Transfer functions of flexible beams and implication of flexibilty on controller performance

Abstract

Dynamic behavior of many mechanical motion systems having distributed flexibility are described by linear partial differential equations, i.e. flexible beams, satellite appendages, plates. Understanding the open loop transfer function (poles, zeros, d.c. gain) is a prerequisite for a successful controller design. The open loop pole-zero patterns of a flexible beam (using its infinite dimensional model) are studied as a function of actuator and sensor locations. The physics of the flexible beam dynamics is discussed in order to explain the physical source and the meaning of zeros, and its implications in terms, of the limitations imposed on the maximum closed loop bandwidth achievable. Although the actual system dynamics involve an infinite number of modes, finite dimensional models are needed for the design of a real time controller. The accuracy of finite dimensional models using different mode shapes are compared from a controller design point of view.