Gain-scheduled linear-quadratic-regulator synthesis for the centre of gravity variations of Boeing 747-100 longitudinal modes

Ezzeddin M. Elarbi, Dina S. Laila, Nadjim M. Horri

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    For the variation in the centre of gravity (CG) of Boeing 747-100 (B747-100) longitudinal flight, the gain scheduling (GS) method is proposed to manage it over the flight envelope. The full-state feedback linear quadratic regulator (FSFLQR) has been synthesised with the GS, named (GS-FSFLQR), to obtain a realistic controller for Mach numbers (M) and altitudes (H) envelope. Such a practised control law demonstrates the CG mean aerodynamic chord (MAC) shifts correlated with M-H and actuator actions. The intermediate variable responses have been accomplished at (M, H) simulations of (0.2, 0), (0.5, 6096 m) and (0.9, 12190 m). Local controllers at M and H scheduled parameters are gained using the cubic spline method of 0.2 to 0.9 and sea level to 12190 m. Swift levelled convergences illustrated the B747-100 CG variations throughout most responses for a coupled elevator and throttle-controlled flight. These findings are validated for the flying quality requirements showing the competent merits of the GS-FSFLQR as opposed to without control flight. The maximum elevator capacity transmits the CG from the 17% MAC at (0.3, 6096 m) to 30% MAC at (0.7, 3048 m), whereas the maximum throttle occurs for the CG at 25% MAC at (0.5, 6096 m). Their minimum operations lead to 22% MAC at (0.6, sea level). The dominated CG location of the elevator is fore than 25% MAC whereas the aft and fore locations of the throttle float around that. 50% actuator effectiveness due to operable elevator and throttle adequately copes with the CG longitudinal stability.

    Original languageEnglish
    Pages (from-to)868-887
    Number of pages20
    JournalInternational Journal of Advanced Technology and Engineering Exploration
    Issue number92
    Publication statusPublished - Jul 2022

    Bibliographical note

    ©2022 Ezzeddin M. Elarbi et al. This is an open access article distributed under the Creative Commons Attribution (CC BY)
    License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly


    Thanks to the University of Tripoli for the support and the subsidy under Grand 2018. The MTRC Coventry University is also acknowledged for previous supportive consultations.


    • Boeing 747-100 flight envelope
    • Centre of gravity variation
    • Cubic spline
    • Elevator and throttle coupling
    • Gain scheduling
    • Linear quadratic regulator
    • Tracking longitudinal modes

    ASJC Scopus subject areas

    • Control and Systems Engineering
    • Civil and Structural Engineering
    • Mechanical Engineering
    • Computer Networks and Communications
    • Computer Graphics and Computer-Aided Design
    • Computational Theory and Mathematics
    • Artificial Intelligence
    • Electrical and Electronic Engineering


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