AC18 B767 aircraft at a flutter condition Davison see AC10! reduced order system generated by /export/home/leibfr/bsp37/bsp37bal.m
simulation.py
# This file was autogenerated from the template: simulation.py.template (2022-10-10 15:53:24).
import numpy as np
import system_model
from scipy.integrate import solve_ivp, odeint
from ackrep_core import ResultContainer
from ackrep_core.system_model_management import save_plot_in_dir
import matplotlib.pyplot as plt
import os
from ipydex import Container
# link to documentation with examples: https://ackrep-doc.readthedocs.io/en/latest/devdoc/contributing_data.html
def simulate():
"""
simulate the system model with scipy.integrate.solve_ivp
:return: result of solve_ivp, might contains input function
"""
model = system_model.Model()
rhs_xx_pp_symb = model.get_rhs_symbolic()
rhs = model.get_rhs_func()
# initial state values
xx0 = np.ones(model.sys_dim)
t_end = 10
tt = np.linspace(0, t_end, 1000)
simulation_data = solve_ivp(rhs, (0, t_end), xx0, t_eval=tt)
# using odeint for models with large state vectors
# res = odeint(rhs, y0=xx0, t=tt, tfirst=True)
# simulation_data = Container()
# simulation_data.y = res.transpose()
# simulation_data.t = tt
# postprocessing: calc output
ny = 2
C = model.get_parameter_value("C")
D21 = model.get_parameter_value("D21")
output = np.zeros((ny, len(tt)))
for i in range(len(tt)):
output[:,i] = np.matmul(C, simulation_data.y[:,i]) # + np.matmul(D21, w)
simulation_data.output = output
save_plot(simulation_data)
return simulation_data
def save_plot(simulation_data):
"""
plot your data and save the plot
access to data via: simulation_data.t array of time values
simulation_data.y array of data components
simulation_data.uu array of input values
:param simulation_data: simulation_data of system_model
:return: None
"""
for i in range(simulation_data.output.shape[0]):
plt.plot(simulation_data.t, simulation_data.output[i], label=f"$y_{i}$")
plt.legend()
plt.tight_layout()
save_plot_in_dir()
def evaluate_simulation(simulation_data):
"""
assert that the simulation results are as expected
:param simulation_data: simulation_data of system_model
:return:
"""
expected_final_state = np.array([ 2.73485791e-06, 9.19818719e-07, -3.15388824e-06, -2.00360408e-05,
-1.32973217e-05, 8.30823206e-06, -7.13694925e-06, 5.37979739e-06,
2.41468043e+00, -3.10756760e+00])
rc = ResultContainer(score=1.0)
simulated_final_state = simulation_data.y[:, -1]
rc.final_state_errors = [
simulated_final_state[i] - expected_final_state[i] for i in np.arange(0, len(simulated_final_state))
]
rc.success = np.allclose(expected_final_state, simulated_final_state, rtol=0, atol=1e-2)
return rc
system_model.py
# This file was autogenerated from the template: system_model.py.template (2022-10-10 15:53:24).
import sympy as sp
import numpy as np
import symbtools as st
import importlib
import sys, os
#from ipydex import IPS, activate_ips_on_exception
from ackrep_core.system_model_management import GenericModel, import_parameters
# Import parameter_file
params = import_parameters()
#link to documentation with examples: https://ackrep-doc.readthedocs.io/en/latest/devdoc/contributing_data.html
class Model(GenericModel):
def initialize(self):
"""
this function is called by the constructor of GenericModel
:return: None
"""
# Define number of inputs -- MODEL DEPENDENT
self.u_dim = 2
# Set "sys_dim" to constant value, if system dimension is constant
self.sys_dim = 10
# check existence of params file
self.has_params = True
self.params = params
# ----------- SET DEFAULT INPUT FUNCTION ---------- #
def uu_default_func(self):
"""
define input function
:return:(function with 2 args - t, xx_nv) default input function
"""
def uu_rhs(t, xx_nv):
"""
sequence of numerical input values
:param t:(scalar or vector) time
:param xx_nv:(vector or array of vectors) numeric state vector
:return:(list) numeric inputs
"""
u = np.zeros(self.u_dim)
return u
return uu_rhs
# ----------- SYMBOLIC RHS FUNCTION ---------- #
def get_rhs_symbolic(self):
"""
define symbolic rhs function
:return: matrix of symbolic rhs-functions
"""
if self.dxx_dt_symb is not None:
return self.dxx_dt_symb
x = self.xx_symb
A, B, B1, C1, C, D11, D12, D21 = self.pp_symb # parameters
w = np.zeros(3) # noise
u = self.uu_symb # inputs
# define symbolic rhs functions
self.dxx_dt_symb = np.matmul(A,x) + np.matmul(B1,w) + np.matmul(B,u)
return self.dxx_dt_symb
parameters.py
# This file was autogenerated from the template: parameters.py.template (2022-10-10 15:53:24).
import sys
import os
import numpy as np
import sympy as sp
import tabulate as tab
#link to documentation with examples: https://ackrep-doc.readthedocs.io/en/latest/devdoc/contributing_data.html
# set model name
model_name = 'B767 aircraft at a flutter condition'
# ---------- create symbolic parameters
A = sp.MatrixSymbol('A', 10, 10)
B = sp.MatrixSymbol('B', 10, 2)
B1 = sp.MatrixSymbol('B1', 10, 3)
C1 = sp.MatrixSymbol('C1', 5, 10)
C = sp.MatrixSymbol('C', 2, 10)
D11 = sp.MatrixSymbol('D11', 5, 3)
D12 = sp.MatrixSymbol('D12', 5, 2)
D21 = sp.MatrixSymbol('D21', 2, 3)
pp_symb = [A, B, B1, C1, C, D11, D12, D21]
# ---------- create auxiliary symbolic parameters
# set numerical values of auxiliary parameters
# trailing "_nv" stands for "numerical value"
A_nv = sp.Matrix(np.array([[-1.96218173e+00, 2.93478561e+01, 7.09938479e+00,
-4.27052563e+00, -2.19720836e+00, 7.02022433e+00,
2.35656948e+00, -1.40306963e+00, 0.00000000e+00,
0.00000000e+00],
[-2.89729781e+01, -3.83047005e-01, -2.45254213e+00,
6.87681195e+00, 6.38239536e-01, -2.31607847e+00,
-1.21423520e+00, 7.87197471e-01, 0.00000000e+00,
0.00000000e+00],
[-6.44710154e+00, 1.83216052e+00, -8.04826868e-01,
4.36597956e+01, 2.01284810e+00, -2.92931277e+00,
-2.17952258e+00, 1.45964753e+00, 0.00000000e+00,
0.00000000e+00],
[-5.53605690e-01, -6.43547046e+00, -4.33013521e+01,
-3.91559217e+00, -4.22367888e+00, 1.77005820e+01,
3.36727549e+00, -2.29564242e+00, 0.00000000e+00,
0.00000000e+00],
[ 1.52819246e+00, 1.87500302e-01, -1.61371325e+00,
2.75649933e+00, -7.99488823e-01, 3.65849001e+01,
3.48459826e+00, -1.77183757e+00, 0.00000000e+00,
0.00000000e+00],
[-4.79608198e+00, -1.72327607e-01, -1.95196537e+00,
-1.71293232e+01, -3.42626087e+01, -9.67071839e+00,
-2.06893198e+01, 1.07436612e+01, 0.00000000e+00,
0.00000000e+00],
[-1.18111938e-01, 6.90456628e-01, 1.60965467e+00,
1.74630944e+00, -2.04901942e+00, 2.00082173e+01,
-3.12200502e+00, 2.76301358e+01, 0.00000000e+00,
0.00000000e+00],
[-6.49363841e-01, -4.28785767e-01, -1.22836446e+00,
-9.82039173e-01, 4.32613018e-01, -9.07399499e+00,
-2.53592198e+01, -1.46376176e+00, 0.00000000e+00,
0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 1.16397307e+01,
1.69018602e+02],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, -3.10015383e+00,
-1.14367307e+01]]))
B_nv = sp.Matrix(np.array([[ 1.96050016e+02, -2.48625964e+02],
[ 1.35519420e+02, -1.08092698e+02],
[ 8.22820478e+01, 3.45059108e+01],
[ 3.88173470e+02, -8.16977915e+01],
[-8.64042347e+01, 8.09998941e+01],
[ 4.11451840e+02, 1.08055257e+02],
[-2.11799057e+02, -1.12447245e+02],
[ 1.62719831e+01, -8.03096928e+01],
[-6.75043395e+00, -5.13305891e+00],
[-3.80529228e-01, -1.98627271e-01]]))
B1_nv = sp.Matrix(np.array([[ 1.96050016e+02, -2.48625964e+02],
[ 1.35519420e+02, -1.08092698e+02],
[ 8.22820478e+01, 3.45059108e+01],
[ 3.88173470e+02, -8.16977915e+01],
[-8.64042347e+01, 8.09998941e+01],
[ 4.11451840e+02, 1.08055257e+02],
[-2.11799057e+02, -1.12447245e+02],
[ 1.62719831e+01, -8.03096928e+01],
[-6.75043395e+00, -5.13305891e+00],
[-3.80529228e-01, -1.98627271e-01]]))
C1_nv = sp.Matrix(np.array([[-5.17831065e-02, 4.97408918e-03, 3.05824415e-02,
-4.74937127e-03, -3.40836085e-02, 2.08896197e-03,
8.48048683e-02, 2.93624869e-02, -4.29143581e-01,
1.38941769e+00],
[-2.51959506e-02, 8.46171194e-02, -1.27201614e-02,
-1.88764130e-02, -2.73381391e-02, -2.53508129e-02,
1.27010131e-01, 1.06588519e-02, -2.94542997e+00,
8.51492319e-01],
[-3.49186404e-02, -1.37979567e-02, -4.81092443e-03,
1.39399957e-02, -9.43321237e-04, -1.37398529e-02,
7.81378714e-02, -8.93968773e-02, -1.42117826e+00,
-7.72993515e+00],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00]]))
C_nv = sp.Matrix(np.array([[ 2.53925381e-03, -1.16707666e-03, 1.27739519e-04,
-4.18514541e-03, 6.34051980e-05, 2.14779377e-03,
-3.03778405e-03, -3.95940559e-03, 9.61325407e-03,
-3.63057818e-02],
[ 4.15967367e+02, -1.79554835e+02, -2.32410488e+02,
4.94159169e+02, 1.68026991e+02, -5.58302763e+02,
-2.47012577e+02, 1.62864214e+02, 8.83344413e+03,
4.68785017e+04]]))
D11_nv = sp.Matrix(np.array([[0., 0., 0.],
[0., 0., 0.],
[0., 0., 0.],
[0., 0., 0.],
[0., 0., 0.]]))
D12_nv = sp.Matrix(np.array([[0. , 0. ],
[0. , 0. ],
[0. , 0. ],
[0.13503703, 0. ],
[0. , 0.02700926]]))
D21_nv = sp.Matrix(np.array([[0., 0., 0.],
[0., 0., 0.]]))
# ---------- create symbolic parameter functions
# parameter values can be constant/fixed values OR set in relation to other parameters (for example: a = 2*b)
# list of symbolic parameter functions
# tailing "_sf" stands for "symbolic parameter function"
pp_sf = [A_nv, B_nv, B1_nv, C1_nv, C_nv, D11_nv, D12_nv, D21_nv]
# ---------- list for substitution
# -- entries are tuples like: (independent symbolic parameter, numerical value)
pp_subs_list = []
# OPTONAL: Dictionary which defines how certain variables shall be written
# in the table - key: Symbolic Variable, Value: LaTeX Representation/Code
# useful for example for complex variables: {Z: r"\underline{Z}"}
latex_names = {}
# ---------- Define LaTeX table
# Define table header
# DON'T CHANGE FOLLOWING ENTRIES: "Symbol", "Value"
tabular_header = ["Symbol", "Value"]
# Define column text alignments
col_alignment = ["center", "left"]
# Define Entries of all columns before the Symbol-Column
# --- Entries need to be latex code
col_1 = []
# contains all lists of the columns before the "Symbol" Column
# --- Empty list, if there are no columns before the "Symbol" Column
start_columns_list = []
# Define Entries of the columns after the Value-Column
# --- Entries need to be latex code
col_4 = []
# contains all lists of columns after the FIX ENTRIES
# --- Empty list, if there are no columns after the "Value" column
end_columns_list = []