Application of control theory to large flexible structures using the Independent Modal-Space Control method

Abstract

The control problem of a large-order flexible system in the form of a beam-lattice is presented using the Independent Modal-Space Control (IMSC) method. The method is based on a transformation of the system equations of motion to modal space, yielding internally independent modal equations of motion. The control laws are designed in the modal space, permitting independent control of each mode, providing complete decoupling of the equations of motion. Linear optimal control with quadratic performance index is designed to control the response of the elastic as well as the rigid body modes, using the IMSC method.

Actuators placement is of fundamental importance in the control of two-dimensional domains if IMSC is used. A method is presented as to the selection of actuators configuration in order to avoid singularity in the mode participation matrix, guaranteeing system controllability.

The minimum-fuel problem is a very important one in the design of various space structures. Solution of the minimum-fuel problem is feasible in a coupled form for a fourth order system at most, but will be of insurmountable computational difficulty in the control of a flexible structure, since the model of such system will require a large number of degrees of freedom. A reformulation of the problem in the framework of "Modal Minimum-Fuel Problem" is presented, using the IMSC method. By this method, the complexity inherent in a high-order system is reduced, thus treatment of the coupled high-order system is avoided.

Numerical examples for linear optimal control, with quadratic performance index, as well as for the minimum-fuel problem, are presented.