Multi-disciplinary aircraft modelling and simulation

The development of aircraft flight dynamics models of appropriate fidelity is a key aspect of the flight control law design process. These models must allow all relevant multi-disciplinary design criteria (e.g. handling qualities, structural loads) to be computed efficiently and with sufficient accuracy.

The modelling approach

The basic modelling philosophy is to construct aircraft models around a backbone describing the nonlinear equations of motion of a (possibly flexible) flight vehicle with respect to the (rotating) earth, see the Figure below.

Structure of a flexible aircraft model, using the equations of motion (EQM) with respect to the earth as backbone. Connections reflect kinematic constraints, energy flows, etc.

Pressure distribution around an aircraft, computed using the Vortex Lattice Method (VLM)
The equations of motion are driven by forces and moments, computed using model data or components that are obtained from involved engineering disciplines. To this end, the institute has developed strong competence in the field of aircraft model integration. For example, the choice of mean body axes allows direct incorporation of modal data obtained from free-free finite element model analysis in the equations of motion. Tools for rational function approximation in combination with order reduction have been developed to transform deformation-induced unsteady aerodynamics models, computed using the Doublet Lattice method, from the frequency into the time domain. The so-called residualised model method has been developed to integrate the result with flight shape-based flight mechanics aerodynamics models.

In the near future control law parameters will be optimised along side aircraft geometry parameters. For this reason, fast routines have been developed that estimate aerodynamic loads in case no data is available, see the Figure below.

The Modelica Flight Dynamics Library

For implementation of hierarchic multi-disciplinary aircraft models the institute has developed the Flight Dynamics Library, based on the multi-physics modelling language Modelica, see the next Figure. As a unique feature, Modelica allows one-to-one implementation of the model structure of the first Figure. An early version of this library was used to generate rigid aircraft models for the GARTEUR Action Group 08 on Robust Flight Control. Besides being the standard for multi-disciplinary modelling, efficient code can be generated from Modelica models, suitable for all kinds of analysis in the control design process.

 Model construction from the Modelica –based Flight Dynamics Library.
zum Bild Model construction from the Modelica –based Flight Dynamics Library.

The library has been used to model several aircraft in detail:

  • The VFW-614 Advanced Technology Demonstator (ATD) in the frame of the project First Shot Approach in flight control law design (FSA);
  • DLR’s Advanced Technologies Testing Aircraft System (ATTAS) and the generic large transport aircraft model RealCAM in the frame of REAL (Robust and Efficient Autopilot control Laws design);
  • an agile generic fighter model for GARTEUR AG-11;
  • the thrust-vectored X-31 in the frame of the VECTOR project;
  • a generic flexible aircraft in the frame of the DFG project AMANDA (A Multidisciplinary High Performance Numerical Development System for Aircraft), see the Figure below.

Implementation of a generic flexible aircraft model in Modelica
VarLOADS flight loads model environment
Matlab-based GUI for defining and solving trimming problems
In all implementations, model parameters are accessible for robustness analyses. Forward as well as inverse model code has been generated for simulation, linear analysis (eigenvalues, frequency responses),Linear Fractional Transformations, trimming, and Nonlinear Dynamic Inversion-(NDI) based control laws.

For example, in the AMANDA project code for model simulation and NDI control laws was generated, allowing the nonlinear flight and aeroelastic dynamics to be simulated and visualised in real time and flown interactively using the desktop simulator AVDS (Aviator’s Design Simulator), see the next Figure.

Modelling for loads analysis (VarLOADS)

Besides the Flight Dynamics Library, the institute has been closely involved in development of the Airbus modelling environment VarLOADS, intended for special flight loads related investigations. Modelling methods and integration techniques addressed above have been extensively used. Flight mechanics models only require total forces and moments around the vehicle’s centre of gravity. Models used for loads analysis require the distribution of external forces over the airframe to be explicitly accounted for, allowing dynamic loads at specific locations of interest to be computed. The VarLOADS tool has been successfully used for flight clearance in the Awiator project, and will be used in pre-design studies.

Tools for trimming and linearization

For aircraft flight dynamics, various types of equilibrium conditions may need to be determined. Typical examples are straight and level flight, turns, constant angle of attack (fighter aircraft), 2.5g pull-up (for loads analysis), etc. In order to assist the model user in specifying and finding these equilibrium conditions, a Matlab-based graphical user interface (GUI) and reliable numerical routines have been developed. The GUI displays inputs, outputs, states, parameters, etc. (e.g. as found in the Modelica model) and guides the user in defining the characteristic flight state. From the defined trim set-up a trimming script can be generated. The mex-routine trimex solves the actual trimming problem by determining free parameters using a nonlinear equation solver or least-squares optimisation. For model linearization around the found trim solution, improved routines have been implemented in Matlab.

Real-time desktop flight simulation

In order to support the flight control design engineer in qualitative assessment of manual, autopilot and structural control laws, the institute has developed an interface between the desktop simulator AVDS (Aviator’s Design Simulator) and simulation models generated from Modelica (see the picture above). This provides the engineer with cheap and easy access to a real-time simulation facility that runs on his own desktop computer, based on the same model code as used for design.

A new simulation environment has been developed by AeroLabs AG, based on our specifications. This environment features high-quality 3-D visualisation with the help of special projection techniques and glasses, tremendously improving the reality effect.

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Design of control laws for automatic landing (REAL) (
Optimisation-based flight control law assessment (GARTEUR AG11) (
Control laws for the X-31A with reduced vertical tail (VECTOR) (