LQG optimal compensator transfer function for the NASA LaRC CSI Evolutionary Model

Abstract

Following the general form for LQG optimal compensators for flexible structures with collocated rate sensors we develop an explicit compensator transfer function for the NASA LaRC CSI Evolutionary model in the form: psi(i omega) = g i omega B(sub u)(sup *)(-M(sub b)omega(exp 2) + T(i omega) + i gamma omega B(sub u)Bu(sub u)(sup *))(exp -1)B(sub u) where T(i omega) is a 48 x 48 positive definite matrix whose derivation is the main result of this report. The undamped mode frequencies can be expressed in terms of T(i omega) as the zeros of Det (-omega(exp 2)M(sub b) + T(i omega)) while 'clamped-clamped' modes of the structure (with all nodes clamped) are the poles.