System Parameters of Output Feedback Controlled Flexible Structures

Abstract

The combined system consisting of the baseline flexible structure modified by the system of active controllers is considered as a unified dynamical system. Techniques based on computer algebra are used to derive expressions for the transfer functions of the modified system, using the known transfer functions of the baseline flexible structure and the feedback gains of the active controller. The roots of the characteristic polynomial of this transfer function give the system resonant frequencies and damping parameters. Using the computer algebraic system MACSYMA, expressions for these parameters that are ex plicitly dependent on the output feedback gains of the active controller are presented. These results permit the parametric study of the placement of the resonant frequencies and damping parameters of the combined system as functions of the feedback gains. Numeri cal examples are used to illustrate the application of these results to the calculation of active controller feedback gains based on the requirement that certain modes have specified modal damping while the closed-loop frequencies remain unchanged.

Get full access to this article

View all access options for this article.

References

Atluri, S.N. and A.K. Amos , eds. 1988. Large Space Structures: Dynamics and Control , Springer-Verlag.

Butkovskyi, A.G. 1982. Green's Functions and Transfer Functions Handbook, Elhs Horwood Ltd., Halsted Press.

Butkovskyi, A.G. 1983. Structural Theory of Distributed Systems, Ellis Horwood Ltd.

Chen, Y. 1966. Vibrations: Theoretical Methods, Addison-Wesley .

Fabunmi, J.A. 1989. 'Analysis of Modes and Frequencies of Modified Structures Using Computer Algebra", Proceedings International Conference on Noise and Vibration, Aug. 16-18, 1989, Singapore.

Garcia, E. , D.J. Inman. 1990. "Control Formulations for Vibration Suppression of an Active Structure in Slewing Motions", ASME Publication DSC, Advances in Dynamics and Control of Flexible Spacecraft and Space-Based Manipulations , S. M. Joshi , T. E. Alberts , Y. P. Kakad , eds., 20:1-5.

Horner, G.C. , J.E. Walz. 1985. "A Design Technique for Determining Actuator Gains in Spacecraft Vibration Control", AIAA/ASME/ASCE/AHS 26th Structures, Structural Dynamics and Materials Conference, Part 2, Orlando, Florida, pp. 143-151.

Junkins, J.L. , D.W. Rew. 1988. Unified Optimization of Structures and Controllers, Atluri and Amos , eds., pp. 323-354.

Keener, J.P. 1988. Principles of Applied Mathematics: Transformation and Approximation, Addison-Wesley

10.

Lynch, P.J. and S.S. Banda. 1988. Active Control for Vibration and Damping , Atluri and Amos , eds., pp. 239-262.

11.

Meirovitch, L. 1988. Control of Distributed Structures, Atluri and Amos , eds., pp. 195-212.

12.

O'Donoghue, P.E. and S.N. Atluri. 1985. "Control of Dynamic Response of a Continuum Model of a Large Space Structure", AIAA/ASME/ASCE/AHS 26th Structures, Structural Dynamics and Materials Conference, Part 2, Orlando, Florida, pp. 31-42.

13.

Pavelle, R. , ed. 1985. Applications of Computer Algebra, Kluwer.

14.

Rand, R.H. 1984. Computer Algebra in Applied Mathematics: An Introduction to MACSYMA, Pit-man.

15.

Stakgold, I. 1979. Green's Functions and Boundary Value Problems, Wiley Interscience.

16.

Various Authors , 1984. "Large Space Structure Control: Early Experiments", AIAA Journal of Guidance, Control, and Dynamics, Vol. 7, Special Section, September-October (1984).

17.

Wright, Robert L. 1986. NASA/DOD Control/Structures Interaction Technology-Parts 1 and 2 NASA Conference Publication 2447, November (1986).