Nonlinear Multivariate Spline-Based Control Allocation for High-Performance Aircraft

Abstract

High performance flight control systems based on the nonlinear dynamic inversion (NDI) principle require highly accurate models of aircraft aerodynamics. In general, the accuracy of the internal model determines to what degree the system nonlinearities can be canceled; the more accurate the model, the better the cancellation, and with that, the higher the performance of the controller. In this paper a new control system is presented that combines NDI with multivariate simplex spline based control allocation. We present three control allocation strategies which use novel expressions for the analytical Jacobian and Hessian of the multivariate spline models. Multivariate simplex splines have a higher approximation power than ordinary polynomial models, and are capable of accurately modeling nonlinear aerodynamics over the entire flight envelope of an aircraft. This new method, indicated as SNDI, is applied to control a high performance aircraft (F-16) with a large flight envelope. The simulation results indicate that the SNDI controller can achieve feedback linearization throughout the entire flight envelope, leading to a significant increase in tracking performance compared to ordinary polynomial based NDI.

Nonlinear and Fault-Tolerant Flight Control Using Multivariate Splines

“…The aim of this setup is to update an a-priory aerodynamic model online in case of a failure with adaptive simplex splines to eliminate model errors within the NDI control system. In [12] the F-16 aerodynamic model is identified with multivariate splines using flight testing based system identification techniques from [10,16,17]. This is an accurate global model and is used as the a-priori nominal onboard aerodynamic model in this study.…”

“…This is an accurate global model and is used as the a-priori nominal onboard aerodynamic model in this study. Refer to [12] for the complete structure, the accuracy and error bounds of the model. Consider the aircraft state equations in the input affine form:…”

“…Recently a new framework for spline model based NDI flight control is introduced in [12]. It is shown that the use of splines significantly improves the performance of NDI based control systems compared with ordinary polynomial based NDI.…”

“…It is shown that the use of splines significantly improves the performance of NDI based control systems compared with ordinary polynomial based NDI. The controller from [12] is now augmented with a real time identification and applied for fault-tolerant flight control. First the aircraft model and the failure scenarios are discussed in Sec.…”

Quadrotor System Identification Using the Multivariate Multiplex B-Spline

“…Recently the multivariate simplex B-spline was presented as an alternative. [1][2][3] The main benefit of this technique over neural networks is the fact that it is linear in the parameters. This allows for the use of efficient least squares solvers.…”