Shape Control with Karhunen-Loéve-Decomposition: Theory and Experimental Results

The Finite Element Method is a powerful method that can be used to describe the dynamic behavior of mechanical systems. The most crucial problem to use this method is the large degree of freedom in FE-models. It is very difficult or even impossible to design controllers. Consequently, it is necessary to reduce the model. However, the model reduction deals only with the state variables, therefore the model reduction is not sufficient for the shape control, because a great number of reference and measured data are needed for the shape description and control. In [Zhang, W. and Michaelis, B. 2000. “Shape Control with Karhunen-Loève-Decomposition,” 11th Int. Conference on Adaptive Structures and Technologies, Nagoya, Japan, October 23-26, pp. 119-126.], we have developed a new method using the Karhunen-Loève-Decomposition to realize the shape control. In this paper, we will first give the theory briefly and then the experimental results.