Static H∞ loop shaping control of a fly-by-wire helicopter

This paper introduces a novel static output feedback version of the design procedure of [McFarlane & Glover, 1992. IEEE Trans. Aut. Control 37(6), 759-769]. Existence conditions for a static output loop shaping controller are given in terms of two coupled matrix inequalities. Simple linear sufficient conditions can be derived from these coupled nonlinear inequalities and the determination of a static, sub-optimal, H∞ loop shaping controller reduces to an optimization problem over Linear Matrix Inequalities. The new procedure is demonstrated by its application to the design of a flight control system for the Canadian NRC fly-by-wire Bell 205 research helicopter. The resulting H∞ controller has just three states and would appear to be the simplest flight control system used on this helicopter. The system was successfully flight-tested and high levels of performance were achieved.