
,
111
120
(
1998
).
9.
A.
Roure
, “
Self-adaptive Broadband Active Sound Control System
,”
J. Sound Vib.
101
,
429
441
(
1985
).
10.
D. S.
Bernstein
and
W. M.
Haddad
, “
LQG control with an H performance bound: A Riccati equation approach
,”
IEEE Trans. Autom. Control
34
,
293
305
(
1989
).
11.
P. P.
Khargonekar
and
M. A.
Rotea
, “
Mixed H2/H control: A convex optimization approach
,”
IEEE Trans. Autom. Control
36
,
824
837
(
1991
).
12.
C. W.
Scherer
, “
Multiobjective H2/H control
,”
IEEE Trans. Autom. Control
40
,
1050
1062
(
1995
).
13.
Y.
Theodor
and
U.
Shaked
, “
Output-feedback mixed H2/H control-A dynamic game approach
,”
Int. J. Control
64
(
2
),
263
279
(
1996
).
14.
C. W. Scherer, “Mixed H2/H control,” in Proc. European Contr. Conf. (ECC95) (1995), pp. 173–216.
15.
J. Y.
Lin
and
Z. L.
Luo
, “
Internal model-based LQG/H design of robust active noise controllers for acoustic duct system
,”
IEEE Trans. Control Syst. Technol.
8
,
864
872
(
2000
).
16.
P. B.
Boyd
,
V.
Balakrishnan
,
C. H.
Barrat
,
N. M.
Khraishi
,
X.
Li
,
D. G.
Meryer
, and
S.
Norman
, “
A new CAD method and associated architectures for linear controllers
,”
IEEE Trans. Autom. Control
33
,
268
283
(
1988
).
17.
D. C.
Youla
,
J. J.
Bongiorno
, and
H. A.
Jabr
, “
Modern Wiener-Hopf design of optimal controllers. Part I: The single-input-output case
,”
IEEE Trans. Autom. Control
21
,
3
13
(
1976
).
18.
M. Morari and E. Zafiriou, Robust Process Control (Prentice-Hall, Englewood Cliffs, NJ, 1989).
19.
E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, New York, 1981).
20.
A. Grace, Matlab Optimization Toolbox, The Math Works, Inc. (1995).
21.
M. R.
Bai
and
H. H.
Lin
, “
Plant uncertainty analysis in a duct active noise control problem by using the H theory
,”
J. Acoust. Soc. Am.
104
,
237
247
(
1998
).
22.
P. A. Nelson and S. J. Elliott, Active Control of Sound (Academic, London, 1992).
23.
J. C. Doyle, B. A. Francis, and A. R. Tannenbaum, Feedback Control Theory (MacMillan, New York, 1992).
24.
J. W.
Helton
and
A.
Sideris
, “
Frequency response algorithms for H optimization with time domain constraints
,”
IEEE Trans. Autom. Control
34
,
427
434
(
1989
).
25.
B. Rafaely and S. J. Elliott, “H2/H output feedback design for active control,” ISVR, Univ. Southhampton, U.K., Tech. Memo 800 (July 1996).
26.
J. S. Arora, Introduction to Optimum Design (McGraw–Hill, New York, 1989).
27.
S. Boyd, L. Vandenberghe, and M. Grant, “Efficient convex optimization for engineering design,” in Proc. IFAC Symp. Robust Contr. Design, Rio de Janeiro, Brazil (Sept. 1994)
28.
B.
Rafaely
and
S. J.
Elliott
, “
H2/H active control of sound in a headset: Design and implementation
,”
IEEE Trans. Control Syst. Technol.
7
,
79
84
(
1999
).
29.
P. J. Titterton and J. A. Olkin, “A practical method for constrained optimization controller design: H2 or H optimization with multiple H2 and/or H constraints,” in Proc. 29th IEEE Asilomar Conf. Signals, Syst., Comput. (1995), pp. 1265–1269.
This content is only available via PDF.
You do not currently have access to this content.