The VIB model library is designed as an object-oriented Modelica library consisting of several levels. The hierarchy of the library is illustrated by the figure to the right and can be summarised as follows: Physical interface definitions are the basic modules for generic physical models on the level “Physical Domains” such as electrics, mechanics, hydraulics and pneumatics. Aircraft components – and in the next step aircraft systems – are implemented using basic physical models and component models respectively so that each level is based on the underlying levels of the entire library.

Hierarchical model library structure

The hierarchy ends at the aircraft architecture level (the top level) that comprises the feasible and reference aircraft configurations. The generation of different aircraft level models can be realised in a very flexible and easy way by exchanging the accordant model classes. This can be done automatically if it becomes necessary due to the number of diverse aircraft architectures. An example for an aircraft architecture model with its systems and components is shown in the figure. The electrical power generation system (EPGS) is extracted from the aircraft architecture model and indicates one of the generators on component level.

2 Modelica diagram of a hierarchical aircraft model

For the VIB simulations an inverse rather than a direct modelling approach is used. An inverse model can be seen as a model where the meaning of input and output variables is exchanged. The approach is discussed using an example focusing on an electromechanical actuator (motor and gearboxes) and control surface model. The input variables for the direct model are the motor current (derived from the demanded and actual position by means of the motor controller), the generator voltage (impressed at the actuator motor) and the acting load torque at the control surface (see figure below). The unknown variables in this case are the real motion of the control surface and its derivatives , which are calculated according to the given load profile. On the basis of this direct actuator model, the necessary electrical power can be computed by means of the actual actuator motor current and its corresponding actuator motor voltage. For the inverse electromechanical actuator and surface model, the input variables are the predefined motion and load found at the control surface and the generator voltage , impressed at the actuator motor. The output variable (unknown variable) for the inverse model is the motor current . The resulting necessary power of the generator and engine can be calculated in the same manner as for the direct model.

In Dymola, the DAE (differential-algebraic equation system) corresponding to the inverse model is handled by the same methods as the DAE of any other (direct) model. The methods applied by Dymola are the Pantelides algorithm and the dummy derivative method. Since the Pantelides algorithm will differentiate equations, the known input functions may also be differentiated, which leads to the well known effect that the derivatives of the input functions must exist up to a certain order.

Due to the fact that in Modelica the models are described in an object-oriented and physical manner, an inverse model is almost identical to the corresponding direct model. The only significant difference is that the inverse model does not require any representation of the controller structure existing in the real system or component, whereas the direct model generally comprises the controller structure for calculation of the motor current as a function of actual and demanded motor position. The main advantage of the inverse modelling approach is the lower model complexity due to the absence of possibly complicated and proprietary controllers from partner companies.

References

Bals, J., Hofer, G., Pfeiffer, A., Schallert, C., Object-Oriented Inverse Modelling of Multi-Domain Aircraft Equipment Systems with Modelica. Modelica 2003, 3rd International Modelica Conference, Linköping, Sweden, November 3-4, pp.377-384, (2003)