Active Mode Localization in Distributed Parameter Systems with Consideration of Limited Actuator Placement, Part 1: Theory

1995 ◽  
Vol 122 (2) ◽  
pp. 160-164 ◽  
Author(s):  
Franz J. Shelley ◽  
William W. Clark
Keyword(s):  
Distributed Parameter Systems ◽  
Theoretical Development ◽  
Distributed Parameter ◽  
Limiting Factor ◽  
Sensors And Actuators ◽  
Mode Localization ◽  
Active Mode ◽  
Value Decomposition ◽  
Actuator Placement ◽  
Do So

The purpose of this two-part work is to apply active mode localization to distributed parameter systems where the number of control sensors and actuators is a limiting factor. In this part, the theoretical development portion of the study, two approaches are presented that shape system eigenvectors using feedback control, generating localization to produce areas of isolation with relatively low vibration amplitudes compared to other parts of the structure. The first approach uniformly shapes all eigenvectors of a vibrating system, but can require many actuators to do so. The second more general approach uses singular value decomposition (SVD) to shape selected eigenvectors of a system, localizing the response of these modes to any disturbance, and requiring few actuators. [S0739-3717(00)70202-9]

Active Mode Localization in Distributed Parameter Systems With Consideration of Limited Actuator Placement

1995 ◽  
Author(s):  
Franz J. Shelley ◽  
William W. Clark
Keyword(s):  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Limiting Factor ◽  
Beam Model ◽  
Sensors And Actuators ◽  
Lower Mode ◽  
Mode Localization ◽  
Active Mode ◽  
Value Decomposition ◽  
Actuator Placement

Abstract The purpose of this work is to investigate the application of active mode localization to discretized models of distributed parameter systems where the number of control sensors and actuators is a limiting factor. A modified eigenvector scaling technique using singular value decomposition is developed which scales the lower-mode eigenvectors, producing localization over the range of these lower natural frequencies. An example using a simply supported beam model is provided, with mode localization achieved in at least the lower 3 modes utilizing as few as two control sensor/actuator pairs.

Active Mode Localization in Distributed Parameter Systems with Consideration of Limited Actuator Placement, Part 2: Simulations and Experiments

1995 ◽  
Vol 122 (2) ◽  
pp. 165-168 ◽  
Author(s):  
F. J. Shelley ◽  
W. W. Clark
Keyword(s):  
Vibration Isolation ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Limiting Factor ◽  
Parameter System ◽  
Sensors And Actuators ◽  
Mode Localization ◽  
Active Mode ◽  
Shaping Technique ◽  
Actuator Placement

The purpose of this two-part work is to apply active mode localization techniques to distributed parameter systems where control actuator and sensor placement is a limiting factor. In this paper, Part 2 of the study, the SVD eigenvector shaping technique examined in Part 1 is utilized to numerically and experimentally localize the response of a simply supported beam. This is done for two reasons. First, it demonstrates the application of this modified mode localization technique to a distributed parameter system. Second, it shows that it is possible to use this method to produce vibration isolation, reducing the absolute displacements in designated portions of the system while simultaneously curtailing the number of necessary control sensors and actuators. [S0739-3717(00)70302-3]

Transfer Function Formulation of Constrained Distributed Parameter Systems, Part II: Applications

1993 ◽  
Vol 60 (4) ◽  
pp. 1012-1019 ◽  
Author(s):  
C. H. Chung ◽  
C. A. Tan
Keyword(s):  
Transfer Function ◽  
Elastic Foundation ◽  
Normal Modes ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Displacement Method ◽  
Mode Localization ◽  
Function Formulation ◽  
Free Beam ◽  
Symmetric Systems

In this paper, the application of the transfer function formulation and the generalized displacement method (GDM) to the analysis of constrained distributed parameter systems is illustrated. Two kinds of classical examples are considered. In the constrained free-free beam example, it is shown how the GDM gives the eigensolutions without requiring knowledge of the normal modes of the unconstrained beam. In the string on a partial elastic foundation example, mode localization and eigenvalue loci veering phenomena are examined. It is shown that mode localizaation can occur in spatially symmetric systems and for modes whose frequency loci do not veer.

Active Control of Mechanical Vibrations in a Circular Disk

1992 ◽  
Vol 114 (1) ◽  
pp. 104-112 ◽  
Author(s):  
C. Y. Kuo ◽  
C. C. Huang
Keyword(s):  
Mechanical Vibration ◽  
Circular Disk ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Sensors And Actuators ◽  
Mechanical Vibrations ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Finite Dimensional ◽  
And Control

Mechanical vibration is a common phenomenon observed in the operation of many machines and arises from the inertia effect of machine parts in motion. While many control system design methods for distributed parameter systems have already been proposed in the literature, generally they are either based on truncated models and, as a result, suffer from computational and “spillover” difficulties or require distributed parameter actuators which are rarely available in reality. Therefore, there is a definite need for the development of a class of controllers which can be realized by spatially discrete sensors and actuators and whose design specifically includes stabilization and control of all the higher frequency vibration modes. To address this need, we propose the design of linear compensators whose design is based on root locus arguments for infinite dimensional systems. Since the design is not based on finite dimensional models of the plant to be controlled, we expect it to perform well for those distributed parameter systems for which sufficiently accurate data on pole and zero locations can be obtained. In this paper we apply this approach to control mechanical vibrations in those physical systems which can be accurately modeled as a flexible circular disk. Computer simulation results indicate that all the predominant lower frequency vibrations can be efficiently eliminated by just a few pairs of colocated sensor and actuator.

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