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Aircraft Simulation Model and Flight Control Laws Design Using Scilab
and Xcos
André Ferreira da Silva, Altran
Scilab Conference 2019
2www.esi-group.com
Copyright © ESI Group, 2019. All rights reserved.
Agenda
The flight control laws problem;1
The control design process;2
Building a 6-DoF flight
mechanics model;3
Building the model using Scilab
scripts;4
Building the model using Xcos
diagrams;5
Model-based design vs. Scilab
scripts;6
Pitch rate controller design
example;7
How close are we from industry?8
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The flight control laws problem (1)
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The flight control laws problem (2)
Fly-By-Wire
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The flight control laws problem (3)
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The control design process
6 DoF Aircraft
Model
Open-Loop
Linear model
Linear Controller
Design
6 DoF Aircraft
Model
Closed-Loop
● Study the
plant;
● Define
requirements
for closing the
loop;
● Study the
plant
dynamics;
● Refine
requirements
for closing
the loop;
● Choose a
controller
architecture;
● Calculate the
gains;
● Linear analysis
(margins and
performance);
● Non-linear
controller design;
● Controller
discretization;
● Handling qualities
assessment;
● To be used by other
clients (loads);
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Aircraft flight mechanics model (6 DoF)
Roughly speaking:
• Rotational: roll, pitch and yaw;
• Translational: upwards, forwards, sidewards;
Detailed mathematical description requires:
• Fixed-body reference frame;
• Earth-fixed inertial frame;
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Aircraft flight mechanics model (6 DoF)
• Position in the inertial frame: x, y, z;
• Aircraft attitude: 𝛙, 𝛟, 𝛉;
• Aerodynamic variables: 𝛂, 𝛃,
airspeed, Mach;
Inputs (at least): Outputs (at least):
• Aerodynamic surfaces deflection
or stick/column/wheel command;
• Throttle command;
• Aerodynamic configuration
change command (flaps, slats,
landing gear);
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Aircraft flight mechanics model (6 DoF)
• Atmosphere: implementation of
International Standard Atmosphere
model;
• Aerodata: aerodynamic data;
• Engine: engine dynamics model;
• Params: geometric and mass
properties of the aircraft;
• EQM: equations of motion;
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Scilab script implementation
• Implementation based on data for F16 model
presented at Steven & Lewis (2003, 2nd edition);
• Unit test for each module comparing outputs with
data from the book (trim conditions, etc.);
• Modularization following the presented
component diagram;
• Simulator, linearizer and trimmer make use of
Scilab functions for solving ordinary differential
equations, for linearizing, etc;
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Atmosphere example (Scilab script)
function [T_K, p_Pa, rho_kgpm3]=atmosphere(h_m, deltaIsa)
● International Standard Atmosphere (1976);
● Physical model for temperature, pressure and density
calculations with many tabulated values;
● Tables extracted from the official document to a CSV
and used for unit test;
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Flight simulation example
1. Trim the aircraft (find an equilibrium condition);
S = fminsearch(costf16, S0);
1. Apply an input (surface deflection);
controls.elev_deg = elev_step;
1. Solve the system of the ordinary differential
equations;
y = ode(X0, t(1), t, f16_model);
1. Check the time history of the outputs;
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Model-based design approach: Xcos
• Visual modeling to
improve readability;
• Solver embedded in the
framework;
• Makes componentization
straightforward;
• Standard approach in the
aerospace industry.
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Atmosphere example (Xcos)
• Two inputs: altitude and deltaISA;
• Three outputs: temperature,
pressure and density;
• Unit test using a comparison
between the output of the block
and the literature data;
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Xcos Full Model Implementation
• A diagram block for each component
shown previously;
• Unit test for each block based on
data in the reference book and in
other sources of data;
• No trimmer yet;
• No linearizer yet.
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Flight simulation example
1. Trim the aircraft using the scilab
script version;
1. Run a script to initialize the
variables context;
1. Start the Xcos simulation;
1. Check the outputs.
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Xcos implementation vs Script implementation
• Xcos readability is mostly
straightforward (not always for
equations);
• Xcos makes possible to have
continuous and discrete time
implementations in the same
simulation;
• Xcos is easier to be translated
automatically to another programming
language (like C, for example);
• Xcos full aircraft model is very slow to
change (2.5-GHz Intel Core i5-7200U);
• Script version can take much more
advantage of version control system
(including merge features);
• Script version is easily adaptable to find
an equilibrium condition (trimming);
18www.esi-group.com
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Pitch rate controller design example
• What is pitch?
• And pitch rate?
• Why control pitch rate?
19www.esi-group.com
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Pitch rate controller design example
1. Linearize the 6-DoF aircraft model
around an equilibrium condition;
[A, B, C, D] = lin(sim_f16, X0_lin, U0);
1. Use the state-space representation to
design the controller (in this example,
using root locus);
ss_pi = syslin("c", 0, 3, 1, 1); //PI = (s+3)/s
ss_cl_alpha_pi = ss_cl_alpha*ss_pi;
//evans(ss_cl_alpha_pi(2,1),10);
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Getting closer to the industry
Source: Wikipedia at
https://upload.wikimedia.org/wikipedia/commons/b/b
d/AltitudeEnvelopeText.GIF
Design points
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Getting closer to the industry
Model based
design
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Getting closer to the industry
For example, at least:
• 6 aerodynamic coefficients;
• 4 parameters;
• Resolution of 0.1 deg or 0.01 Mach for each
parameter;
• Several configurations (flaps, slats, landing
gear, spoilers);
• Easily achieving gigabytes of data to lookup;
Source: Wikipedia at
https://en.wikipedia.org/wiki/Wind_tunnel#/media/File:MD-
11_12ft_Wind_Tunnel_Test.jpg
Amount of data and computational performance
23www.esi-group.com
Copyright © ESI Group, 2019. All rights reserved.
Getting closer to the industry
• Integration with Version Control
System and Issue tracking System;
• Merge feature for models;
• Traceability;
• Traceability (again);
Source: Wikipedia at https://en.wikipedia.org/wiki/DO-178C#/media/File:DO-178C_Traceability.png
Version Control
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Copyright © ESI Group, 2019. All rights reserved.
Thank you

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Aircraft Simulation Model and Flight Control Laws Design Using Scilab and XCos

  • 1. 1www.esi-group.com Copyright © ESI Group, 2019. All rights reserved.Copyright © ESI Group, 2019. All rights reserved. www.esi-group.com Aircraft Simulation Model and Flight Control Laws Design Using Scilab and Xcos André Ferreira da Silva, Altran Scilab Conference 2019
  • 2. 2www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Agenda The flight control laws problem;1 The control design process;2 Building a 6-DoF flight mechanics model;3 Building the model using Scilab scripts;4 Building the model using Xcos diagrams;5 Model-based design vs. Scilab scripts;6 Pitch rate controller design example;7 How close are we from industry?8
  • 3. 3www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. The flight control laws problem (1)
  • 4. 4www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. The flight control laws problem (2) Fly-By-Wire
  • 5. 5www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. The flight control laws problem (3)
  • 6. 6www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. The control design process 6 DoF Aircraft Model Open-Loop Linear model Linear Controller Design 6 DoF Aircraft Model Closed-Loop ● Study the plant; ● Define requirements for closing the loop; ● Study the plant dynamics; ● Refine requirements for closing the loop; ● Choose a controller architecture; ● Calculate the gains; ● Linear analysis (margins and performance); ● Non-linear controller design; ● Controller discretization; ● Handling qualities assessment; ● To be used by other clients (loads);
  • 7. 7www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Aircraft flight mechanics model (6 DoF) Roughly speaking: • Rotational: roll, pitch and yaw; • Translational: upwards, forwards, sidewards; Detailed mathematical description requires: • Fixed-body reference frame; • Earth-fixed inertial frame;
  • 8. 8www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Aircraft flight mechanics model (6 DoF) • Position in the inertial frame: x, y, z; • Aircraft attitude: 𝛙, 𝛟, 𝛉; • Aerodynamic variables: 𝛂, 𝛃, airspeed, Mach; Inputs (at least): Outputs (at least): • Aerodynamic surfaces deflection or stick/column/wheel command; • Throttle command; • Aerodynamic configuration change command (flaps, slats, landing gear);
  • 9. 9www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Aircraft flight mechanics model (6 DoF) • Atmosphere: implementation of International Standard Atmosphere model; • Aerodata: aerodynamic data; • Engine: engine dynamics model; • Params: geometric and mass properties of the aircraft; • EQM: equations of motion;
  • 10. 10www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Scilab script implementation • Implementation based on data for F16 model presented at Steven & Lewis (2003, 2nd edition); • Unit test for each module comparing outputs with data from the book (trim conditions, etc.); • Modularization following the presented component diagram; • Simulator, linearizer and trimmer make use of Scilab functions for solving ordinary differential equations, for linearizing, etc;
  • 11. 11www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Atmosphere example (Scilab script) function [T_K, p_Pa, rho_kgpm3]=atmosphere(h_m, deltaIsa) ● International Standard Atmosphere (1976); ● Physical model for temperature, pressure and density calculations with many tabulated values; ● Tables extracted from the official document to a CSV and used for unit test;
  • 12. 12www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Flight simulation example 1. Trim the aircraft (find an equilibrium condition); S = fminsearch(costf16, S0); 1. Apply an input (surface deflection); controls.elev_deg = elev_step; 1. Solve the system of the ordinary differential equations; y = ode(X0, t(1), t, f16_model); 1. Check the time history of the outputs;
  • 13. 13www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Model-based design approach: Xcos • Visual modeling to improve readability; • Solver embedded in the framework; • Makes componentization straightforward; • Standard approach in the aerospace industry.
  • 14. 14www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Atmosphere example (Xcos) • Two inputs: altitude and deltaISA; • Three outputs: temperature, pressure and density; • Unit test using a comparison between the output of the block and the literature data;
  • 15. 15www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Xcos Full Model Implementation • A diagram block for each component shown previously; • Unit test for each block based on data in the reference book and in other sources of data; • No trimmer yet; • No linearizer yet.
  • 16. 16www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Flight simulation example 1. Trim the aircraft using the scilab script version; 1. Run a script to initialize the variables context; 1. Start the Xcos simulation; 1. Check the outputs.
  • 17. 17www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Xcos implementation vs Script implementation • Xcos readability is mostly straightforward (not always for equations); • Xcos makes possible to have continuous and discrete time implementations in the same simulation; • Xcos is easier to be translated automatically to another programming language (like C, for example); • Xcos full aircraft model is very slow to change (2.5-GHz Intel Core i5-7200U); • Script version can take much more advantage of version control system (including merge features); • Script version is easily adaptable to find an equilibrium condition (trimming);
  • 18. 18www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Pitch rate controller design example • What is pitch? • And pitch rate? • Why control pitch rate?
  • 19. 19www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Pitch rate controller design example 1. Linearize the 6-DoF aircraft model around an equilibrium condition; [A, B, C, D] = lin(sim_f16, X0_lin, U0); 1. Use the state-space representation to design the controller (in this example, using root locus); ss_pi = syslin("c", 0, 3, 1, 1); //PI = (s+3)/s ss_cl_alpha_pi = ss_cl_alpha*ss_pi; //evans(ss_cl_alpha_pi(2,1),10);
  • 20. 20www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Getting closer to the industry Source: Wikipedia at https://upload.wikimedia.org/wikipedia/commons/b/b d/AltitudeEnvelopeText.GIF Design points
  • 21. 21www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Getting closer to the industry Model based design
  • 22. 22www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Getting closer to the industry For example, at least: • 6 aerodynamic coefficients; • 4 parameters; • Resolution of 0.1 deg or 0.01 Mach for each parameter; • Several configurations (flaps, slats, landing gear, spoilers); • Easily achieving gigabytes of data to lookup; Source: Wikipedia at https://en.wikipedia.org/wiki/Wind_tunnel#/media/File:MD- 11_12ft_Wind_Tunnel_Test.jpg Amount of data and computational performance
  • 23. 23www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Getting closer to the industry • Integration with Version Control System and Issue tracking System; • Merge feature for models; • Traceability; • Traceability (again); Source: Wikipedia at https://en.wikipedia.org/wiki/DO-178C#/media/File:DO-178C_Traceability.png Version Control
  • 24. 24www.esi-group.com Copyright © ESI Group, 2019. All rights reserved. Thank you