Modal Control of Structural Systems

Abstract : There is much interest in the practical control of large space structures such as space transportation systems and large communication satellites. The control task is normally thought of in terms of maintaining specified shape configurations, orientation and alignment, vibration suppression and pointing accuracy, etc. Because of their inherent flexibility, they are generally analyzed as distributed parameter systems which creates difficulties in the design and analysis of controllers for them. Modal control techniques have been developed to bypass problems associated with distributed parameter theory. Modal control is built upon the notion that certain specified system modes can be controlled by appropriate design of the associated closed-loop eigenvalues. This reduces the number of sensors and actuators needed to effect the control of the structure. An undesirable phenomenon, referred to as observation and control spillover, can occur if the number of sensors and actuators used is small. Spillover refers to the phenomenon in which energy intended to go solely into the controlled modes leaks into the uncontrolled modes. This report discusses the control of flexible systems described by a generalized one-dimensional wave equation which relates the structure displacement to the force distribution acting on the structure. Optimal control involving the minimization of a quadratic performance index representing control and modal energy content is considered. Typically this control formulation leads to a state feedback algorithm.