Sage Journals: Discover world-class research

Abstract

This paper provides methodology for designing reduced-order controllers for large-scale, linear systems represented by differential equations having time-periodic coefficients. The linear time-periodic sys tem is first converted into a form in which the system stability matrix is time invariant. This is achieved by the application of Lyapunov-Floquet transformation. Then a completely time-invariant auxiliary system is constructed and order reduction algorithms are applied to this system to obtain a reduced-order system. The control laws are calculated for the reduced-order system by minimizing the least square error between the auxiliary and the transformed system. These control laws are then transformed to obtain the desired control action in the original domain. The schemes formulated arc illustrated by designing full-state feedback and output feedback controllers for a five-mass inverted pendulum exhibiting parametric instability

Keywords

Order reduction control parametric excitations Lyapunov-Floquet transformation

Get full access to this article

View all access options for this article.

References

Aoki, M. , 1968, "Control of large-scale dynamic systems by aggregation ," IEEE Transaction on Automatic Control AC-13, 246-253.

Bellman, R.E. , 1953, Stability Theory of Differential Equations, McGraw-Hill, New York.

Boghiu, D. , Sinha, S.C. , and Marghitu, D.B. , 1998, "Stability and control of a parametrically excited rotating system. Part II: controls," Dynamics and Control 8, 19-35.

Butcher, E.A. and Sinha, S.C. , 1996, "A hybrid formulation for the analysis of time-periodic linear systems via Chebyshev polynomials," Journal of Sound and Vibration 195(3), 518-527.

Keel, L.H. , Bhattacharyya, S.P. , and Howze, W. Jo , 1988, "Robust control with structured perturbation," IEEE Transaction on Automatic Control 33(1), 68-77.

Kwakemaak, H. and Sivan, R. , 1972, Linear Optimal Control Systems, Wiley Interscience, New York.

Lee, Y.J. and Balas, M.J. , 1998, "Controller design of periodic time-varying systems via time-invariant methods," AIAA Journal of Guidance, Control and Dynamics 22(3), 486-488.

Mahmood, M.S. , Hassan, M.F. , and Darwish, M.G. , 1985, Large Scale Control Systems: Theories and Techniques , Dekker, New York.

Mahmood, M.S. and Singh, M.G. , 1981, Large Scale Systems Modeling, Pergamon , Oxford, UK.

10.

Sinha, S.C. and Joseph, P. , 1994, "Control of general dynamic systems with periodically varying parameters via Lyapunov-Floquet transformation," ASME, Journal of Dynamic Systems, Measurement and Control 116, 650-658.

11.

Sinha, S.C. , Pandiyan, R. , and Bibb, J.S. , 1996, "Liapunov-Floquet transformation: Computation and applications to periodic systems," Journal of Vibration and Acoustics 118, 209-219.

12.

Sinha, S.C. and Wu, D.H. , 1991, "An efficient computational scheme for the analysis of periodic systems," Journal of Sound and Vibration 151(1), 91-117.

13.

Utkin, V.I. , 1992, Sliding Modes in Control and Optimization, Springer-Verlag, New York/ Berlin .

14.

Vidyasagar, M. and Desoer, C. , 1975, Feedback Systems: Input-Output Properties, Academic Press, San Diego.

15.

Yakubovich, V.A. and Starzhinskii V M. , 1975, Linear Differential Equations With Periodic Coefficients, vols. I and 2, John Wiley, New York.

Order Reduction and Control of Parametrically Excited Dynamical Systems

Abstract

Keywords

Get full access to this article

References