Adaptive control of elastic aircraft

Abstract

This thesis documents the development of an adaptive controller designed to control the elastic aircraft dynamics of a generic general aviation aircraft. The elastic aircraft equations of motion are derived using Lagrange’s equation and the principal of virtual work. A minimum kinetic energy axis system is chosen as the body reference axis, which results in structural equations of motion that are decoupled from the rigid body equations of motion. An aerodynamic strip method is utilized to develop closed-form expressions for the longitudinal generalized structural forces. The adaptive controller is designed using a model reference adaptive control scheme, modified for general aviation to use an “E-Z fly” decoupled control architecture, which tracks vertical flight path angle and true airspeed. The adaptive control signal is computed using a weighted least mean square optimization, which gives the control designer more influence on the behavior of the adaptation. A notch filter is designed to decouple the controller and adaptation from the structural modes. The controller is implemented in the MATLAB®/Simulink® environment, and the equations of motion are integrated in simulation for a range of structural flexibility and plant failures. Results show that the controller is capable of handling the uncertainties associated with unmodeled aeroelastic modes. Additionally, the controller shows resilience to “A” and “B” matrix failures, such as 25% loss in elevator and throttle effectiveness. Actuator speed is found to limit the amount of failure the system can recover from, where a fast actuator facilitates adaptation to much larger failures. The notch filter is shown to be successful at decoupling the controller from the structural modes, even for a highly flexible aircraft. Performance without the notch filter is not degraded when the structural modes are outside the controller bandwidth; however, when structural modes fall within the controller bandwidth, the notch filter is required to damp excessive control activity. The proposed controller shows balance between good tracking performance and time delay margin, which is a measure of robustness in the system. This is attributed to the weighted least mean square optimization procedure that gives the control designer more influence over the behavior of the adaption.