The SISO LQG compensator for lightly damped structures

An analytical examination of the linear quadratic Gaussian compensator designed for lightly damped structures is conducted. The expensive and cheap control asymptotes of the linear quadratic regulator, and the dual Kalman filter, are derived. A useful form of the SISO LQG compensator is developed, which is utilized in the derivation of the SISO LQG asymptotes. Insight into the strengths and weaknesses of LQG compensators designed for controlled structures is developed through a rigorous examination of the compensator structure, and asymptotes for four distinct structural control topologies of a low order model of a beam.