Robust Gain-Scheduled Flight Controller for an In-Flight Simulator

Conservatism reduction for linear parameter‐varying control design facing inexact scheduling parameters illustrated on flight tests

“…Our supposed LPV systems in this article are slightly relaxed from parametrically affine LPV systems 16,17 to parametrically multiaffine LPV systems 18‐20 without introducing huge numerical complexity in the design process. As a practical application of our method, we design discrete‐time LPV flight controllers for the lateral‐directional motions of a research airplane MuPAL‐α in the same problem setup adopted in Reference 6, and confirm that our method produces better LPV controllers than the method in Reference 6 w.r.t. control performance, that is, model‐matching performance.…”

“…In Reference 8 for continuous‐time case and in Reference 6 for discrete‐time case, the following formulation is used to overbound the term related to the scheduling parameter discrepancies, that is, in (1).…”

“…Using Lemma 1, we propose a design method of LPV output feedback controllers depending on inexact scheduling parameters, and show the conservatism reduction compared with the methods in References 6,8.…”

“…Most of them implicitly suppose that exact scheduling parameters are available; however, it does not always hold true in practical systems due to aging effect, finite resolutions, and other unexpected uncertainties of the measurement equipment of scheduling parameters. For example, airspeed is widely used as one of the scheduling parameters in gain‐scheduled flight controller design, 4 and Pitot tube is widely used to measure airspeed in aeronautical community; however, it is also well known that so‐called position error always exists due to the effect of aircraft fuselage and thus the precise value is not always available, as illustrated in References 5,6.…”

“…On the uncertainties in the inexactly provided scheduling parameters, particular uncertainties are first supposed, 7,8 then the supposition has been relaxed 10,11 . On this issue, it has been established in Reference 6 that as long as the design matrix inequalities are given as parametrically affine, bounded uncertainties in the provided scheduling parameters can be supposed by using the convexity of design matrix inequalities with respect to (w.r.t.) parameters; viz., any type uncertainties can be supposed in the provided scheduling parameters as long as they are bounded and the design matrix inequalities are given as parametrically affine.…”