Adaptive Backstepping Flight Control for Modern Fighter Aircraft

Abstract

The main goal of this thesis is to investigate the potential of the nonlinear adaptive backstepping control technique in combination with online model identification for the design of a reconfigurable flight control system for a modern fighter aircraft. Adaptive backstepping is a recursive, Lyapunov-based, nonlinear design method, that makes use of dynamic parameter update laws to deal with parametric uncertainties. The idea of backstepping is to design a controller recursively by considering some of the state variables as ‘virtual controls’ and designing intermediate control laws for these. Backstepping achieves the goals of global asymptotic stabilization of the closed-loop states and tracking. The proof of these properties is a direct consequence of the recursive procedure, since a Lyapunov function is constructed for the entire system including the parameter estimates. The tracking errors drive the adaptation process of the procedure. Furthermore, it is possible to take magnitude and rate constraints on the control inputs and system states into account in such a way that the identification process is not corrupted during periods of control effector saturation. A disadvantage of the integrated adaptive backstepping method is that it only yields pseudo-estimates of the uncertain system parameters. There is no guarantee that the real values of the parameters are found, since the adaptation only tries to satisfy a total system stability criterion, i.e. the Lyapunov function. Increasing the adaptation gain will not necessarily improve the response of the closed-loop system, due to the strong coupling between the controller and the estimator dynamics. The immersion and invariance (I&I) approach provides an alternative way of constructing a nonlinear estimator. This approach allows for prescribed stable dynamics to be assigned to the parameter estimation error. The resulting estimator is combined with a backstepping controller to form a modular adaptive control scheme. The I&I based estimator is fast enough to capture the potential faster-than-linear growth of nonlinear systems. The resulting modular scheme is much easier to tune than the ones resulting from the standard adaptive backstepping approacheswith tracking error driven adaptation process. In fact, the closed-loop system resulting from the application of the I&I based adaptive backstepping controller can be seen as a cascaded interconnection between two stable systems with prescribed asymptotic properties. As a result, the performance of the closed-loop system with adaptive controller can be improved significantly. To make a real-time implementation of the adaptive controllers feasible the computational complexity has to be kept at a minimum. As a solution, a flight envelope partitioning method is proposed to capture the globally valid aerodynamic model into multiple locally valid aerodynamic models. The estimator only has to update a few local models at each time step, thereby decreasing the computational load of the algorithm. An additional advantage of using multiple, local models is that information of the models that are not updated at a certain time step is retained, thereby giving the approximator memory capabilities. B-spline networks are selected for their nice numerical properties to ensure smooth transitions between the different regions. The adaptive backstepping flight controllers developed in this thesis have been evaluated in numerical simulations on a high-fidelity F-16 dynamicmodel involving several control problems. The adaptive designs have been compared with the gain-scheduled baseline flight control system and a non-adaptive NDI design. The performance has been compared in simulation scenarios at several flight conditions with the aircraft model suffering from actuator failures, longitudinal center of gravity shifts and changes in aerodynamic coefficients. All numerical simulations can be easily performed in real-time on an ordinary desktop computer. Results of the simulations demonstrate that the adaptive flight controllers provide a significant performance improvement over the non-adaptive NDI design for the simulated failure cases. Of the evaluated adaptive flight controllers, the I&I based modular adaptive backstepping design has the overall best performance and is also easiest to tune, at the cost of a small increase in computational load and design complexity when compared to integrated adaptive backstepping control designs. Moreover, the flight controllers designed with the I&I based modular adaptive backstepping approach have even stronger provable stability and convergence properties than the integrated adaptive backstepping flight controllers, while at the same time achieving a modularity in the design of the controller and identifier. On the basis of the research performed in this thesis, it can be concluded that a RFC system based on the I&I based modular adaptive backstepping method shows a lot of potential, since it possesses all the features aimed at in the thesis goal.