Orthogonal Eigenstructure Control: Theory and Application to Vibration Suppression

Thursday, March 26, 2009
9:00 - 10:00 AM
Room 229, Norris Hall

Dr. Mohammad Rastgaar-Aagaah
Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA 02139

Orthogonal eigenstructure control is a feedback control methodology applicable to general multi-input multi-output linear systems. While the available control design methodologies for large flexible structures offer a large and complex design space of options that can often overwhelm a designer, this control methodology offers a significant simplification of the design task while still allowing some experience-based design freedom. Specifically, this control methodology eliminates the need for shaping and defining the desirable eigenstructure as required in eigenstructure assignment methods. Mode shapes of a structure can be defined by its open-loop eigenvectors that are the intersections of the open-loop and achievable eigenvector sets. Orthogonal eigenstructure control defines the achievable eigenvector sets for the target modes and generates a class of the vectors within the achievable eigenvector sets that are orthogonal to the open-loop eigenvectors and substituted them as the eigenvectors of the controlled system. This simplifies the design process and eliminates any guesswork by the controller designer. Orthogonal eigenstructure control has several key advantages: it is relatively easy to design and implement for large scale multiple-input multiple-output systems; it enables control engineers to achieve good performing designs regardless of their design experience; and it is able to perform robustly in the presence of a wide variety of disturbances. Orthogonal eigenstructure control can significantly reduce the controller development cycle through a mathematically sound approach that is easily implemented to a broad range of structures and dynamical systems. The application of this control methodology for vibration cancellation of a steel test plate is investigated through experiments for tonal and wideband disturbances using piezoelectric actuators. The results show a significant reduction in vibration using the orthogonal eigenstructure control with relative ease in finding the control gain matrix. This lecture covers the mathematical aspects of orthogonal eigenstructure control as well as the results of implementing this method to different applications.

Biographical Sketch: Dr. Rastgaar is currently a postdoctoral associate in the mechanical engineering department at the Massachusetts Institute of Technology working on stochastic estimation of human ankle dynamic stiffness. He received his Ph.D. in mechanical engineering from Virginia Tech in 2008. He has worked as a graduate research assistant at the Center for Vehicle Systems & Safety, where he developed the orthogonal eigenstructure control. Dr. Rastgaar earned his BS degree in mechanical engineering, majored in mechanical design, from Sharif University of Technology and his MS degree in mechanical engineering, majored in solid mechanics, from Tehran Polytechnic. He held several positions as research engineer, design engineer, and lecturer. He received his second MS degree in mechanical engineering form North Dakota State University, working on micro-fluidics, MEMS, and Nanotechnology. Dr. Rastgaar is the member of ASME, SAE, AIAA, and SPIE and has served in the organizing committees of the SPIE Conference on Smart Structures and Materials and the SAE Commercial Vehicle Engineering Congress and Exhibition.

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