Real Km-synthesis via generalized Popov multipliers

The authors refine their H-infinity control designs presented at the 1990 and 1991 American Control Conference by introducing a new real Km-synthesis technique involving the use of generalized Popov multipliers. This multiplier technique substantially reduces, and in some cases may even eliminate altogether, the conservativeness associated with traditional Km-synthesis solutions in which all uncertainties are treated as complex, even when they arise from real parameters such as the masses and spring constants in the benchmark problem. The design results demonstrate how this approach permits a very precise analysis of the intrinsic tradeoffs between robustness, performance, and control energy requirements. Also included is an open-loop H-infinity prefilter design that makes it possible to address the command response shaping issue. The design concept has been applied to the benchmark problem no. 4 and successfully removes the initial undesired transient and cuts down the percent overshoot.