Identification and Modeling of the Airbrake of an Experimental Unmanned Aircraft

Abstract

This paper presents the modeling, system identification, simulation and flight testing of the airbrake of an unmanned experimental aircraft in frame of the FLEXOP H2020 EU project. As the aircraft is equipped with a jet engine with slow response an airbrake is required to increase deceleration after speeding up the aircraft for flutter testing in order to remain inside the limited airspace granted by authorities for flight testing. The airbrake consists of a servo motor, an opening mechanism and the airbrake control surface itself. After briefly introducing the demonstrator aircraft, the airbrake design and the experimental test benches the article gives in depth description of the modeling and system identification referencing also previous work. System identification consists of the determination of the highly nonlinear (saturated and load dependent) servo actuator dynamics and the nonlinear aerodynamic and mechanical characteristics including stiffness and inertia effects. New contributions relative to the previous work are a unified servo angular velocity limit model considering opening against the load or closing with it, the detailed construction and evaluation of airbrake normal and drag force models considering the whole deflection and aircraft airspeed range, the presentation of a unified aerodynamic - mechanic nonlinearity model giving direct relation between airbrake angle, dynamic pressure and servo torque and the transfer function-based modeling of stiffness and inertial effects in the mechanism. The identified servo dynamical model includes system delay, inner saturation, the aforementioned load dependent angular velocity limit model and a transfer function model. The servo model was verified based-on test bench measurements considering the whole opening angle and dynamic load range of the airbrake. New, unpublished measurements with gradually increasing servo load as the servo moves are also considered to verify the model in more realistic circumstances. Then the full airbrake model is constructed and tested in simulation to check realistic behavior. In the next step the airbrake model integrated into the nonlinear simulation model of the FLEXOP aircraft is tested by flying simulated test trajectories with the baseline controller of the aircraft in software-in-the-loop (SIL) Matlab simulation. First, the standalone airbrake simulation is compared to the SIL results to verify flawless integration of airbrake model into the nonlinear aircraft simulation. Then deceleration times with and without airbrake are compared underlining the usefulness of the airbrake in the test mission. Finally, real flight data is used to verify and update the airbrake model and show the effectiveness of the airbrake.

Appendix

ϕ − c_D fit:

$$ c_{D}(\phi)=0.88\cdot \phi [rad] $$

$\phi -{c}_{N}^{\prime }$ fit:

$$ \begin{array}{@{}rcl@{}} {c}_{N_{L}}^{\prime}(\phi) &=& \phi^{2} [rad^2] + 1.8706\phi [rad] \ \ if \ 0 \leq \phi < 0.6962rad\\ {c}_{N_{H}}^{\prime}(\phi)&=&0.0514\phi [rad] +1.7512 \ \ if \ 0.6962rad\leq\phi \end{array} $$

(1)

ϕ − s_a fit:

$$ \begin{array}{@{}rcl@{}} s_a(\phi) [m]&=&-0.02735\phi^5 [rad^{5}]+0.09069\phi^4 [rad^4]-0.11428\phi^{3} [rad^{3}]\\ &&+0.071245\phi^{2} [rad^2]-0.02437\phi [rad]+0.006 \end{array} $$

(2)

α − ϕ curve:

$$ \phi(\alpha) [rad]=-0.01864\alpha^{3} [rad^{3}]+0.213425\alpha^{2} [rad^{2}]+0.20056\alpha [rad] $$

ϕ − α curve:

$$ \begin{array}{@{}rcl@{}} \alpha(\phi) [rad]&=&-1.83448\phi^4 [rad^4]+5.03271\phi^{3} [rad^{3}]\\ &&- 5.28037\phi^{2} [rad^2]+3.9602\phi [rad] \end{array} $$

(3)

Stiffness formula:

$$ k_{\phi}=1383.097\phi^{3} [rad^{3}]-3028.264\phi^{2} [rad^{2}]+1764.837\phi [rad]+45.722 $$

System dynamics from angular velocity reference to angular velocity:

$$ G_{sys}(z)=\frac{1.039}{1+0.0149z^{-1}+0.238z^{-2}-0.2361z^{-3}} $$

System dynamics from delayed load to angle:

$$ G_{T_{L}}(z)=\frac{-0.002181}{1-0.5267z^{-1}} $$