Thesis - Beaver simulation

Figure F-1.Main level of the system BEAVER.

Main

Figure F-2. Internalstructure of the subystem block

Beaver dynamics and output equations.

Main \ Beaver dynamics

purposes. The time values are sent to the vector time in the MATLAB workspace.

A limited number of output signals have been connected to Outport blocks (the shaded square blocks which have been numbered sequentially), which makes it possible to connect these signals to other systems. Notice that it is not possible to connect a vector line to a single Outport block; output vectors need to be demultiplexed with a DeMux block first! Here, sixteen output signals have been coupled to Outport blocks. These signals are:

V, a,p, p, q, r, y~,0, 9,xe,y e , H, and (these variables are used by the control laws of the 'Beaver' autopilot), and:

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Control System of the 'Beaver', see part 11)

In this report, only the output variables mentioned above will be connected to other subsystems. If the system BEAVER is to be used for other purposes, it might be necessary to include other Outport blocks to the first level of the system BEAVER. From now on, the variables which have been connected to Outport blocks in the first level of the system BEAVER will be called S-func- tion outputs. Notice that the number of S-function outputs is much smaller than the number of outputs which are sent to the matrix Out in the MATLAB workspace. The latter variables can not be used by other subsystems on-line during the simulation!

The number of S-function outputs must be in accordance with the number of inputs of subsystems which have to be connected to BEAVER. The system BEAVER can be connected to other systems with an S-function block from the SIMULINKNonlinear library (see appendix E). Chapter 6 and part I1 of this report contain some practical examples which illustrate the inclusion of BEAVER within other systems.

There are twelve inputvariables: four aerodynamic inputs (ti,, 6,, 6,, and tif) which are combined into the vector u, ,two engine inputs (n, andp, ) which are combined into the vector u, , three wind velocity components along the body axes of the aircraft (u, , u,, and w, ), which form the first half of the vector u,, and the three time derivatives of these wind velocity components, which form the second half of u,.

Table F-5 contains a list of all input variables, which are stored in the vector In, all output variables which are stored Out, and all variables that have been coupled to Outport blocks (the S-function outputs). The variables which are sent to the vectors I n and Out can be transferred to S-function outputs if they are also connected to Outport blocks.

F.2.5 Beaver dynamics and o u t p u t equations (second level of BEAVER).

Figure F-2 shows the general structure of the 'Beaver' simulation model. There are a number of subsystem blocks and a number of blocks with the blockname displayed within the block itself. The latter ones will be called basic blocks in this appendix. The internal structure of the basic blocks cannot be accessed by

the user directly, unless they are 'unmasked' 'I. We will now zoom in to the different blocks and groups which are visible in figure 5-2.

a. Airdata Group.

Figure F-3 shows the internal structure of the subsystem block Airdata Group. This subsystem contains the following basic blocks:

Atmosph. In this block, some atmosphere variables are calculated, using the US Standard Atmosphere model. Although the acceleration of gravity is assumed to be constant (g = go),g has been included in the outputvector which makes it possible to implement g as a function of altitude in the future. Type help atmosph a t the MATLABcommand line for on-line help. The structure of Atmosph is shown in figure F-4.

Inputvector: x

Outputvector: Yntm

Airdatal. In this block, the dynamic pressure qdp ,the speed of sound a, and the Mach number M are calculated. Type help airdatal a t the MATLAB command line for on-line help. The internal structure ofAirdatal is shown in figure F-5.

Airdata2. This block is used to calculate the impact pressure q, ,the equivalent airspeed Ve,and the calibrated airspeed V,. Type help airdata2 a t the MATLABcommand line for on-line help. Figure F-6 shows the internal structure of Airdata2.

Airdata3. This block calculates the total temperature T,and the Reynolds numbers Re and R,. Type help airdata3 a t the MATLABcommand line for on-line help. The structure ofAirdata3 is shown in figure F-7.

The variable cbar, used by Airdata3 is defined in the Mask-definition line:

cbar = GMl(10);

See table F-3 for the definition of GM1.

See section E.8 of appendix E for more details about the Mask utility.

Atmosph

yatm

I

Airdatal -

yad1

Figure F-3. Internal structure of the subsystem block Airdata Group.

Main \ Beaver dynamics \ A i r a a Group

I p Mux

(1.458'1OA(-6)'u[2IA1.5)/(~[2]+110.4)

yatm

mu

Figure F-4.Internal structure of the 'basic9block Atmosph.

Main \ Beaver dynamics \ Airdata Group \ Atmosph

El-

yatm

Mux

yad1

J- Mux 4

Figure F-5. Internal structure of the 'basic' block AilrEatal.

Main \ Beaver dynamics \ Airdata Group \ Airdatal

vc

Figure F-6. Internal structure of the 'basic' block AilrEata2.

Main 1 Beaver dynamics \ Airdata Group \ Airdata2

yw

yadl

Figure F-7.Internal structure of the 'basic' block Ainlata3.

Main \ Beaver dynamics \ Airdata Group \ Airdata3

b. Aerodynamics Group.

Figure F-8 shows the internal structure of the subsystem Aerodynamics Group, which contains the following basic blocks:

Dimless. This block is used to calculate the dimensionless rotational velocities along the aircraft's body-axes. Type help dimless for on-line help a t the MATLABcommand line. Figure F-9 shows the internal structure of Dimless.

The variables b and cbar have been defined in the Mask-definition line:

cbar = GMl(1); b = GMl(2);

See table F-3 a t the end of this appendix for the definition of GM1.

Aeromod (Beaver). In this block the aerodynamic forces and moment coefficients along the body axes are calculated. This aerodynamic model is valid for the DHC-2 'Beaver' aircraft, see equations (2-5) in section 2.2.2 and ref.[30]. To implement another aerodynamic model which expresses the aerodynamic forces in terms of aerodynamic lift, drag, and sideforce, in stead of forces along the body axes, it is necessary to make some changes in the equations for V , , and P, which are contained in the block Equations of motion\State deriuatives\Vabdot. The appropriate equations have been derived in appendix A.

On-line help is available a t the MATLABcommand line (type help aeromod). See figure F-10 for the internal structure of Aeromod (Beaver).

The block Matrix product has been created with the SIMULINKMask utility. This block has been stored in the library TOOLS, containing some useful Masked SIMULINKblocks which are not included in the standard SIMULINKlibraries. Here, the Matrix product is used to multiply the help vector y, which leaves the Mux block:

with the matrix AM to obtain the aerodynamic force and moment coefficients. AM contains all stability and control derivatives of the nonlinear aerodynamic model of the 'Beaver', see table F-1a t the end of this chapter for its definition.

FMdims. This block ('Force and Moment dimensions') is used to calculate non-dimensionless forces and moments from the dimensionless coefficients.

Figure F-8.Internal structure of the subsystem block Aerodynamics Group.

Main \ Bemer dynamics I Aerodynamics Group

Figure F-9. Internal structure of the 'basic' block Dimless.

Main I Beauer dynamics I Aerodynamics Gmup \ Dimka8

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Figure F-10. Internal structure of the 'basic' block Aeromod (Beaver).

Main \ Beaver dynamics 1 Aerodynamics Group \ Aeromod (Beaver)

Forces and

moments

coefficients

qdyn 'S Cm

qdyn 'S * Cn

Figure F-11. Internal structure of the 'basic' block FMdims.

Main \ Beaver dynamics \ Aerodynamics Group \ FMdims, or: Main \ Beaver dynamics \ Engine Group \ FMdimcr

Figure F-12. Internal structure of the subsystem block Engine Group.

Main \ Beaver dynamics \ Engine Group

w

X

ytmp = [dpt dptA3 alpha'dptA2dpt'alphaA2]'

Figure F-14. Internal structure of the 'basic' block Engmod (Beaver).

Main \ Beauer dynamics \ Engine Group I Engrnod (Beauer)