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

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Copyright © ESI Group, 2019. All rights reserved.Copyright © ESI Group, 2019. All rights reserved.
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Aircraft Simulation Model and Flight Control Laws Design Using Scilab
and Xcos
André Ferreira da Silva, Altran
Scilab Conference 2019

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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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Fly-By-Wire

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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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• 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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• 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);

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Pitch rate controller design example
• What is pitch?
• And pitch rate?
• Why control pitch rate?

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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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Model based
design

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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

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• 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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Thank you

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