Nonlinear Control Allocation Using Piecewise Linear Functions

A novel method is presented for the solution of the control allocation problem where the control variable rates or moments are nonlinear functions of control position. Historically, control allocation has been performed under the assumption that a linear relationship exists between the control induced moments and the control effector displacements. However, aerodynamic databases are discrete valued and almost always stored in multidimensional lookup tables, where it is assumed that the data are connected by piecewise linear functions. The approach that is presented utilizes this piecewise linear assumption for the control effector moment data. This assumption allows the control allocation problem to be cast as a piecewise linear program that can account for nonlinearities in the moment/effector relationships, as well as to enforce position constraints on the effectors. The piecewise linear program is then recast as a mixed-integer linear program. It is shown that this formulation accurately solves the control allocation problem when compared to the aerodynamic model. It is shown that the control effector commands for a reentry vehicle by the use of the piecewise linear control allocation method are markedly improved when compared to the performance of more traditional control allocation approaches that use a linear relationship between the control moments and the effectors. The technique is also applied to determine those flight conditions (angle of attack and Mach number) at which the reentry vehicle can be trimmed for the purpose of providing constraint estimates to trajectory reshaping algorithms.

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