The assumed modes approach is a widely used technique in modeling of distributed systems. Such models often consist of a large number of modes. For controller design purposes these models are simplified by truncating the modes that lie out of the bandwidth of interest. Truncation can alter zeros of the system. This paper presents a method of minimizing the truncation error by adding a second order term to the truncated model. This extra term is determined such that the in-bandwidth error is minimized in an optimal $H2$ sense. The technique is extended to multivariable systems. [S0739-3717(00)02003-1]

1.
Meirovitch, L., 1986, Elements of Vibration Analysis, 2nd edition, McGraw-Hill, Sydney.
2.
Fraser, A. R., and Daniel R. W., 1991, Perturbation Techniques for flexible Manipulators, Kluwer Academic, Massachusetts.
3.
Alberts
,
T. E.
, and
Colvin
,
J. A.
,
1991
, “
Observations on the nature of transfer functions for control of piezoelectric laminates
,”
J. Intell. Mater. Syst. Struct.
,
8
, No.
5
, pp.
605
611
.
4.
Hong
,
J.
,
Akers
,
J. C.
,
Venugopal
,
R.
,
Lee
,
M.
,
Sparks
,
A. G.
,
Washabaugh
,
P. D.
, and
Bernstein
,
D.
,
1996
, “
Modeling, identification, and feedback control of noise in an acoustic duct
,”
IEEE Trans. Control Syst. Technol.
,
4
, No.
3
, pp.
283
291
.
5.
Clark
,
R. L.
,
1997
, “
Accounting for out-of-bandwidth modes in the assumed modes approach: Implications on colocated output feedback control
,”
ASME J. Dyn. Syst., Meas., Control
,
119
, pp.
390
395
.
6.
Moheimani, S. O. R., 2000, “Minimizing the effect of out of bandwidth modes in truncated structure models,” to appear in ASME J. Dyn. Syst., Meas., Control.
7.
Lewis, F. L., 1992, Applied Optimal Control and Estimation, Prentice Hall, New York.
8.
Moheimani, S. O. R., 1999, “Minimizing the effect of out of bandwidth modes in the truncated assumed modes models of structures,” in Proc. American Control Conference, pp. 2718–2722, San Diego, CA.