Design of gain-scheduled controllers based on parametric H<SUB align="right">∞ loop shaping

Abstract

Synthesis conditions for the design of gain-scheduled controllers based on a parametric H ∞ loop shaping approach are presented for linear parameter-varying (LPV) systems. The main procedures to find such robust controllers are given. The design problem has been formulated via static H ∞ output feedback control, considering the uncertainty as normalised coprime factors of the shaped plant. The shaped plant must be chosen appropriately to satisfy the robustness requirements of the closed-loop system. The design procedure features free parameters to increase the flexibility of the design ensuring robust stabilisation of the LPV system. For the existence of a gain-scheduled parametric H ∞ loop shaping controller, a set of sufficient conditions has been derived in an LMI framework. Numerical examples illustrate the use of the proposed control design with applications to two physical systems: a two-mass-spring system and a hover system.