  Nonlinear control allocation is an important part of modern nonlinear dynamic
inversion based flight control systems which require highly accurate model of
aircraft aerodynamics. Generally, an accurately implemented onboard model
determines how well the system nonlinearities can be canceled. Thus, more
accurate model results in better cancellation, leading to the higher
performance of the controller. In this paper, a new control system is presented
that combines nonlinear dynamic inversion with a piecewise multi-linear
representation based control allocation. The piecewise multi-linear
representation is developed through a new generalization of Kronecker product
for block matrices, combined with the canonical piecewise linear representation
of nonlinear functions. Analytical expressions for the Jacobian of the
piecewise multi-linear model are also presented. Proposed formulation gives an
exact representation of piecewise multi-linear aerodynamic data and thus is
capable of accurately modeling nonlinear aerodynamics over the entire flight
envelope of an aircraft. Resulting nonlinear controller is applied to control
of a tailless flying wing aircraft with ten independently operating control
surfaces. The simulation results for two innovative control surface
configurations indicate that perfect control allocation performance can be
achieved, leading to better tracking performance compared with ordinary
polynomial-based control allocation.
