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Control Allocation with Adaptive Augmentation for Aerodynamic Optimization of Trailing Edge Morphing Aircraft
Mark Spiller, Lennart Kracke, Johannes Autenrieb
TL;DR
Morphing-wing aircraft require control allocation that can stabilize uncertain dynamics while using shared actuators to adapt wing shape. This paper combines a nominal-model baseline controller, adaptive augmentation, and an allocation objective favoring an elliptical lift distribution. Simulations report stable tracking with augmentation and wing shapes approaching the target where compatible with aircraft dynamics.
Problem
The paper addresses control allocation for an over-actuated trailing-edge morphing aircraft under uncertain dynamics while optimizing aerodynamic efficiency.
Source: §I · p. 1Method
A nominal-model baseline defines reference dynamics, while adaptive augmentation imposes a stability constraint in control allocation that minimizes deviation from the aerodynamically optimal wing shape.
Source: §I · p. 2, §III · p. 3, §V · p. 4Results
With adaptive augmentation, simulations achieve precise tracking despite uncertainties with small matching errors, whereas yaw dynamics become unstable without augmentation.
Source: §VI · p. 6Takeaways & Limitations
The approach keeps tracking error bounded while morphing degrees of freedom move the wing toward the target elliptical lift distribution where compatible with required aircraft dynamics.
Source: §VII · p. 7
Abstract
from arXiv · showhide
This paper presents a control allocation framework with adaptive augmentation for a trailing edge morphing aircraft, providing stability guarantees under uncertainty while exploiting the available morphing degrees of freedom to optimize aerodynamic efficiency. A baseline controller is designed using the nominal aircraft model to establish the desired closed-loop reference dynamics. For the aerodynamics, the wing shape is optimized dependent on the flight state to achieve a target elliptical lift distribution corresponding to minimum induced drag. The adaptive augmentation is tailored to the control allocation problem to account for the uncertain system dynamics and stabilize the aircraft around the reference dynamics. The resulting stabilization condition is formulated as hard constraint in the allocation problem while minimizing deviations from the corresponding state-dependent aerodynamically optimal wing shape. Numerical results demonstrate that the adaptive augmentation compensates for matched uncertainties while the control allocation optimizes the wing shape with respect to the reference elliptical lift distribution.
I. INTRODUCTION
Morphing wings can adapt lift distribution across flight conditions, but their coupled, time-varying dynamics make control challenging. This paper combines flight-dynamics control and wing-shape adaptation, using adaptive augmentation for uncertain dynamics while allocating control to favor an aerodynamically optimal shape.
I. INTRODUCTION
- Morphing wings can redistribute lift in flight to improve aerodynamic efficiency and maneuverability across changing mission profiles.Examples include long-endurance surveillance combined with high-speed transit and maneuver-intensive missions.Source: §I · p. 1
- Morphing introduces fast time-varying dynamics and strong couplings, while prior adaptive approaches cited here leave uncertainty quantification or control-effectiveness assumptions unresolved.The paper frames its focus as aircraft-dynamics control under morphing and integrated use of morphing actuators.Source: §I · p. 1
- Camber morphing uses the same inputs for flight-dynamics control and wing shaping, unlike morphing concepts with separate actuation channels.The cited prior approach determined wing shape implicitly through its control objective.Source: §I · p. 1
- The approach uses a nominal model to define reference dynamics, then constrains control allocation with adaptive augmentation while minimizing weighted distance from the aerodynamically optimal wing shape.The target is a reference elliptical lift distribution.Source: §I · pp. 1–2
II. AIRCRAFT DYNAMICS
The aircraft model describes nonlinear forces and moments from flight conditions, conventional controls, and trailing-edge morphing inputs. The paper derives a reduced-order lateral model, represents uncertainty as matched perturbations, and restricts controller design to lateral dynamics.
II. AIRCRAFT DYNAMICS
- The nonlinear aircraft model defines forces and moments from flight state, trailing-edge servos, elevator and rudder deflections, and throttle.The model includes dynamic pressure and normalized angular rates.Source: §II · p. 2
- The design is limited to the lateral controller relevant to morphing and control allocation.The paper mostly omits explicit dependence on scheduling grid points for notational simplicity.Source: §II · pp. 2–3
- The reduced-order lateral dynamics are derived from grid-linearized aircraft dynamics, with perturbations representing parametric uncertainty and unmodeled nonlinear effects.The state choice ensures all uncertainties are matched; perturbations scale with uncertainty and distance from the operational point.Source: §II · pp. 2–3
- The control objective is allocation for an over-actuated uncertain system while optimizing aerodynamic efficiency.All admissible perturbations preserve a zero structure in the last state row because that state is a pure kinematic integrator.Source: §II · p. 3
III. BASELINE CONTROLLER DESIGN
The baseline controller is designed from the nominal model to establish desired reference dynamics before adaptive augmentation addresses uncertainty. The design is local to scheduling grid points and targets yaw rate and roll angle.
III. BASELINE CONTROLLER DESIGN
- The controller design is restricted to local controllers at scheduling grid points; synthesis of a global LPV controller is out of scope.The paper names gain-scheduling and polytopic approaches as examples of global synthesis.Source: §III · p. 3
- Yaw rate and roll angle are the control variables, with corresponding reference values denoted by δyr.Source: §III · p. 3
- The nominal-system baseline controller establishes desired closed-loop reference dynamics before adaptive augmentation accounts for uncertainty.The state-feedback matrix may use LQR, pole placement, or a robust control method; a prefilter is designed for stationary accurate reference tracking.Source: §III · p. 3
IV. AERODYNAMIC OPTIMIZATION
The section uses morphing degrees of freedom to optimize wing lift distribution alongside the control objective. It selects servo deflections to match an elliptical target lift distribution, a proxy for minimum induced drag, using nominal aerodynamics.
IV. AERODYNAMIC OPTIMIZATION
- In steady wings-level flight, morphing degrees of freedom support lift-shape optimization beyond stabilization, using an elliptical distribution as a proxy for minimum induced drag.The section frames this as a secondary objective alongside the control objective.Source: §IV · p. 3
- Aerodynamic optimization uses the nominal model and parameters because uncertain aerodynamic characteristics are generally unknown a priori.The nominal model does not fully capture true aerodynamic behavior under uncertainty.Source: §IV · p. 3
- Servo deflections minimize squared deviations between nominal segment lift and target elliptic lift, while the optimal rudder deflection is set to zero.The target elliptic distribution corresponds to the aerodynamically optimal condition of minimum induced drag.Source: §IV · p. 4
V. ADAPTIVE AUGMENTATION AND CONTROL ALLOCATION
The section integrates adaptive augmentation into control allocation to preserve stability under uncertain dynamics while optimizing the wing shape. It gives a boundedness guarantee for matching and parameter-estimation errors under stated conditions, with bounds that depend on uncertainty magnitude and parameter variation.
V. ADAPTIVE AUGMENTATION AND CONTROL ALLOCATION
- Adaptive augmentation enters the control allocation as a hard constraint to preserve stability under uncertain dynamics while wing shape is optimized.The allocation objective weights distance from aerodynamically optimized inputs.Source: §V · pp. 4, 6
- The uncertainty terms are treated as explicitly time-varying and assumed uniformly bounded, continuously differentiable, and to have bounded derivatives.The analysis also assumes the uncertainty matrix and its estimate are nonsingular.Source: §V · p. 4
- A calibrated closed-loop reference model is introduced to improve transient behavior during adaptation and coincides with the desired closed-loop model when matching error reaches zero.Source: §V · p. 5
- Under the theorem's control-input constraint and parameter-update conditions, matching error and parameter-estimation errors are uniformly ultimately bounded.The result assumes bounded matching parameters within the projection operator's convex set.Source: §V · p. 5
- The ultimate bound can be made small when overall uncertainty effects are small and true matching parameters evolve slowly.The passage identifies these as familiar restrictions of adaptive control with time-varying parameters.Source: §V · p. 6
VI. NUMERICAL EXAMPLE
The Proteus simulation evaluates adaptive allocation under perturbed aerodynamic coefficients and changing flight commands. Adaptive augmentation maintains precise tracking despite uncertainty, while the allocation approaches the target lift distribution in wings-level flight and adapts during turns.
VI. NUMERICAL EXAMPLE
- The simulation uses the nonlinear dynamics of the Proteus demonstrator, which has ten trailing-edge morphing servos per wing, and perturbs nominal aerodynamic coefficients by bounded relative amounts.Nominal coefficients come from an offline Athena Vortex Lattice look-up table.Source: §VI · p. 6, Figure 1 · p. 6
- The autopilot tests course changes at 30 s and 60 s and altitude and airspeed changes at 50 s.Course switches among 0, π/2, and 0; altitude between 500 m and 700 m; and airspeed between 30 m/s and 40 m/s.Source: §VI · p. 6
- With adaptive augmentation, the aircraft achieves precise tracking despite uncertainty and small matching errors; without it, yaw becomes unstable and matching error rapidly increases.The comparison is shown in Fig. 2(a,b).Source: §VI · p. 6, Figure 2 · p. 7
- In wings-level flight, the wing approaches the symmetric elliptical lift distribution, with deviations during turns from approximately 30 s to 80 s.Left and right wing servo inputs are symmetric except during that turning interval; adaptive parameters remain bounded and smooth.Source: §VI · pp. 6–7, Figure 2 · p. 7
VII. CONCLUSIONS
The proposed adaptive control allocation accounts for uncertainty while optimizing aerodynamic efficiency. Numerical results demonstrate bounded reference tracking and use of morphing degrees of freedom to approach the target elliptical lift distribution when compatible with aircraft dynamics.
VII. CONCLUSIONS
- The framework combines adaptive augmentation for stabilization under uncertainty with control allocation that optimizes aerodynamic efficiency.The paper reports that tracking error relative to desired reference behavior is guaranteed to remain bounded.Source: §VII · p. 7
- Numerical results demonstrate stable tracking while exploiting morphing degrees of freedom to approach the target elliptical lift distribution where compatible with required aircraft dynamics.Source: §VII · p. 7
- The target elliptical lift distribution serves as the aerodynamic objective, subject to compatibility with the aircraft's required dynamics.Source: §VII · p. 7