Improving Control Allocation Accuracy for Nonlinear Aircraft Dynamics

Abstract

The forces and moments produced by a vehicle’s aerodynamic control surfaces are often nonlinear functions of control surface deflection. This phenomenon limits the accuracy of state-of-the-art control allocation algorithms since all of the approaches are based on the assumption that the control variable rates are linear functions of the surface deflections and that control variable rate increments are not produced for zero deflections. The errors introduced by this assumption are currently mitigated by the robustness resulting from feedback control laws. A method for improving the performance of the feedback control/control allocation system is presented that directly attacks the inaccuracies introduced by these linear assumptions. The approach is demonstrated using a dynamic inversion-based control law developed for a lifting body with four control surfaces. The commanded body rates constitute the input to a dynamic inversion control law that forms the inner-loop control structure. The outputs of the dynamic inversion algorithm serve as the inputs to a linear programming based control allocator. The control allocation algorithm is a mixed optimization scheme that minimizes the norm of the error and the deviation of the control input from a preferred value. Whether the underlying dynamic system is linear or nonlinear in the way that the controls affect the system state, the control allocator requires a linear approximation to the system inputs. In this work, instead of using a linear approximation to describe the control variable rate due to a control surface deflection (a control subspace, that contains the zero element), an affine relationship is utilized. This allows one to modify the input to the control allocator by providing an additional intercept term that corrects for the errors introduced by the control allocation algorithm’s assumption of linearity. Since on-line control allocators perform computations at flight control system update rates, the decision about how far to move the control surface in the next time interval is critical. In order to accurately compute the next set of surface deflection commands, the local slope at the current operating point is used and the intercept is accounted for at the input to the control allocator. With relatively little computational and design overhead, the accuracy of current control allocation algorithms can be improved utilizing an affine relationship for a vehicle’s control dependent accelerations. Simulation experiments show a significant improvement in tracking commanded body rates when the control allocation correction term is used.