1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
|
#
# MIT No Attribution
#
# Copyright (C) 2010-2023 Joel Andersson, Joris Gillis, Moritz Diehl, KU Leuven.
#
# Permission is hereby granted, free of charge, to any person obtaining a copy of this
# software and associated documentation files (the "Software"), to deal in the Software
# without restriction, including without limitation the rights to use, copy, modify,
# merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
# permit persons to whom the Software is furnished to do so.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
# INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
# PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
# HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
# OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
#
#
# -*- coding: utf-8 -*-
import casadi as ca
from matplotlib import pyplot as plt
import numpy as np
# Simulating a bouncing ball with DaeBuilder and event handling
# Joel Andersson, 2025
# Start with an empty DaeBuilder instance
dae = ca.DaeBuilder('bouncing_ball')
# Model variables
t = dae.add('t', 'independent')
h = dae.add('h', 'output', dict(start = 5, initial = 'exact'))
v = dae.add('v', 'output', dict(start = 0, initial = 'exact'))
# Dynamic equations
dae.eq(dae.der(h), v)
dae.eq(dae.der(v), -9.81)
dae.disp(True)
# Event dynamics: When h < 0, reinitialize v to -0.8*v
dae.when(h < 0, [dae.reinit('v', -0.8*dae.pre(v))])
dae.disp(True)
# Simulate over 7s
tgrid = np.linspace(0, 7, 100)
sim = ca.integrator('sim', 'cvodes', dae.create(), 0, tgrid,
dict(transition = dae.transition()))
simres = sim(x0 = dae.start(dae.x()))
# Visualize the solution
plt.figure(1)
plt.clf()
plt.plot(tgrid, simres['xf'][0, :].T)
plt.grid()
plt.show()
# Export FMU
fmu_files = dae.export_fmu()
print('Generated files: {}'.format(fmu_files))
# Compile DLL
import os
casadi_root = os.path.dirname(os.path.dirname(os.path.dirname(os.path.dirname(__file__))))
cfiles = " ".join([f for f in fmu_files if f.endswith('.c')])
sofile = dae.name() + '.so'
os.system(f'gcc --shared -fPIC -I{casadi_root}/external_packages/FMI-Standard-3.0/headers/ {cfiles} -o {sofile}')
print(f'Compiled {sofile}')
# Package into an FMU
import zipfile
fmuname = dae.name() + '.fmu'
with zipfile.ZipFile(fmuname, 'w') as fmufile:
# Add generated files to the archive
for f in fmu_files:
arcname = f if f == 'modelDescription.xml' else 'sources/' + f
fmufile.write(f, arcname = arcname)
os.remove(f)
# Add compile DLL to the archive (assume Linux 64 bit)
fmufile.write(sofile, arcname = f'binaries/x86_64-linux/{sofile}')
os.remove(sofile)
print(f'Created FMU: {fmuname}')
# Load the FMU in FMPy
try:
import fmpy
fmpy.dump(fmuname)
# Simulate the generated FMU
res = fmpy.simulate_fmu(fmuname, stop_time=7)
import matplotlib.pyplot as plt
plt.figure(1)
plt.clf()
plt.plot(res['time'], res['h'],'-', label = 'h')
plt.xlabel('time')
plt.legend()
plt.grid()
plt.show()
except ImportError as e:
print('FMPy not installed. Skipping FMU simulation.')
|
