L1 Adaptive Control Augmentation Configuration for a Hypersonic Glider in the Presence of Uncertainties

Abstract

The descent longitudinal trajectory control methodology of a hypersonic glider is presented. The overall desired trajectory is presented, followed by a basic analysis of the control methodology used to carry out a pull up maneuver; bringing the glider from a descent trajectory to horizontal flight. A dynamic pole placement controller is implemented to carry out this maneuver. This controller is augmented with an adaptive controller to cancel out the matched uncertainties. Only the longitudinal dynamics are considered in this analysis. The fundamental differences between only the pole placement and the augmented pole placement with the adaptive controller are presented in terms of robust stability and robust performance. When the INS/GPS module is turned on, of the altitude error, flight path angle error and angle of attack error are bounded compared to the unfiltered values. The dynamic pole placement controller is shown to have robustness in the presence of time invariant, Gaussian and time varying errors in the aerodynamic coefficients. The augmentation set up improves the performance of the baseline controller in the presence of these uncertainties. With the help of Monte Carlo Simulations the performance, robustness and stability bounds of the baseline and the adaptive augmented controller are presented and are compared to the performance of the pole placement controller. All the simulations and implementations are carried out in CADAC++ which is written in C++. The system presented is a nonminimum phase system. The uncertainties presented in this paper are matched uncertainties. The main contribution of this paper lies in the application and determining robustness and performance of a piecewise constant augmentation setup to a Linear Time Varying (LTV) System. Nomenclature , = body, inertial coordinates , , = roll, pitch and yaw principle moments of inertia, kgm 2 = component xy of moment of inertia matrix, kgm 2 = closed loop system matrix = desired closed loop system matrix = plant model system matrix = body acceleration with respect to inertial frame = input gain matrix = output matrix = wing chord length, m = reference length, m = drag force, N ( ) = tracking error dynamics = state transition matrix = control coefficient matrix = pitch moment of inertia, kgm 2 , = angle of attack autopilot feedback gains ! = lift force, N ! " = lift coefficient slope as a function of angle of attack, m/s 2 ! #$ = dimensional lift slop with elevator deflection derivative, m/s 2 = pitching moment control derivative, 1/s 2 ) "= dimensional normal force slope derivative, m/s 2 ) #$ = normal force slope with elevator deflection derivative, m/s 2 * = pitch rate, rad/s + = pitch rate, rad/s + = rate of change of pitch rate , = velocity vector -= state vector -.= state estimate vector / 0 = output estimate 1 = angle of attack, rad 1 = rate of change of angle of attack, rad/s 2 = elevator deflection command 3 4 5 6 = multiplicative uncertainty in longitudinal stability 3 4 7 6 = multiplicative uncertainty in lift coefficient 3 4 ...

L1 adaptive control augmentation for a hypersonic glider

“…Compared with the studies in the control of powered HSVs, limited research is available on the development of controllers for unpowered HSVs [10,16,19,[47][48][49][50][51]. Consequently, this distinct focus on developing control methodologies for powered HSV leaves a large gap in the literature relating to development of control systems for unpowered HSVs once the SCRAMJET has been fired and tested.…”

“…Furthermore, the comparison of the performance of controllers is also very limited [49,50,63,[75][76][77][78]. The studies that present a comparison between a baseline and an augmented baseline controller are mainly for the case of missiles, helicopters and supersonic aircraft.…”

“…Over the past few decades, research into the control of HSVs, especially hypersonic gliders, has become a distinctive part of research into the control of re-entry vehicles [10,19,[47][48][49][50][51]102]. Initial studies mainly focused on the static stability of hypersonic gliders [19] followed by studies of control along a re-entry trajectory of the shuttle [58,103,104].…”

“…As an alternative, nonlinear adaptive controllers have been employed in the HSV configuration domain [10,16,22,33,[37][38][39][40][41][42][43]. In the research positioning matrix of Fig 1.3, quadrants A and B represent the studies undertaken for linear and nonlinear control methodologies to stabilise powered HSV.Thus, while in the area of control research a large body of scholarly work exists, the extent of research is directed at linear and nonlinear control of powered vehicles [1,30,[44][45][46].Compared with the studies in the control of powered HSVs, limited research is available on the development of controllers for unpowered HSVs [10,16,19,[47][48][49][50][51]. Consequently, this distinct focus on developing control methodologies for powered HSV leaves a large gap in the literature relating to development of control systems for unpowered HSVs once the SCRAMJET has been fired and tested.…”

“…The re-entry aerodynamics of the Space Shuttle (which is a bulky flat bottomed re-entry vehicle) are very different from those of a slender winged hypersonic vehicle intended to fly like an aircraft [71][72][73][74]. As a result, the literature review in Chapter 2 concentrates on the studies that has been carried out for slender hypersonic vehicles.Furthermore, the comparison of the performance of controllers is also very limited [49,50,63,[75][76][77][78]. The studies that present a comparison between a baseline and an augmented baseline controller are mainly for the case of missiles, helicopters and supersonic aircraft.…”