HE4 Helicopter control "Multivariable feedback control Analysis and design" S. Skogestad and I. Postlethwaite John Wiley and Sons, 1996, Section 12.2 Note Matlab files http//www.nt.ntnu.no/users/skoge/book/matlab.html stored in /export/home/leibfr/Lipinski/matlab/.. ..Examples_Multi_Feedback_Control/matlab_m/ F. Leibfritz, 16.09.2003 Data matrices unscaled in Sec12_2.m in directory above cf. page 472
simulation.py
# This file was autogenerated from the template: simulation.py.template (2022-10-10 15:53:25).
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 = 6
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([8.41628036e-01, 8.77468311e+00, 1.07217950e+00, 5.39520771e+00,
4.00094822e-01, 4.52932857e+02, 2.67378024e+02, 4.13042948e+01])
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 15:53:25).
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 = 4
# Set "sys_dim" to constant value, if system dimension is constant
self.sys_dim = 8
# 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(8) # 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 15:53:25).
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 = 'Helicopter control'
# ---------- create symbolic parameters
A = sp.MatrixSymbol('A', 8, 8)
B = sp.MatrixSymbol('B', 8, 4)
B1 = sp.MatrixSymbol('B1', 8, 8)
C1 = sp.MatrixSymbol('C1', 12, 8)
C = sp.MatrixSymbol('C', 6, 8)
D11 = sp.MatrixSymbol('D11', 12, 8)
D12 = sp.MatrixSymbol('D12', 12, 4)
D21 = sp.MatrixSymbol('D21', 6, 8)
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([[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
9.98573780e-01, 5.33842742e-02, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, 1.00000000e+00,
-3.18221934e-03, 5.95246553e-02, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, -1.15704956e+01,
-2.54463768e+00, -6.36026263e-02, 1.06780529e-01,
-9.49186683e-02, 7.10757449e-03],
[ 0.00000000e+00, 0.00000000e+00, 4.39356565e-01,
-1.99818230e+00, 0.00000000e+00, 1.66518837e-02,
1.84620470e-02, -1.18747074e-03],
[ 0.00000000e+00, 0.00000000e+00, -2.04089546e+00,
-4.58999157e-01, -7.35027790e-01, 1.92557573e-02,
-4.59562242e-03, 2.12036073e-03],
[-3.21036072e+01, 0.00000000e+00, -5.03355026e-01,
2.29785919e+00, 0.00000000e+00, -2.12158114e-02,
-2.11679190e-02, 1.58115923e-02],
[ 1.02161169e-01, 3.20578308e+01, -2.34721756e+00,
-5.03611565e-01, 8.34947586e-01, 2.12265700e-02,
-3.78797352e-02, 3.54003860e-04],
[-1.91097260e+00, 1.71382904e+00, -4.00543213e-03,
-5.74111938e-02, 0.00000000e+00, 1.39896348e-02,
-9.06753354e-04, -2.90513515e-01]]))
B_nv = sp.Matrix(np.array([[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[ 1.24335051e-01, 8.27858448e-02, -2.75247765e+00,
-1.78887695e-02],
[-3.63589227e-02, 4.75095272e-01, 1.42907426e-02,
0.00000000e+00],
[ 3.04491520e-01, 1.49580166e-02, -4.96518373e-01,
-2.06741929e-01],
[ 2.87735462e-01, -5.44506073e-01, -1.63793564e-02,
0.00000000e+00],
[-1.90734863e-02, 1.63674355e-02, -5.44536114e-01,
2.34842300e-01],
[-4.82063293e+00, -3.81469727e-04, 0.00000000e+00,
0.00000000e+00]]))
B1_nv = sp.Matrix(np.array([[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[ 1.24335051e-01, 8.27858448e-02, -2.75247765e+00,
-1.78887695e-02],
[-3.63589227e-02, 4.75095272e-01, 1.42907426e-02,
0.00000000e+00],
[ 3.04491520e-01, 1.49580166e-02, -4.96518373e-01,
-2.06741929e-01],
[ 2.87735462e-01, -5.44506073e-01, -1.63793564e-02,
0.00000000e+00],
[-1.90734863e-02, 1.63674355e-02, -5.44536114e-01,
2.34842300e-01],
[-4.82063293e+00, -3.81469727e-04, 0.00000000e+00,
0.00000000e+00]]))
C1_nv = sp.Matrix(np.array([[1., 0., 0., 0., 0., 0., 0., 0.],
[0., 1., 0., 0., 0., 0., 0., 0.],
[0., 0., 1., 0., 0., 0., 0., 0.],
[0., 0., 0., 1., 0., 0., 0., 0.],
[0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., 0., 0., 0., 1., 0.],
[0., 0., 0., 0., 0., 0., 0., 1.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.]]))
C_nv = sp.Matrix(np.array([[ 0. , 0. , 0. , 0. , 0. , 0.0595 ,
0.05329, -0.9968 ],
[ 1. , 0. , 0. , 0. , 0. , 0. ,
0. , 0. ],
[ 0. , 1. , 0. , 0. , 0. , 0. ,
0. , 0. ],
[ 0. , 0. , 0. , -0.05348, 1. , 0. ,
0. , 0. ],
[ 0. , 0. , 1. , 0. , 0. , 0. ,
0. , 0. ],
[ 0. , 0. , 0. , 1. , 0. , 0. ,
0. , 0. ]]))
D11_nv = sp.Matrix(np.array([[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 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., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
[1., 0., 0., 0.],
[0., 1., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.]]))
D21_nv = sp.Matrix(np.array([[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 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 = []