A Parameter Robust LQG Design Synthesis with Applications to Control of Flexible Structures

An asymptotic LQG design synthesis technique is described which explicitly includes a class of structured plant uncertainties by viewing plant parameter variations as an internal feedback loop. A direct structural relationship between this class of parameter uncertainties and the weighting matrices in the design of the LQG compensator is exploited by an asymptotic procedure in which either the regulator or the filter become insensitive to parameter vaiations. This asymptotic approach represents a generalization of the LQG/LTR technique. Controllers designed by this new LQG method and LQG/LTR are compared by application to a mass-spring-damper system which approximates the dynamics of flexible structures. For both colocated and noncolocated sensors and actuators configurations, the LQG/LTR design is extremely sensitive to parameter variations whereas the new LQG design allows considerably improved parameter robustness.