Model Reduction of Flexible Manipulators

Abstract

Flexible manipulators can be characterized by a dynamic model with a large number of vibration modes, and the use of the model in the model-based control schemes requires reduction of model order. Balanced truncation is an effective method for model reduction of asymptotically stable systems by transforming the states to a coordinate system in which the controllability and observability Gramians are equal and diagonal, and eliminating the states which contribute weakly to the input-output map. An elastic flexible manipulator, however, is a marginally stable system and thus the balanced truncation method can not be directly applied. In this report, we present a method of reducing the order of a marginally stable system based on the fact that translation transformations in the frequency domain preserve input-output properties of the system. We address the successful application of the method to model reduction of flexible manipulators with infinite-dimensional or finite-dimensional model. The method is also applicable for any other marginally stable model, such as elastic space trusswork and multi-dimensional space vehicle structure.