Thesis - Beaver simulation

E.7 Conclusions.

A general aircraft trim algorithm has been derived in this appendix. It can be implemented straigthforwardly as a MATLABroutine, which uses the SIMULINK system BEAVER to calculate the time-derivatives of the state variables. The trim routine can be used to find steady-state level-flight conditions, steady turns (skidding or coordinated), steady pull-ups (or push-overs), and steady rolls. It can be applied to every model which uses the same inputs and states as the system BEAVER, independently from the internal structure of the aircraft model. Moreover, it shouldn't be too difficult to change the programs for application to aircraft models which use other state or input vectors.

F.2 Nonlinear model of the aircraft dynamics: state and output equations.

F.2.1 Introduction.

The aircraft dynamics model contains the nonlinear Ordinary Differential Equations (ODES)for the twelve state variables, all equations which must be solved to calculate the external forces and moments, and a large number of additional output equations, which are not really necessary for solving the state equations, but which can be applied for many different applications involving flight dynamics analysis. It is not difficult to enhance this list of output variables even further.

The equations have been implemented as SIMULINKFunction blocks. Small sets of interrelated variables have been grouped together into a limited number of 'basic' blocks, which together build the whole simulation model. To prevent the system from becoming really inextricable, a limited number of output vectors are used. Every output vector is created by one 'basic' block, which Muxes different output variables into one output vector. Some 'basic' blocks use output vectors from other blocks as inputs, in which case often only a few elements are actually used in the equations of that block. This seems somewhat confusing, but it keeps the number of output lines within reasonable limits.

To add new blocks to the aircraft model, one should know exactly which variables are calculated by the other blocks, but how that is done internally doesn't really matter, as long as the results are correct. For this reason, all 'basic' blocks have been Masked, thus hiding their internal structure from the user (black-box approach). See section E.8 of appendix E for more details about the Mask option.

Hiding the internal structure from the user is particularly useful for implementing aircraft-dependent blocks such as the aerodynamic model of an aircraft. For instance: the aerodynamic model of the 'Citation 500' aircraft as used in the DUT-flightsimulator, interpolates multi-dimensional tables to obtain the aerodynamic forces and moments, whereas the 'Beaver' model expresses these forces and moments as nonlinear polynomials. Both models can be implemented in 'basic' blocks, which look exactly the same from the outside, but completely different from the inside.

This section will show the internal structure of all 'basic' blocks from the 'Beaver' model, which already has been outlined in general terms in chapter 4. First, a list of all variables will be given. Then, the internal structure of all blocks will be shown and explained. Finally, some routines to define model parameters and routines to compute steady-state trim values or define arbitrary initial conditions will be presented.

F.2.2 List of variables, used for the aircraft state and output models.

Although the system itself has been built up as a block-diagram, still a standardized list of acronyms has been used within the block-diagrams of the aircraft model, the help files, etc. to make the diagrams better readable for the user. Note that the SIMULINKFunction blocks use u as standard input variable. If u is a vector - this is true for most Function blocks of the 'Beaver' model - the

The data matrix AM, which can be loaded from the file AEROMOD.MAT, contains all parameters of the aerodynamic model of the 'Beaver', see equations (2-5) of chapter 2. The parameters of the 'Beaver' engine forces and moments model (equations (2-lo), chapter 2) have been included in the matrix EM, which has been stored in the file ENGMOD.MAT. The matrices GM1 and GM2, which can be loaded from the file AIRCRAFT.MAT, contain data about the aircraft geometry and inertia parameters (GM stands for 'Geometry and Mass').

The MAT-files must be loaded into the MATLABworkspace before starting a simulation by calling the function LOADER. If the MAT-files are not present in the workdirectory, it is necessary to run MODBUILD first. The MATLAB functions LOADER and MODBUILD will be described in section F.2.6. The data matrices are only valid for the models of the 'Beaver'. The aircraft geometry and mass distribution are considered to remain constant during the motions of interest. The definition of these matrices can be found in tables F-1 to F-3 a t the end of this appendix.

F.2.3 The aircraft model library and the complete aircraft model.

All basic blocks of the aircraft model have been logically stored in the library ACLIB ('AC' = 'aircraft'). This library includes some examples which illustrate how different blocks can be combined into 'groups'. The system BEAVER contains the complete aircraft model, which results after connecting all blocks and groups from the library ACLIB to eachother. Here, we'll use the system BEA- VER as a starting point for the discussion of all blocks from ACLIB, since this immediately explains the relations between the different blocks. A list with available blocks in BEAVER and ACLIB is included in table F-4 a t the end of this chapter. Note: ACLIBl to ACLIB8 are sublibraries of ACLIB.

F.2.4 First level of the simulation model BEAVER.

Figure F-1shows the first level of the system BEAVER, which will be called the main level in the figures. This level is used to arrange the inputs and outputs in such way that other systems can be connected to BEAVER. The large subsystem block, called Beaver dynamics and output equations, contains the actual aircraft model, i.e., the state and output equations themselves.

All outputs from the subsystem Beaver dynamics and output equations are sent to the matrix Out in the MATLABworkspace (notice the use of upper-case!). The inputs to this subsystem are sent to the matrix In. See table F-5 at the end of this report for the current definitions of I n and Out (it is quite easy to change these definitions if more output equations are added or if the outputs are reshuffled), or type help inputs or help outputs at the MATLABcommand line. The system BEAVER also contains a Clock block, connected to a To Workspace block, which will create a time-axis in the MATLABworkspace for plotting