This paper introduces a new control design for a dynamic system subject to stationary or nonstationary parametric excitations. In this new design, the system dynamics is transformed into one with a null system matrix using the variation of parameters method. A stabilizing state feedback control can then be immediately obtained by following the gradient algorithm that is originally developed for the parameter identification purpose. Such a design has the advantage that the control requires only past and present information of the time-varying parametric excitations while previous control designs usually require prediction of future information of the excitations. The closed-loop system stability is guaranteed if the open-loop state response does not diverge too fast. The control design approach can also be applied to the observer design in case where there is only partial observation of the system state.

Issue Section:
Research Papers
Topics:
Design, Gradient methods, Excitation, Closed loop systems, Dynamic systems, Stability, State feedback, System dynamics
1.
Bittanti
S.
,
Colaneri
P.
, and
Guardabassi
G.
,
1986
, “
Analysis of the Periodic Lyapunov and Riccatic Equations via Canonical Decomposition
,”
SIAM. J. Control and Optimization
, Vol.
24
, pp.
1138
–
1149
.
2.
Calico
R. A.
, and
Wiesel
W. E.
,
1984
, “
Control of Time-Periodic Systems
,”
J. of Guidance
, Vol.
7
, pp.
671
–
676
.
3.
Callier, F., and Desoer, C. A., 1992, Linear System Theory, Springer-Verlag, Hong Kong.
4.
Chen, C. T., 1984, Linear System Theory and Design, Holt, Rinehart and Winston, New York.
5.
Follinger
O.
,
1978
, “
Design of Time-Varying Systems by Pole Assignment
,”
Regelungstechink
, Vol.
26
, pp.
85
–
95
.
6.
Kane
T. R.
, and
Bara
P. M.
,
1966
, “
Attitude Stability of a Spinning Satellite in an Elliptical Orbit
,”
ASME Journal of Applied Mechanics
, Vol.
33
, pp.
402
–
405
.
7.
Kano
H.
, and
Nishimura
T.
,
1979
, “
Periodic Solutions of Matrix Riccati Equations with Detectability and Stabilizability
,”
Int. J. Control
, Vol.
29
, pp.
471
–
487
.
8.
Kwakernaak, H., and Sivan, R., 1972, Linear Optimal Control Systems, Wiley, New York.
9.
Narendra, K. S., and Annaswamy, A. M., 1989, Stable Adaptive Systems, Prentice-Hall, Englewood Cliffs, New Jersey.
10.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, Wiley-Interscience. New York.
11.
O’Neil, P. v., 1991, Advanced Engineering Mathematics, Wadsworth, New York.
12.
Rugh, W. J., 1993, Linear System Theory, Prentice-Hall, Englewood Cliffs, New Jersey.
13.
Sastry, S., and Bodson, M., 1989, Adaptive Control, Stability, Convergence, and Robustness, Prentice-Hall, New York.
14.
Sinha
S. C.
, and
Joseph
P.
,
1994
, “
Control of General Dynamic Systems with Periodic Varying Parameters via Lyapunov-Floquet Transformation
,”
ASME Journal of Dynamic Systems, Measurement, and Control
, Vol.
116
, pp.
650
–
658
.
15.
Valasek, M., and Olgac, O., 1993, “Generalization of Ackermann’s Formula for Linear MIMO Time-Invariant and Time-Varying Systems,” Proceedings of Conference on Decision and Control, pp. 827–831.
16.
Webb
S. G.
,
Calico
R. A.
, and
Wiesel
W. E.
,
1991
, “
Time-Periodic Control of a Multiblade Helicopter
,”
J. of Guidance
, Vol.
14
, pp.
1301
–
1308
.
17.
Wolovich
W. A.
,
1968
, “
On the Stabilization of Controllable Systems
,”
IEEE Trans. on Automatic Control
, Vol.
13
, pp.
569
–
572
.
This content is only available via PDF.
Copyright © 1998
 by The American Society of Mechanical Engineers
You do not currently have access to this content.