Non-Linear Control Allocation Using Piecewise Linear Functions

A novel method is presented for the solution of the non-linear control allocation problem. Historically, control allocation has been performed by assuming 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 look-up tables where it is assumed that the data is connected by piecewise linear functions. The approach that is presented utilizes the piecewise linear assumption for the control effector moment data. This assumption allows the non-linear control allocation problem to be cast as a piecewise linear program. The piecewise linear program is ultimately cast as a mixed-integer linear program, and it is shown that this formulation solves the control allocation problem exactly. The performance of a re-usable launch vehicle using the piecewise linear control allocation method is shown to be markedly improved when compared to the performance of a more traditional control allocation approach that assumes linearity.

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