Control of Aircrafts with Structural Resonance Modes

Control of Aircrafts with Structural Resonance Modes

Sebastien Gros


Design of flying machines is a strongly constrained optimization
problem. In aeronautics, all design constraints result in performance
losses. Hence, any method or technology that reduces or removes
constraints from the design stage is valuable. Among the many design
constraints, passive stability is required so that the human can
safely pilot the aircraft.

However, control technology has broadened the design spectrum by
removing the passive stability constraint. This is extensively
undertaken in the design of military fighting aircrafts.

The design of a control-loop for unstable systems in the presence of
unknown or changing dynamics is critical. In the frequency domain,
models for aircraft dynamics are known to be accurate up to the
frequency of the first resonance mode of the structure (c.f. “Respect
the Unstable”, G. Stein, IEEE CSM), as this mode tends to move
substantially with flight conditions (mass distribution & loading).
Limitations in the model accuracy translate into limitations in the
performances of the close-loop dynamics.

Keywords : Glider;




1) The video “AdverseYaw” shows the highly coupled MIMO characteristic of the system. An action on the ailerons results in a strong adverse yaw (noise pointing in the direction opposite to the desired turn), and a dive.

2) The video “Phugoid” shows the reaction of the system to an off-trim speed. The system enters an unstable phugoid oscillation, often encountered in aircrafts with high energetic performances

CLOSED LOOP BEHAVIOR (controlled outputs : aliltude, speed, side slip, alignement with a virtual axis)

3) Ignoring the wings flexibility in the controller design requires using a reasonably low closed-loop bandwidth. Pushing the closed-loop bandwidth too far results in closed-loop instability. The video “Stable” shows the reaction of the (closed loop) system to a turbulence. Note that the wings oscillation is poorly damped.

The video “Unstable” shows the same situation as before, but the closed loop bandwidth is chosen too high resulting in closed loop instability.

4) The wings flexibility can be taken into account in the control design, resulting in a good damping of the wings oscillation. The video “FullControl” shows the reaction of the system to the same situation as before. The wings deformation are supposed measured (or correctly observed).


In this project, the dynamic behavior of a large aspect-ratio
aircraft is studied. In this type of configuration, the first
resonance modes are due to the wing flexibility. The limitations in control performances when ignoring the wings flexibility is characterized and compared to the performances obtainable when modeling the wings flexibility.

Main model features

– The aerodynamic model is based on the single lifting line theory
– The wings are modeled as finite elements.

The local dynamics are studied through the linearization of the model
at steady-state configurations. The resulting state-space linear
models are converted into transfer functions and reduced to capture
only the first N resonance modes.
The performance of the close-loop system resulting from measurements
of the wing flexion will be compared to the performance of the close-
loop system in the classical situation where the wing flexion is
considered unknown.