Improved Eigenstructure Assignment Controller Design Using a Substructure-Based Coordinate System

A new control coordinate system based on the Craig -Bampton substructure representation is examined for reduced-order-model-based controller design. Eigenstructure assignment controller design using the proposed modeling approach is shown to exhibit improved accuracy over conventional normal mode modeling in both closed-loop eigenvalue and eigenvector attainment. The improvement is due to the coordinate system' s ability to accurately predict actuator boundary conditions and, thus, actuator command forces, when extensive model reduction has been employed. Two multi-input/multi-output design examples are used to illustrate the practicality of the method and the resulting improved closed-loop behavior. EROSPACE vehicles are extremely large e exible structures requiring very accurate shape and vibration control to meet performance objectives. The presence of very low-frequency struc- tural dynamics and dense packing of very lightly damped modes in such systems may lead to a strong interaction between the structure and its control system. These vehicles are ine nite dimensional dis- tributed parameter systems, which are usually modeled by the e nite element method as a set of ordinary differential equations. This re- sults in a lumped parameter system of e nite dimension. Although e nite in dimension, these models often contain thousands or even hundreds of thousands of degrees of freedom (DOF) and require extensive model reduction to be practical for structural and control design and simulation. Recent literature has investigated the use of a new control co- ordinate system based on the Craig -Bampton (CB) substructure representation. 1i4 The CB coordinate system is the most common representation for loads analysis used in the aerospace industry today. 5 Large CB e nite element models (FEM) may be reduced to accurate design and simulation models by truncating dynami- cally unimportante xed interfacemodesusing theeffectiveinterface mass(EIM)measure of controllability/observability. 6 This measure has been shown to preserve controller/structure interaction in the reduced-order models (ROM) providing accurate closed-loop con- trol designs. This paper specie cally addresses the advantages of reduced CB- based control coordinate systems in closed-loop modern control design applications over reduced normal mode representations. In particular, eigenstructure assignment 7;8 algorithms (ESA) applied to the natural second-order form of the CB equations of motion are shown to lead to more accurate attainment of the desired closed- loop eigenstructure. Two examples are presented to illustrate the improved ESA controller designs obtained. The CB designs are shown to produce smaller gain norms, ree ecting more accurate pre- dictionofactuationcommandsbythereduced-ordermodel.Closed- loop improvements are found in both the closed-loop eigenvalues and right and left eigenvectors. Eigenvector shaping in complex systems has typically been directed at producing robust minimum norm gain solutions in the control design process. The ability to shape eigenvectorelements in a simple and highly accurate manner, as presented here, may offer additional e exibility in the selection