Nonlinear Control Allocation Using a Piecewise Multilinear Representation

Abstract

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