Feasibility of Piezoelectric Actuation with a Reduced Number of Drivers: A Periodic Control Approach

Abstract

The problem of controlling several piezoelectric actuators using a smaller number of power drivers is considered. A multiplexed arrangement is examined where power and control are applied cyclically to subsets of actuators, introducing periodicity in the dynamics of the controlled plant. A model for the multiplexed scheme along with a periodic quadratic regulator are presented, as well as an observer-based arrangement. The feasibility of the proposed technique is demonstrated experimentally by using a single power driver to control a cantilever beam fitted with three piezoelectric actuators.

Keywords

piezoelectric actuators multiplexing periodic systems periodic control digital control.

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References

Bittanti, S. , Colaneri, P. and De Nicolao, G. 1991. ``The Periodic Riccati Equation,'' In: Bittanti, S. , Laub, J.A. and Willems, J.C. (eds), The Riccati Equation., pp. 127-162, Springer.

Demetriou, M.A. 2001. ``Optimal Switching Policy of Smart Actuators in Flexible Structures,'' Proceedings of SPIE: Smart Structures and Materials 2001: Modeling, Signal Processing and Control in Smart Structures , Vol. 4326 of pp. 220-231, Newport Beach , California.

Demetriou, M.A. and Potami, R. 2006. ``Scheduling Policies of Intelligent Sensors and Sensors/Actuators in Flexible Structures,'' Proceedings of SPIE: Smart Structures Materials 2006: Sensors and Smart Structures for Civil, Mechanical and Aerospace Systems, p. 6174, San Diego, California.

Geromel, J.C. 1989. ``Convex Analysis and Global Optimization of Joint Actuator Location Control Problems,'' IEEE Transactions on Automatic Control, 34(7):711-720.

Grasselli, O.M. 1984. ``A Canonical Decomposition of Linear Periodic Systems ,'' International Journal of Control, 40(1):201-214.

Madgav, A.V.G. and Soh, C.K. 2008. ``Uniplexing and Multiplexing of PZT Transducers Structural Health Monitoring,'' Journal of Intelligent Material Systems and Structures, 19:457-467.

Richter, H. , Singaraju, A.V. and Litt, J.S. 2008. ``Multiplexed Predictive Control of a Large Commercial Turbofan Engine,'' AIAA Journal of Guidance, Dynamics and Control, 31(2):273-281.

Song, H. , Simonov, A.N. and Vdovin, G. 2005. ``Multiplexing Control of a Multichannel Piezoelectric Deformable Mirror,'' 5th International Workshop on Adaptive Optics for Industry and Medicine, Beijing, China, pp. 419-428.

Sreedhar, J. and Van Dooren, P. 1994. ``On Finding Stabilizing State Feedback Gains for a Discrete Time Periodic System,'' Proc. 1994 American Control Conference, pp. 1167-1168, Baltimore, Maryland.

10.

Varga, A. 1997. ``Periodic Lyapunov Equations: Some Applications and New Algorithms,'' International Journal of Control, 67(1):69-87.