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

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);

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

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