Modal Scheduling and Switching Systems

This paper defines a modal scheduling method for obtaining reduced order systems. In contrast to most order reduction schemes for linear structural systems, the methodology in this paper introduces a switched system to achieve order reduction. The switched system model is based on modal participation factors calculated from an input forcing function and the initial conditions at each switching time. Stability of the reduced order model is discussed, and necessary conditions for stability of the proposed switched model are derived. A numerical example that considers a flexible beam provides a testbed for the study of mode switching. The transient response in the testbed example is constructed such that it oscillates between two distinct subspaces. Numerical experiments show that an error indicator based on modal participation factors provides an effective switching strategy.