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A predictive envelope protection system using linear, parameter-varying models

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Abstract

A parameter-varying, model-predictive envelope protection system is developed simplifying the controller structures required to keep the aircraft within a safe angle-of-attack and normal load factor envelope. The idea of a quasi-steady flight condition is used to map the flight envelope limits onto the setpoint values of a single flight control law. Since no mode switching is required, the selected level of automation, i.e., autopilot and flight management functionalities, is independent from the proximity to any angle-of-attack and normal load factor limit. In contrast to previous approaches, the proposed algorithm makes use of a quasi-linear, parameter-varying control loop model to adapt to the true nonlinear aircraft behavior. A variance-based sensitivity analysis highlights the most significant scheduling variables within this control loop model and, therefore, indicates the option of model reduction and improvement in efficiency, respectively. The proposed envelope protection system is evaluated throughout virtual flight tests with the unmanned flight test platform ULTRA-Dimona showing promising overall performance also in the presence of wind and turbulence.

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Notes

  1. ULTRA-project: http://www.fst.tu-harburg.de/ultra.

Abbreviations

ANOVA:

Analysis of variances

CG:

Center of gravity

DOE:

Design of experiments

DT:

Dynamic trim

LPV:

Linear, parameter-varying

LTI:

Linear, time-invariant

LTV:

Linear, time-varying

MITL:

Model-in-the-loop

q-LPV:

Quasi-linear, parameter-varying

ULTRA:

Unmanned low-cost testing research aircraft

\(b\) :

Aerodynamic wing span

\(c\) :

Aerodynamic wing chord

\(e_j\) :

jth matrix element

\(g\) :

Gravitational acceleration

\(m\) :

Aircraft mass

\(n_z\) :

Normal load factor

\(p\) :

Roll rate

\(\mathbf {p}\) :

Linearization point

\(q\) :

Pitch rate

\(r\) :

Yaw rate

\(\mathbf {r}\) :

Lever arm vector

\(u\) :

Velocity component x-axis

\(\mathbf {u}\) :

Control input vector

\(v\) :

Velocity component y-axis

\(w\) :

Velocity component z-axis

\(\mathbf {x}\) :

State variable vector

\(\mathbf {y}\) :

Vector of limited variables

\(\mathbf {A}\) :

System matrix

\(\mathbf {B}\) :

Input matrix

\(C\) :

Aerodynamic coefficient

\(\mathbf {C}\) :

Output matrix

\(\mathbf {D}\) :

Feedforward matrix

\(G\) :

Gravity vector

\(I\) :

Moment resp. product of inertia

\(\mathbf {I}\) :

Inertia tensor

\(L\) :

Moment x-axis

Set of linearized, critical control movements

\(M\) :

Moment y-axis

\(\mathbf {M}\) :

Dynamic trim sensitivity to state variables

Rotation matrix

\(N\) :

Moment z-axis

\(\mathbf {N}\) :

Dynamic trim sensitivity to state variable time rates of change

\(\mathbf {Q}\) :

Moment vector

\(\mathbf {R}\) :

Force vector

\(S\) :

Aerodynamic wing area

\(S_M\) :

Main effect

\(S_T\) :

Total effect

\(S({\varvec{\varTheta }})\) :

Parameter-varying system

\(\mathbf {S}\) :

Dynamic trim sensitivity to control inputs

\(U\) :

Set of critical control inputs

\(V\) :

Speed

\(\mathbf {V}\) :

Velocity

\(X\) :

Force x-axis

\(Y\) :

Force y-axis

\(Z\) :

Force z-axis

\(\alpha\) :

Angle-of-attack

\(\beta\) :

Angle-of-sideslip

\(\zeta\) :

Rudder deflection

\(\eta\) :

Elevator deflection

\(\eta _F\) :

Thrust lever position

\(\xi\) :

Aileron deflection

\(\rho\) :

Air density

\({\varvec{\rho }}\) :

Scheduling variable vector

\(\varTheta\) :

Pitch attitude

\({\varvec{\varTheta }}\) :

Scheduling parameter vector

\(\varPhi\) :

Bank angle

\({\varvec{\varOmega }}\) :

Angular velocity

\(a\) :

Aerodynamic coordinate system

\(b\) :

Body-fixed coordinate system

\(e\) :

Experimental coordinate system

\(\rm{ext}\) :

External

\(f\) :

Fast

\(g\) :

Earth-fixed coordinate system

\(i\) :

ith variable

\(\rm{int}\) :

Internal

\(l\) :

Rolling moment related

\(\rm{lim}\) :

Limit

\(m\) :

Pitching moment related

\(n\) :

Yawing moment related

\(s\) :

Slow

\(x\) :

x-axis component

\(y\) :

y-axis component

\(z\) :

z-axis component

\(A\) :

Aerodynamic related

\(D\) :

Drag related

\(\rm{DT}\) :

Dynamic trim related

\(F\) :

Propulsion related

\(K\) :

Flight path related

\(L\) :

Lift related

\(W\) :

Wind related

\(Y\) :

Sideforce related

0:

Base point

\(^*\) :

Dimensionless variable

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Authors and Affiliations

  1. Institute of Aircraft Systems Engineering, Hamburg University of Technology, Nesspriel 5, 21129, Hamburg, Germany

    Matthias Krings & Frank Thielecke

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  1. Matthias Krings
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  2. Frank Thielecke
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Correspondence to Matthias Krings.

Additional information

This paper is based on a presentation at the German Aerospace Congress, September 10–12, 2013, Stuttgart, Germany.

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Krings, M., Thielecke, F. A predictive envelope protection system using linear, parameter-varying models. CEAS Aeronaut J 6, 95–108 (2015). https://doi.org/10.1007/s13272-014-0129-9

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