Method for determination of nonlinear attainable moment sets

A method for generating attainable moment sets for left-right pairs of nonlinear control effectors on aircraft is presented. It is shown that the determination of the attainable moment set boundary can be posed as a constrained, nonlinear optimization problem. The first-order necessary conditions for a point to be on the boundary are simply the Kuhn-Tucker first-order necessary conditions. An algorithm is given where the Kuhn-Tucker points for a given point in the pitch-roll plane are constructed for each control effector configuration that forms a candidate boundary. The Kuhn-Tucker points are then checked for feasibility, and the points on the boundary are those that produce extremal values of the objective function. The nonlinear attainable moment set boundary is used to determine feasibility of moment commands generated by the flight control system. Infeasible commands are clipped to the boundary of the attainable moment set. If a commanded moment is feasible, a constrained optimization problem is solved for the control surface deflections.

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