The feedback gains in state-of-the-art flight control laws for commercial aircraft are scheduled as a function of values such as airspeed, mass, and centre of gravity (CoG). If measurements or estimates of these are lost due to multiple simultaneous sensor failures, the pilot must revert to an alternative control law, or, in the ultimate case, directly command control surface positions. This work develops a robust backup load-factor tracking control law, that does not depend on these parameters, based on application of theory from robust MPC and H 2 optimal control. Firstly, the methods are applied with loss only of airdata, and subsequently also with loss of mass and CoG estimates. Local linear analysis indicates satisfactory performance over a wide range of operating points. To keep the aircraft within an acceptable operating region, an outer protection loop is implemented using an override approach, based on ground speed, a model of the trim angle of attack and variation of load factor with respect to angle of attack, and a priori bounds on the wind speed. Finally, the resulting control laws are demonstrated on the nonlinear RECONFIGURE benchmark, which is derived from an Airbus high fidelity, industrially-validated simulator.

A method based on a quantifier elimination algorithm is suggested for obtaining explicit model predictive control (MPC) laws for linear time invariant systems with quadratic objective and polytopic constraints. The structure of the control problem considered allows Weispfenning's 'quantifier elimination by virtual substitution' algorithm to be used. This is applicable to first order formulas in which quantified variables appear at most quadratically. It has much better practical computational complexity than general quantifier elimination algorithms, such as cylindrical algebraic decomposition. We show how this explicit MPC solution, together with Weispfenning's algorithm, can be used to check recursive feasibility of the system, for both nominal and disturbed systems. Extension to cases beyond linear MPC using Weispfenning's algorithm is part of future work.

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