Suppression of vibration with optimal actuators and sensors placement
Treść / Zawartość
It is proposed to place the actuators to maximize the mean value of energy transmitted from or dissipated by the actuators, while the sensor location should maximize the mean square value of system output, which also maximizes the signal-to-noise ratio. By using explicit expressions for controllability and observability grammians as well as modal energies, it is shown that the approaches based on the system responses to transient and persistent disturbances are closely related, and are equivalent for structures which damping is small and the natural frequencies of which are well spaced. The method of actuator and sensor optimal location via grammians was proposed and compared it with results given by the method of matrix norms.
Bibliogr. 28 poz., rys., wzory
-  A. ARBEL: Controllability measures and actuator placement in oscillatory systems. Int. J. of Control, 33 (1981) 565-574.
-  R. BARBONI, A. MANNINI, E. FANTINI and P. G AUDENZI: Optimal placement of PZT actuators for the control of beam dynamics. Smart Mater Struct., 9 (2000), 110-120.
-  A. BENSOUSSAN: Lecture Notes on Mathematics Optimization of sensors location in a distributed filtering problem. University of Warwick, Coventry, 294 (1972), 62-84.
-  I. BRUANT and L. PROSLIER: Optimal location of actuators and sensors in active vibration control. J. of Intel. Material Systems and Structures, 16 (2005), 197-206.
-  A. E. BRYSON and Y.-C. Ho: Applied optimal control, optimization, estimation, and control. New York, Hemisphere, 1975.
-  M. I. J. CHANG and T. T. SOONG: Optimal controller placement in modal control of complex systems. J. of Mathematical Analysis and Applications, 75 (1980), 340-358.
-  A. HAC and S. RADKOWSKI: Application of Kalman filter technique to measurement of stochastic vibration of distributed parameter systems. Institute of Machine Design Fundamentals Research, 13 (1982), 113-137, (in Polish).
-  A. HAC and L. LIU: Sensor and actuator location in motion control of flexible structures. J. of Sound and Vibration, 167(2), (1993).
-  P. C. HUGHES and R. E. SKELTON: Control-lability and observability of linear matrix-second-order systems. J. of Applied Mechanics, 47 (1980), 415-420.
-  P. C. HUGHES and R. E. SKELTON: Controllability and observability for flexible spacecraft. J. of Guidance and Control, 3 (1980), 452-459.
-  S. KONDOFI, C. YATOMI and K. INOUE: The positioning of sensors and actuators in the vibration control of flexible systems. JSME Int. J., Series II, 133 (1990), 145-152.
-  R. E. LINDENBERG, JR. and R. W. LONGMAN: On the number and placement of actuators for independent modal space control. J. of Guidance and Cantrol, 7 (1984), 215-221.
-  W. LIU, Z. HOU and M. A. DEMETRIOU: Optimal sensor/actuator location for vibration control of structures. 17th ASCE Engineering Mechanics Conf., (2004), 13-16.
-  J. C. E. MARTIN: Optimal allocation of actuators for distributed parameter systems. J. of Dynamic Systems, Measurement, and Control, 100 (1978), 227-228.
-  A. D. NASHIF, D. I. G. JONES and J. P. HENDERSON: Vibration Damping. John Willey & Sons, Inc, New York, 1985.
-  F. PENG, A. NG and Y. HU: Actuator placement optimization and adaptive vibration control of plate smart structures. J. of Intelligent Material Systems and Structures, 16 (2005), 263-271.
-  S. PULTHASTHAN and H. R. POTA: The optimal placement of actuator and sensor structures for active noise control of sound-structure interaction systems. Smart Materials and Struct., (2008), 1-11.
-  G. SCHULZ and G. HEIMBOLD: Dislocated actuator/sensor positioning and feedback design for flexible structures. J. of Guidance and Control, 6 (1983), 361-367.
-  L. STAREK, P. SOLEK, P. STAREKOV A and P. BLESAK: Suppression of vibration of a clamped beam with embedded self-sensing piezoceramics actuator. Elektronika, Warsaw, 8-9 (2004), 22-24.
-  T. H. YAN and R. M. LIN: General optimization of sizes or placement for various sensors/actuators in structure testing and control. Smart Materials and Structures, 15 (2006), 724-736.
-  H. ZHANG, H. WU, X. ZHANG and Z. QIU: Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate. J. of Sound and Vibration, 301 (2006), 521-543.
-  J.-N. JUANG and G. RODRIGUEZ: Formulations and applications of large structure actuator and sensor placements. Proc. of the Second YPI&SU/AIAA Symp. on Dynamics and Control of Large Flexible Spacecraft, (L. Meirovitch, Ed.), (1979), 247-262.
-  R. E. KALMAN, Y.-C. Ho and K.S. NARENDRA: Controllability of linear dynamical systems. Contributions to Differential Equations, 1(2), (1962), 189-213.
-  R. H. MIDDLETON and G. C. GOODWIN: Digital control and estimation: a unified approach. Prentice Hall, 1990.
-  W. GAWRONSKI and J. N. JUANG: Model reduction for flexible structures. Control and Dynamic Systems: Advances in Theory and Applications, (C.T. Leondes, Ed.) 36 (1990), 143-222.
-  K. GLOVER: All optimal Hankel-norm approximations of linear multivariable systems and their L’-errors bounds. Int. J. of Control, 39 (1984), 1115-1193.
-  D. J. INMAN: Vibration and control. John Willey and Sons, Chichester, UK, 2006.
-  C. J. GOH and T. K. CAUGHEY: On the stability problem caused by finite actuator dynamics in the collocated control of large space structures. hit. J. Control, 41(3), (1985), 787-802.