Feedback Structures for a Transfer Function Model of a Circular Vibrating Membrane

The attachment of feedback loops to physical or musical systems enables a large variety of possibilities for the modification of the system behavior. Feedback loops may enrich the echo density of feedback delay networks (FDN), or enable the realization of complex boundary conditions in physical simulation models for sound synthesis. Inspired by control theory, a general feedback loop is attached to a model of a vibrating membrane. The membrane model is based on the modal expansion of an initial-boundary value problem formulated in a state-space description. The possibilities of the attached feedback loop are shown by three examples, namely by the introduction of additional mode wise damping; modulation and damping inspired by FDN feedback loops; time-varying modification of the system behavior.