×

Observer-based self sensing actuation of piezoelastic structures for robust vibration control. (English) Zbl 1244.93043

Summary: This contribution is concerned with Self-Sensing Actuation (SSA) for the adaptive vibration control of smart structures with piezoelectric actuators. The electro-mechanical model of a Kirchhoff plate equipped with two piezoelectric patches is rewritten in the form of an infinite dimensional Port Controlled Hamiltonian system with Dissipation (PCHD) where collocation of input and output is achieved by SSA. In the case of piezoelectric actuators, self sensing requires a robust separation of electric current due to the direct piezoelectric effect from the measured electric current. Because of the unfavorable ratio of these two signals, the design of an approximate observer for the electric current due to the direct piezoelectric effect is proposed. The control design goal is the asymptotic suppression of a harmonic disturbance with unknown frequency, amplitude and phase. The control law is derived for the plant augmented by an appropriate exosystem, which models the properties of the disturbance. The novelty of this contribution is the extension of the control design methods from the finite dimensional case to the infinite dimensional one. The stability analysis for the infinite dimensional system is based on the concept of \(L_{2}\)-stability and the small gain theorem. Vibration attenuation around a dominant eigenfrequency is demonstrated by simulation and experiment.

MSC:

93B35 Sensitivity (robustness)
93C73 Perturbations in control/observation systems
93B07 Observability
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anderson, E.H., Hagood, N.W., & Goodliffe, J.M. (1992). Self-sensing piezoelectric actuation: analysis and application to controlled structures. In Proc. AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, Materials Conference; Anderson, E.H., Hagood, N.W., & Goodliffe, J.M. (1992). Self-sensing piezoelectric actuation: analysis and application to controlled structures. In Proc. AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, Materials Conference
[2] Dong, W., & Sun, B. (2006). Observer-based piezoelectric self-sensing actuator. In Proceedings of SPIE International Conference on Sensor Technology, Vol. 4414; Dong, W., & Sun, B. (2006). Observer-based piezoelectric self-sensing actuator. In Proceedings of SPIE International Conference on Sensor Technology, Vol. 4414
[3] Dosch, J. J.; Inman, D. J.; Garcia, E., A self-sensing piezoelectric actuator for collocated control, Journal of Intelligent Materials, Systems, and Structures, 3, 1, 166-185 (1992)
[4] Ennsbrunner, H., & Schlacher, K. (2006). Modeling of piezoelectric structures — a Hamiltonian approach. In I. Troch, F. Breitenecker (Eds.), CD Proceedings 5th vienna symposium on mathematical modelling, mathmod 2006, serie ARGESIM Report, Vol. 2; Ennsbrunner, H., & Schlacher, K. (2006). Modeling of piezoelectric structures — a Hamiltonian approach. In I. Troch, F. Breitenecker (Eds.), CD Proceedings 5th vienna symposium on mathematical modelling, mathmod 2006, serie ARGESIM Report, Vol. 2 · Zbl 1154.93333
[5] Fuller, C. R.; Elliott, S. J.; Nelson, P. A., Active control of vibration (1993), Academic Press: Academic Press London
[6] Irschik, H., Krommer, M., & Pichler, U. (2001). Collocative control of beam vibrations with piezoelectric self-sensing layers. In Proceedings of IUTAM-symposium on smart structures and structronic systems; Irschik, H., Krommer, M., & Pichler, U. (2001). Collocative control of beam vibrations with piezoelectric self-sensing layers. In Proceedings of IUTAM-symposium on smart structures and structronic systems
[7] Isidori, A.; Marconi, L.; Serrani, L,A., Robust autonomous guidance — an internal model approach (2003), Springer: Springer London · Zbl 0991.93535
[8] Kaufman, H.; Barkana, I.; Sobel, K., Direct adaptive control algorithms — theory and applications (1998), Springer: Springer New York
[9] Khalil, H. K., Nonlinear systems (1996), Prentice Hall Inc.: Prentice Hall Inc. New Jersey · Zbl 0626.34052
[10] Komornik, V., Exact controllability and stabilization: the multiplier method (1994), Masson: Masson Paris · Zbl 0937.93003
[11] Krstic, M.; Kanellakopoulos, I.; Kokotovic, P., Nonlinear and adaptive control design (1995), Wiley: Wiley New York · Zbl 0763.93043
[12] Kugi, A.; Schlacher, K., Passivitätsbasierte regelung piezoelektrischer strukturen, at - Automatisierungstechnik, 9, 422-431 (2002)
[13] Lagnese, J., Boundary stabilization of thin plates (1989), Society for Industrial and Applied Mathematics: Society for Industrial and Applied Mathematics Philadelphia · Zbl 0696.73034
[14] Law, W. W.; Liao, W.-H.; Huang, J., Vibration control of structures with self-sensing piezoelectric actuators incorporating adaptive mechanism, Smart Materials and Structures, 12, 720-730 (2003)
[15] Liu, C.; Peng, H., Disturbance observer based tracking control, Journal of Dynamical Systems, Measurement Control, 122, 2, 332-335 (2000)
[16] Luo, Z. H.; Guo, B. Z.; Morgul, M. J., Stability and stabilization of infinite dimensional systems with applications (1999), Springer: Springer London
[17] Preumont, A., Vibration control of active structures — an introduction (2002), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 1011.74001
[18] Qiu, J.; Haraguchi, M., Vibration control of a plate using a self-sensing piezoelectric actuator and an adaptive control approach, Journal of Intelligent Material Systems and Structures, 17, 661 (2006)
[19] Reza Moheimani, S. O.; Halim, D.; Fleming, A. J., Spatial control of vibration — theory and experiments (2003), World Scientific: World Scientific Singapore · Zbl 1055.74001
[20] Rittenschober, T.; Schlacher, K., Control of plate vibrations with piezo patches using an infinite dimensional PCHD formulation, (Topping, B. H.V.; Adam, J. M.; Pallarés, F. J.; Bru, R.; Romero, M. L., Proceedings of the tenth international conference on computational structures technology (2010), Civil-Comp Press: Civil-Comp Press Stirlingshire, UK), Paper 210
[21] Schlacher, K., Mathematical modeling for nonlinear control: a Hamiltonian approach, Mathematics and Computers in Simulation, 79, 829-849 (2008) · Zbl 1157.93314
[22] Xian, B.; Jalili, N.; Dawson, D. M.; Fang, A., Adaptive tracking control of linear uncertain mechanical systems subjected to unknown sinusoidal disturbances, ASME Journal of Dynamic Systems, Measurements and Control, 125, 1, 129-134 (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.