FDC 1.4 – A SIMULINK Toolbox for
Flight Dynamics and Control Analysis
DRAFT VERSION 7
Marc Rauw
May 25, 2005
The Flight Dynamics and Control Toolbox for MATLAB and SIMULINK is distributed via the Internet, together with
this FDC report, which is available in PostScript and PDF format. If you wish to make a hard-copy of the report, it
is advised to download the PostScript version and send it to a PostScript printer or a software PostScript interpreter
such as GHOSTSCRIPT (see http://www.ghostscript.com for more information).
This document was created with MIKTEX in LATEX2# format. The vector figures were drawn in TEXCAD (part of
the EMTEX package for MS-DOS), MATLAB, SIMULINK, and MAYURA DRAW. The screenshots were created with
IRFANVIEW and the wonderful JPEG2PS tool. The Postscript graphics were prepared with the DVI-driver DVIPS,
GHOSTSCRIPT and GSVIEW; the PDF version was created with GHOSTSCRIPT and ADOBE ACROBAT.
Copyright © 2004, M.O. Rauw. All rights reserved.
The Flight Dynamics and Control Toolbox has been released under and is subject to the terms of the Open Software
License, version 2.0, a copy of which has been included in appendix F.
This report has been released under and is subject to the terms of the Common Documentation License, version
1.0, the terms of which are incorporated in appendix G. Please read it before using this material - your use
of this material signifies your agreement to the terms of the License.
Instead of a list: All trademarks mentioned in this document are registered to whoever it is that owns them.
To contact the author, please send an e-mail to: rauw@dutchroll.com. For the most actual information about the
FDC toolbox, see the Dutchroll homepage: http://www.dutchroll.org or http://www.dutchroll.com.
Contents
Preface vii
1 Flight control system development 1
1.1 Automatic flight control systems . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The FCS design cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Taking a closer look at the FCS design cycle . . . . . . . . . . . . . . . . 4
1.4 FCS design environments . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 FCS design and the FDC toolbox . . . . . . . . . . . . . . . . . . . . . . 8
2 Rigid body equations of motion 11
2.1 General rigid-body equations of motion . . . . . . . . . . . . . . . . . . 11
2.1.1 General force equation for a rigid body . . . . . . . . . . . . . . 11
2.1.2 General moment equation for a rigid body . . . . . . . . . . . . 12
2.1.3 Angular momentum around the center of gravity . . . . . . . . 12
2.1.4 Resulting general equations of motion for a rigid body . . . . . 14
2.2 Expressing translational motions in flight-path axes . . . . . . . . . . . 18
2.2.1 Advantages of relating translations to flight-path axes . . . . . 18
2.2.2 Expressing forces and velocities in terms of flight-path axes . . 19
2.2.3 Derivation of the ˙V -equation . . . . . . . . . . . . . . . . . . . . 20
2.2.4 Derivation of the ˙a-equation . . . . . . . . . . . . . . . . . . . . 20
2.2.5 Derivation of the ˙b-equation . . . . . . . . . . . . . . . . . . . . 21
2.3 Equations of motion in nonsteady atmosphere . . . . . . . . . . . . . . 21
2.4 Kinematic relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5 Assembling the state equations . . . . . . . . . . . . . . . . . . . . . . . 25
3 The aircraft model 27
3.1 General structure of the flight simulation model . . . . . . . . . . . . . 27
3.2 The nonlinear aircraft dynamics . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 External forces and moments . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.1 Aerodynamic Forces & Moments . . . . . . . . . . . . . . . . . . 28
3.3.2 Engine Forces & Moments . . . . . . . . . . . . . . . . . . . . . . 31
3.3.3 Gravitational forces . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.4 Forces and moments due to nonsteady atmosphere . . . . . . . 32
3.4 Converting the implicit state equations to explicit equations . . . . . . 33
3.5 Atmosphere and airdata variables . . . . . . . . . . . . . . . . . . . . . 34
3.6 Additional observation variables . . . . . . . . . . . . . . . . . . . . . . 38
3.6.1 Body-axes velocity rates . . . . . . . . . . . . . . . . . . . . . . . 38
ii CONTENTS
3.6.2 Kinematic accelerations and specific forces . . . . . . . . . . . . 39
3.6.3 Flight-path related variables . . . . . . . . . . . . . . . . . . . . 40
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 External atmospheric disturbances 43
4.1 Deterministic disturbances . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 Stochastic disturbances . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
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