Model Predictive Variable Structure Control with Model Following for Forebody Vortex Flow Control

Aircraft which are required to fly effectively at high angles-of-attack must overcome two fundamental difficulties: generally poor dynamic characteristics, especially with respect to damping, and low control authority of conventional aerodynamic effectors. One solution to improve closed-loop tracking of pilot commands is to employ a model-following controller approach, whereby an aircraft with poor dynamics at high angle-ofattack is made to track the outputs of a model of the same aircraft at low angle-of-attack, thereby emulating its good dynamics. An improved solution is the extension to combine the model-following controller with a controller that can augment the yaw control power by effectively modulating forebody pneumatic vortex flow nozzles. This paper presents the synthesis and design of both high angleof-attack lateral/directional controllers for a generic X-29A equipped with forebody vortex flow control nozzles. Results demonstrate that both controllers are effective in improving closed-loop tracking of input commands and high angle-of-attack maneuverability, compared to a conventional flight control scheme using only aerodynamic control effectors, and without model-following. Nomenclature H altitude feet h integration stepsize seconds M Mach number m number of continuous control variables n number of state variables p number of bang-bang variables, also perturbed body axis roll rate degrees/second __________________ Graduate Research Assistant, Aerospace Engineering Department. Student Member AIAA. Assistant Professor, Aerospace Engineering Department. Senior Member AIAA. Copyright  1999 by Daigoro Ito and John Valasek. Published by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. psf pounds per square feet q dynamic pressure pounds/feet r perturbed body axis yaw rate degrees/second V velocity feet/second PVC pneumatic vortex control α angle-of-attack degrees β sideslip angle degrees δ deflection degrees λ eigenvalue Π sub-matrix of inverted quad-partition matrix φ bank angle degrees  set of real numbers Superscripts * star trajectory · time derivative ’ transpose of matrix or vector -1 inverse of square matrix Subscripts bb bang-bang effector c canard com commanded value df differential flap k value at k th sample time m model aircraft r rudder sf symmetric flap stf strake flap tr tracker aircraft 1 trim value Introduction The deployment of lethal, reliable, all-aspect, short range missiles such as the AIM-9X series into the modern air combat arena has diminished the emphasis on sustained maneuvering capabilities [1]. These "point-andshoot" weapons have prompted interest in controlled flight at angles-of-attack well beyond that for maximum lift. AIAA-99-4216