An approach to the LQG/LTR design problem with specifications for finite-dimensional SISO control systems

This is an expository paper that discusses an approach to the linear quadratic Gaussian/loop transfer recovery (LQG/LTR) design problem for finite-dimensional single-variable (single-input/single-output, SISO) control systems. The approach is based on the utilization of weighting augmentation for incorporating design specifications into the framework of the LTR technique for LQG compensator design. The LQG compensator is to simultaneously meet given analytical low- and high-frequency design specifications expressed in terms of desirable sensitivity and controller noise sensitivity functions. The paper is aimed at non-specialists and, in particular, practitioners in finite-dimensional LQG theory interested in the design of feedback compensators for closed-loop performance and robustness shaping of SISO control systems in realistic situations. The proposed approach is illustrated by a detailed design example: the torque control of a geared DC motor with an elastically mounted output shaft.