Application of Piecewise Linear Control Allocation to Reusable Launch Vehicle Guidance and Control

The moments produced by the aerodynamic control effectors on aircraft are typically non-linear functions of displacement with a region of linearity about zero displacement. In this paper we briefly review a novel approach that was developed at AFRL for solving the control allocation problem where the control moments are piecewise linear functions of the control displacement. The advantages of this approach are that it avoids cumbersome, high-order polynomial curve fits of the aerodynamic data and thus avoids solution of a non-linear programming problem. Stability and control derivatives are almost always stored in multi-dimensional look-up tables where it is assumed that the data is piecewise linear. The approach that is presented utilizes this piecewise linear assumption for the control effector moment data and accounts for non-linearities in the moment-effector relationships and position constraints on the effectors as well. The control allocation problem using piecewise linear functions is posed as a mixed-integer linear program (MILP) and solved using a freely available GNU-licensed mixed-integer linear programming code. We demonstrate two applications of the piecewise linear control allocation (PLCA) approach. The first application to be considered is to use the PLCA approach in the inner-loop control law of a re-usable launch vehicle on approach and landing. The second application is constraint estimation for trajectory reshaping and re-targeting. In order to successfully re-target a trajectory when an aircraft has experienced degraded performance due to a failure or damage to the vehicle, the effects of the failure or damage on the lift, drag, and "trimmability" of the vehicle must be known a priori over the entire flight envelope