An adaptive control scheme is proposed for controlling a certain class of nonlinear, uncertain systems. When a local approximation of the system function using its Taylor’s expansion is possible, this scheme provides an adaptation law to estimate such an approximation. With a proper sampling rule, the neighborhood of approximation can be moved from time to time in order to capture the fast changing system dynamics. Practical implementation issues are also considered to avoid exciting the unmodeled dynamics, to reduce the noise sensitivity, and accommodate the various signal levels in the system response. The important features and performance of the proposed controller are illustrated through simulations and experimental results associated with a magnetic bearing system.

1.
Apostol, T. M., Mathematical Analysis, Addison-Wesley, NY, 1975.
2.
Higabseb
T. A.
, and
Foss
B. A.
, “
Constructing NARMAX Models Using ARMAX Models
,”
Int. J. Contr.
, Vol.
58
, pp.
1125
1154
, Nov.
1993
, Prentice-Hall, Englewood Cliffs, NJ, 1989.
3.
Messner
W.
,
Horowitz
R.
,
Kao
W.-W.
, and
Boals
M.
, “
A New Adaptive Learning Rule
,”
IEEE Trans. on Automat. Control
, Vol.
36
, pp.
188
197
, Feb.,
1991
.
4.
Narendra, K. S., and Annaswamy, A. M., Stable Adaptive Systems, Prentice-Hall, Englewood Cliffs, NJ, 1989.
5.
Narendra
K. S.
, and
Parthassarathy
K.
, “
Identification and Control of Dynamical Systems Using Neural Networks
,”
IEEE Trans. on Neur. Net.
, Vol.
1
, pp.
4
26
, Mar.,
1990
.
6.
Sanner, R. M., and Slotine, J.-J. E., “Gaussian Networkd for Direct Adaptive Control,” Proc. Amer. Contr. Conf., pp. 2153–2159, 1991.
7.
Slotine, J.-J. E., and Li, W., Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs, NJ, 1991.
8.
Slotine, J.-J. E., and Sastry, S. S., “Tracking Control of Nonlinear Systems Using Sliding Surfaces With Applications to Robot Manipulators,” Int. J. Control, Vol. 39, No. 2, 1983.
9.
Utkin, V. I., “Variable Structure With Sliding Mode: A Survey,” IEEE Trans. on Automat. Control, Vol. 2, 1977.
10.
Yeh, T.-J., and Youcef-Toumi, K., “Dynamics and Control of a Five-Axis Magnetically Levitated Turo Pump,” Laboratory for Manufacturing and Productivity Report, Massachusetts Institute of Technology, Sept., 1995.
11.
Youcef-Toumi
K.
, and
Reddy
S.
, “
Dynamic Analysis and Control of High Speed and High Precision Active Magnetic Bearings
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
114
, pp.
623
633
, Dec.,
1992
.
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