Synthesis Techniques for Robust Adaptive Vibration Control

The problem of synthesizing robustly stable gain matrices for the adaptive vibration control of unbalanced rotors is examined and several synthesis techniques are developed. The quite general case of uncertainties entering into the magnetic bearing system model in a linearfractional form are considered. The uncertainties may be highly structured and either parametric or dynamic. It is shown that the resulting robust synthesis problem may be written as a nonlinear matrix inequality in both the gain matrix and scaling matrices. Three synthesis algorithms are then developed. In each, an iteration is conducted between the two problems of gain matrix optimization and scale optimization. It is also shown that the optimization with respect to the gain matrix can be eliminated by the use of a projection allowing direct construction of a satisfactory gain matrix. In each case, the optimization with respect to the scales can be reformulated as either a linear matrix inequality or a structured singular value computation. Furthermore, it is demonstrated that a family of robust gain matrices may be constructed from any satisfactory solution.