On practical fixed order H∞ loop-shaping

In this paper, a fixed order H_∞ synthesis is used to directly shape the open loop transfer function so that it matches as closely as possible, in the singular values sense, a desired frequency gain which captures both performance and robust stability objectives. First, a loop shaping weight is automatically computed, and then it is used in the controller synthesis by solving a well-suited four-block H_∞ control problem with a recently developed nonsmooth H_∞ synthesis routine. Two industrial applications are provided to illustrate the potential of the approach for low order robust controller design: a first one on the control of a piezo-actuated optronic mechanism, a second one dealing with inertial Line Of Sight stabilization loops.