H ∞ Control with μ-analysis of a Piezoelectric Actuated Plate

This paper presents the development of a multimodal H∞controller for piezoelectric actuated plates designed to simultaneously suppress vibrational components of the first two modes. The controller is developed for a reduced structural model. The closed-loop control scheme is subject to both uncertainties due to control and observation spillover in the unmodeled residual modes and to parametric errors in the structural model. The closed-loop stability and performance robustness is analyzed using μ-analysis, and numerical investigations indicate that the controller tolerates uncertainties of significant size.

[1]  Yavuz Yaman,et al.  ACTIVE VIBRATION CONTROL OF A SMART PLATE , 2002 .

[2]  J. Doyle,et al.  Linear control theory with an H ∞ 0E optimality criterion , 1987 .

[3]  Lie Yu,et al.  H(Infinity) Robust Vibration Control of a Thin Plate Covered with a Controllable Constrained Damping Layer , 2004 .

[4]  Amr M. Baz,et al.  H ∞ Control of Active Constrained Layer Damping , 2000 .

[5]  M. Morari,et al.  Computational Complexity of p Calculation , 1994 .

[6]  Ratneshwar Jha,et al.  Experimental Investigation of Active Vibration Control Using Neural Networks , 2001 .

[7]  Haim Baruh,et al.  Active control of flexible structures by use of segmented piezoelectric elements , 1996 .

[8]  Balas,et al.  [ z-analysis and Synthesis Toolbox * ( p-tools ) t , 2002 .

[9]  M. Morari,et al.  Computational complexity of μ calculation , 1994, IEEE Trans. Autom. Control..

[10]  Gustavo Luiz C. M. de Abreu,et al.  On-line control of a flexible beam using adaptive fuzzy controller and piezoelectric actuators , 2003 .

[11]  Huibert Kwakernaak,et al.  Robust control and H∞-optimization - Tutorial paper , 1993, Autom..

[12]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[13]  J. Crassidis,et al.  Control of Active Constrained Layer Damping , 1998 .

[14]  J. W. Helton,et al.  Worst case analysis in the frequency domain: The H ∞ approach to control , 1985 .

[15]  Indra Narayan Kar,et al.  Bending and torsional vibration control of a flexible plate structure using H∞-based robust control law , 2000, IEEE Trans. Control. Syst. Technol..

[16]  P. Seshu,et al.  Active vibration control of a smart beam , 2003, Other Conferences.

[17]  Edvaldo Assunção,et al.  Robust control to parametric uncertainties in smart structures using linear matrix inequalities , 2004 .

[18]  S. O. R. Moheimani,et al.  Spatial control of flexible structures - application of spatial /spl Hscr//sub /spl infin// control to a piezoelectric laminate beam , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[19]  John C. Doyle.  Analysis of Feedback Systems with Structured Uncertainty , 1982 .