Title: Design of gain-scheduled controllers based on parametric H_∞ loop shaping

Authors: Renan Lima Pereira; Karl Heinz Kienitz

Addresses: Instituto Tecnológico de Aeronáutica, Praça Marechal-do-Ar Eduardo Gomes, 50 São José dos Campos – SP, 12228-900, Brazil ' Instituto Tecnológico de Aeronáutica, Praça Marechal-do-Ar Eduardo Gomes, 50 São José dos Campos – SP, 12228-900, Brazil

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.

Keywords: parametric H-infinity loop shaping; gain scheduling; controller design; linear parameter-varying systems; LPV systems; linear matrix inequalities; LMIs; feedback control; two-mass-spring systems; hover systems.

DOI: 10.1504/IJMIC.2015.067717

International Journal of Modelling, Identification and Control, 2015 Vol.23 No.1, pp.77 - 84

Published online: 31 Mar 2015 *

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