Design of Modal Filters Exact on Maximal Spaces of Functions

For the implementation of modal control concepts for linear distributed-parameter systems knowledge of the modal coordinates is mandatory. Modal filters present an approach to extract these coordinates from a set of measurements. Using an array of sensors the design problem involves the choice of proper weighting coefficients and locations for the elements of the sensor array. In this contribution conditions on the sensor positions are derived using knowledge of the mode shapes to design modal filters that are exact for a maximal number of consecutive modes. The application of the given design process is illustrated by two examples.