Control laws for the X-31A with reduced vertical tail (VECTOR)

The VECTOR project

Within the German-American VECTOR Program (Vectoring, Extremely short take-off and landing, Control, Tailless Operations Research), the possibility of reducing the vertical tail size of the existing X-31A aircraft has been investigated, exploiting its thrust-vectoring capability to compensate for the reduced size of the rudder as well as the reduced weathercock stability.

Edited photograph of the X-31A with reduced vertical tail and its thrust vectoring system

Important advantages of tailless aircraft configurations in general are a reduction in radar signature and airframe structural weight. The task of the Control Design Engineering Group was to develop flight control laws that provide stability augmentation and good flying qualities over the flight envelope, including post-stall conditions.

In order to facilitate the assessment of various tail configurations, an important requirement was the easy adaptability of the control laws as a function of vertical tail size. For this reason, a design process based on Nonlinear Dynamic Inversion (NDI) was applied. NDI is based on inverse model equations in the control laws, cancelling nonlinear dynamics and decoupling multivariable command responses. Desired closed loop dynamics are imposed via a simple linear outer loop control law. As its most important advantage, NDI avoids the need for gain scheduling as a function of flight condition and aircraft configuration (i.e., in this case the vertical tail size).

Control law development was conducted in two phases. During the first phase (at DLR, in Oberpfaffenhofen) the model of the original X-31A configuration was implemented in the object-oriented modelling language Modelica (based on the existing Flight Dynamics Library ) with the help of the modelling tool Dymola (Dynamic Modelling Laboratory). A design process based on automatic NDI control law generation from the Modelica model was set up for the application. Command variables were the angle of attack (pitch stick), side slip angle (rudder pedals) and aerodynamic bank angular rate (roll stick). The resulting control laws were evaluated regarding stability, tracking performance, PIO-susceptibility, control activity, etc., using off-line and real-time desktop simulations.

The X-31A controller structure with dynamic inversion

The second phase was performed at Patuxent River Naval Air Station, Maryland, USA, in cooperation with a colleague from the institute of Flight Systems in Braunschweig. First of all, the aerodynamic data for the reduced tail configurations was obtained and implemented in the flight simulator model as well as in the Modelica aircraft model. The figure to the right illustrates the severe degradation of stability due to tail size reduction (eigenvalues). Next, the control laws were automatically regenerated and also implemented in the flight simulator. A test program was developed with the help of the X-31A test pilots, comprising various types of mostly lateral/directional manoeuvres (combat, landing, post-stall, etc.). Flying qualities of the X-31A with full and reduced vertical tail (50%) were then evaluated by five test pilots and one fleet pilot in the simulator. Due to increasing dependency on the thrust vectoring (TV) system as a function of the tail reduction, the bulk of the tasks was flown in max dry and idle power settings.

Open-loop eigenvalues, illustrating the effect of tail reduction on stability of the X-31

The majority of all manoeuvring tasks (flown with full and reduced tail) were rated to be Level 1 on the Cooper-Harper scale (“satisfactory without improvement”) at first go by all pilots. Furthermore, the physical limitations of a configuration with reduced vertical stab/rudder surface area were identified. As expected, weathercock stability deteriorates at low power settings, since rudder effectiveness and TV effectiveness are significantly degraded.

Test pilot in the X31 simulator
The work in Patuxent River included model adaptation for reduced tail configurations, redesign of control laws, implementation in the flight simulator and piloted evaluation. This could be achieved in just three weeks, mainly due to the design process based on object-oriented modelling and automatic generation of dynamic inversion control laws and thanks to good co-operation on-site.


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Multi-disciplinary aircraft modelling and simulation (