Scripts for various aircraft dynamics analysis and simulations
The provided Makefile can be used to compile the scripts if the dependencies are installed
make
This command will compile three scripts
- ac_trim for trimming an aircraft in a given flight condition
- ac_sim for simulating the aircraft
- ac_sim_lin for simulating a linearized version of the aircraft
Currently, this code implements a 6DOF rigid body model under no wind conditions. Linear aerodynamic coefficient models are used to calculate the forces and moments.
The simulations currently use a fixed control. Implementation of control algorithms is future work.
There are several analysis scripts available. Here we describe their usage
Trimming is performed via the script called ac_trim . This script allows for computing the trim conditions for steady trimmed flight. To see what the script does you can give the help flag ./ac_trim -h The
Here is sample output for steady flight at a speed of 120 ft/s with a 10 ft/s straight climb rate. The script also performs linearization around the trim condition because the --linearize flag is specified. Finally it saves both the trim condition and the linearization (A and B) matrices to the the output file trim_conditions.json This file can then be read by the other scripts
$ ./ac_trim vehicles/pioneer_uav.json -s 120 -c 10 -y 0 --linearize -o trim_conditions.json
========================================================
TRIM RESULT
========================================================
Optimizer result = 4
Objective value = 3.01356E-19
Spec : Targets Achieved
---------------------------------------------------------
Speed (ft/s) : 1.20000E+02 1.20000E+02
Climb Rate (ft/s) : 1.00000E+01 1.00000E+01
Yaw Rate (rad/s) : 0.00000E+00 0.00000E+00
State : x dx x (secondary unit)
------------------------------------------------------------------------------
U (ft/s) : 1.19576E+02 -3.71481E-11
V (ft/s) : 0.00000E+00 0.00000E+00
W (ft/s) : 1.00772E+01 1.33937E-12
P (rad,deg/s) : 0.00000E+00 0.00000E+00 0.00000E+00
Q (rad,deg/s) : -5.47605E-10 -9.17324E-13 -3.13755E-08
R (rad,deg/s) : 0.00000E+00 0.00000E+00 0.00000E+00
Roll (rad,deg) : 0.00000E+00 0.00000E+00 0.00000E+00
Pitch (rad,deg) : 1.67506E-01 -5.47605E-10 9.59739E+00
Input :
---------------------------------------------------------------
Elevator (rad,deg) : 8.95386E-03 5.13019E-01
Aileron (rad,deg) : 0.00000E+00 0.00000E+00
Rudder (rad,deg) : 0.00000E+00 0.00000E+00
Thrust (lb-slug) : 8.36081E+01
Derived Quantities :
---------------------------------------------------------------
Angle of Attack (rad,deg) : 8.40760E-02 4.81720E+00
Sideslip Angle (rad,deg) : 0.00000E+00 0.00000E+00
Flight Path Angle (rad,deg) : 8.34301E-02 4.78019E+00
Bank Angle (rad,deg) : 1.49012E-08 8.53774E-07
===============================================================
========================================================
LINEARIZATION RESULT
========================================================
x y z U V W P Q R Roll Pitch Yaw
0.000E+00 0.000E+00 0.000E+00 9.860E-01 0.000E+00 1.667E-01 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -1.000E+01 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -1.008E+01 0.000E+00 1.196E+02
0.000E+00 0.000E+00 0.000E+00 -1.667E-01 0.000E+00 9.860E-01 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -1.196E+02 0.000E+00
0.000E+00 0.000E+00 0.000E+00 -3.883E-02 0.000E+00 2.543E-01 0.000E+00 -1.009E+01 0.000E+00 0.000E+00 -3.172E+01 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 -3.084E-02 0.000E+00 1.008E+01 -0.000E+00 -1.196E+02 3.172E+01 -0.000E+00 -0.000E+00
0.000E+00 0.000E+00 0.000E+00 -3.922E-01 -0.000E+00 -1.642E+00 -0.000E+00 1.172E+02 -0.000E+00 -0.000E+00 -5.364E+00 -0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 -6.262E-02 0.000E+00 -7.954E+00 0.000E+00 4.967E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 2.073E-02 -0.000E+00 -2.459E-01 0.000E+00 -3.835E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.009E-01 0.000E+00 -3.546E-01 0.000E+00 -1.803E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 1.691E-01 -9.259E-11 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 -0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.014E+00 -5.554E-10 0.000E+00 0.000E+00
Elev. Ail. Rud. Thrust
0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000
-0.077 0.000 0.000 0.077
-0.000 -0.000 -0.000 0.000
-16.053 -0.000 -0.000 -0.000
0.000 -41.314 0.809 0.000
-24.586 0.000 0.000 0.000
0.000 4.603 -9.861 0.000
0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 Simulation is performed via the script called ac_sim . This script simulates an aircraft for a given initial condition. To see what the script does you can give the help flag ./ac_sim -h This script requires the specification an initial condition in addition to a vehicle file. A reference initial condition is provided examples/example_ic.json. This initial condition is provided below.
{
"x":0,
"y":0,
"z":0,
"U":119.556604117257407,
"V":0.000000000000000,
"W":10.306231704642098,
"P":0.000000000000000,
"Q":-0.000000001679369,
"R":0.000000000000000,
"roll":0.000000000000000,
"pitch":0.085991201830814,
"yaw":0.0,
"elevator":0.006646961692774,
"aileron":0.000000000000000,
"rudder":0.000000000000000,
"thrust":48.877175456058318,
}An example execution that simulates an aircraft for 100 seconds and saves every 0.1 seconds is shown below. The resulting file has the same name as the initial condition, with an addition ".run" extension.
$ ./ac_sim vehicles/pioneer_uav.json examples/example_ic.json -t 100 -d 0.1
Aircraft filename = vehicles/pioneer_uav.json
Initial condition filename = examples/example_ic.json
========================================================
Simulating Nonlinear Dynamics
========================================================
Time = 1.0000E+02
save_time = 1.0000E-01
nsteps = 1000
Saving simulation to examples/example_ic.json.runThe simulation file is organized as follows:
- The first row are headers indicating what time/state/control the column corresponds to
- The next rows are the perturbed states
- The first column is the time
We can also simulate a linearized aircraft via the script called ac_sim_lin . This script simulates an aircraft around a specified trim condition for a given initial condition. To see what the script does you can give the help flag ./ac_sim_lin -h This script requires the specification of both a trim condition and an initial condition in addition to a vehicle file. A reference initial condition is provided examples/example_ic.json. The trim condition is obtained as an output to the ./ac_trim with the -o flag specified.
An example execution that simulates a linearized version of an aircraft for 100 seconds and saves every 0.1 seconds is shown below. The resulting file has the same name as the initial condition, with an addition ".run" extension.
$ ./ac_sim_lin vehicles/pioneer_uav.json trim.json examples/example_ic.json -t 100 -d 0.1
Aircraft filename = vehicles/pioneer_uav.json
Trim condition filename = trim.json
Initial condition filename = examples/example_ic.json
Loading initial condition
Loading trim condition
Loading A and B matrices
Loading aircraft
========================================================
Simulating Linearized Dynamics at Steady State
========================================================
Time = 1.0000E+02
save_time = 1.0000E-01
nsteps = 1000
Saving simulation to examples/example_ic.json.runThe simulation file is organized as follows:
- The first row are headers indicating what state/control the column corresponds to
- The second row is the steady-state condition around which the linearization was performed
- The next rows are the perturbed states
- The first column is the time
To obtain un-perturbed states, you will have to add the perturbed states to the steady-state condition. Note that this addition only makes sense for the "U, V, W, P, Q, R, Roll, Pitch" variables --- since these states are fixed in steady state.
The stability and control derivatives are taken from the database provided by the UIUC Applied Aerodynamics Group https://m-selig.ae.illinois.edu/apasim/Aircraft-uiuc.html
Author: Alex A. Gorodetsky
Contact: goroda@umich.edu
Copyright (c) 2020 Alex Gorodetsky
License: GPL