Modified H∞ loop-shaping procedure for the two degrees-of-freedom control configuration of an UAV (ARCHER V 1.7)

The robust stabilization problem with respect to both dynamic and parametric uncertainty for linear deterministic systems is analyzed in the present article. The robust design methods consider either the dynamic modelling in frequency domain of the uncertainty or, its parametric representation in the state space realisation. Suitable analysis approaches for parametric uncertainty modelling are provided by Kharitonov and Edge-type theorems. Under some specific assumptions, these methods allow to determine the whole admissible domain of the uncertain parameters for which a system is stable. It shall describe a method that combines the advantages of the control techniques with ones given by the polytopic representation of parametric uncertainty. A modified 𝐻𝐻∞ loop-shaping approach allowing to solve control problems in which robust stabilization, sensitivity reduction, and model following design objectives are formulated is presented and it allows to handle tracking design specifications. The modified loop-shaping procedure allows to design a controller that provides a) robust stability with respect to the normalized left coprime factorization (NLCF); b) reduced sensitivity with respect to output disturbance on a specified range of frequencies, and c) tracking of the output of a given ideal model. The article is finished with a case study in which a two degrees-of-freedom control system with respect to the pitch angle for the longitudinal dynamics of a UAV (ARCHER V1.7) is designed using the modified 𝐻𝐻∞ loop-shaping procedure.