simulation.py
from cProfile import label
import numpy as np
import system_model
from scipy.integrate import solve_ivp
from ackrep_core import ResultContainer
from ackrep_core.system_model_management import save_plot_in_dir
import matplotlib.pyplot as plt
import os
# 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()
print("Computational Equations:\n")
for i, eq in enumerate(rhs_xx_pp_symb):
print(f"dot_x{i+1} =", eq)
rhs = model.get_rhs_func()
# ---------start of edit section--------------------------------------
# initial state values
xx0 = np.zeros(10)
t_end = 3
tt = np.linspace(0, t_end, 10000)
simulation_data = solve_ivp(rhs, (0, t_end), xx0, t_eval=tt)
# ---------end of edit section----------------------------------------
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
"""
# ---------start of edit section--------------------------------------
fig1, axs = plt.subplots(nrows=10, ncols=1, figsize=(12.8, 9))
# print in axes top left
axs[0].plot(simulation_data.t, simulation_data.y[0])
axs[0].set_ylabel("p1") # y-label
axs[0].grid()
axs[1].plot(simulation_data.t, simulation_data.y[1])
axs[1].set_ylabel("p2") # y-label
axs[1].grid()
axs[2].plot(simulation_data.t, simulation_data.y[2])
axs[2].set_ylabel("p3") # y-label
axs[2].grid()
axs[3].plot(simulation_data.t, simulation_data.y[3])
axs[3].set_ylabel("q1") # y-label
axs[3].grid()
axs[4].plot(simulation_data.t, simulation_data.y[4])
axs[4].set_ylabel("q2") # y-label
axs[4].grid()
axs[5].plot(simulation_data.t, simulation_data.y[5])
axs[5].set_ylabel(r"$dot{p}_1$") # y-label
axs[5].grid()
axs[6].plot(simulation_data.t, simulation_data.y[6])
axs[6].set_ylabel(r"$dot{p}_2$") # y-label
axs[6].grid()
axs[7].plot(simulation_data.t, simulation_data.y[7])
axs[7].set_ylabel(r"$dot{p}_3$") # y-label
axs[7].grid()
axs[8].plot(simulation_data.t, simulation_data.y[8])
axs[8].set_ylabel(r"$dot{q}_1$") # y-label
axs[8].grid()
axs[9].plot(simulation_data.t, simulation_data.y[9])
axs[9].set_ylabel(r"$dot{q}_2$") # y-label
axs[9].grid()
# ---------end of edit section----------------------------------------
plt.tight_layout()
# plt.show()
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:
"""
# ---------start of edit section--------------------------------------
# fill in final states of simulation to check your model
# simulation_data.y[i][-1]
expected_final_state = [0.0, -44.14499999999994, 0.0, 0.0, 0.0, 0.0, -29.429999999999964, 0.0, 0.0, 0.0]
# ---------end of edit section----------------------------------------
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
import sympy as sp
import symbtools as st
import importlib
import sys, os
import symbtools.modeltools as mt
# 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
"""
# ---------start of edit section--------------------------------------
# Define number of inputs -- MODEL DEPENDENT
self.u_dim = 4
# Set "sys_dim" to constant value, if system dimension is constant
self.sys_dim = 10
# ---------end of edit section----------------------------------------
# check existence of params file
self.has_params = True
self.params = params
# ----------- SET DEFAULT INPUT FUNCTION ---------- #
# --------------- Only for non-autonomous Systems
def uu_default_func(self):
"""
define input function
:return:(function with 2 args - t, xx_nv) default input function
"""
# ---------start of edit section--------------------------------------
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
"""
u1 = 0
u2 = 0
# if 1 < t < 1.5:
# u3 = 0.5
# else:
u3 = 0
# if 2 < t < 3:
# u4 = 1
# else:
u4 = 0
return [u1, u2, u3, u4]
# ---------end of edit section----------------------------------------
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
x1, x2, x3, x4, x5, x6, x7, x8, x9, x10 = self.xx_symb # state components
xdot1, xdot2, xdot3, xdot4, xdot5 = sp.symbols("xdot1, xdot2, xdot3, xdot4, xdot5")
xx = sp.Matrix([[x1], [x2], [x3], [x4], [x5]])
s2, m1, m2, m3, J2, l0, l1, l2, g = self.pp_symb # parameters
u1, u2, u3, u4 = self.uu_symb # inputs
# unit vectors
ex = sp.Matrix([1, 0])
ey = sp.Matrix([0, 1])
# basis 1 and 2 (cart positions)
S1 = G1 = B1 = sp.Matrix([x4, 0])
S3 = G6 = B2 = sp.Matrix([l0 + x5, 0])
# center of gravity of load
S2 = sp.Matrix([x1, x2])
# suspension points of load
G3 = S2 - mt.Rz(x3) * ex * s2
G4 = S2 + mt.Rz(x3) * ex * s2
# Time derivatives of centers of masses
Sd1, Sd2, Sd3 = st.col_split(st.time_deriv(st.col_stack(S1, S2, S3), xx))
# kinetic energy
T1 = (m1 / 2 * Sd1.T * Sd1)[0]
T2 = (m2 / 2 * Sd2.T * Sd2)[0] + J2 / 2 * (xdot3) ** 2
T3 = (m3 / 2 * Sd3.T * Sd3)[0]
T = T1 + T2 + T3
# potential energy
V = m2 * g * S2[1]
Q1, Q2, Q3, Q4, Q5 = sp.symbols("Q1, Q2, Q3, Q4, Q5")
QQ = sp.Matrix([[Q1], [Q2], [Q3], [Q4], [Q5]])
mod = mt.generate_symbolic_model(T, V, xx, QQ)
F1 = sp.Matrix([u1, 0])
F2 = sp.Matrix([u2, 0])
# unit vectors for ropes to split forces according to angles
rope1 = G3 - S1
rope2 = G4 - S3
uv_rope1 = rope1 / sp.sqrt((rope1.T * rope1)[0])
uv_rope2 = rope2 / sp.sqrt((rope2.T * rope2)[0])
# simplify expressions by using l1, l2 as shortcuts
uv_rope1 = rope1 / l1
uv_rope2 = rope2 / l2
F3 = uv_rope1 * u3
F4 = uv_rope2 * u4
ddelta_theta = st.symb_vector(f"\\delta\\theta_1:{6}")
delta_S1 = S1 * 0
delta_S3 = S3 * 0
delta_G3 = G3 * 0
delta_G4 = G4 * 0
for theta, delta_theta in zip(xx, ddelta_theta):
delta_S1 += S1.diff(theta) * delta_theta
delta_S3 += S3.diff(theta) * delta_theta
delta_G3 += G3.diff(theta) * delta_theta
delta_G4 += G4.diff(theta) * delta_theta
# simple part (carts)
delta_W = delta_S1.T * F1 + delta_S3.T * F2
# rope1 (F3 > 0 means rope is pushing from S1 towards G3)
delta_W = delta_W + delta_G3.T * F3 - delta_S1.T * F3
# rope2 (F4 > 0 means rope is pushing from S3 towards G4)
delta_W = delta_W + delta_G4.T * F4 - delta_S3.T * F4
QQ_expr = delta_W.jacobian(ddelta_theta).T
mod.eqns = mod.eqns.subs(
[(QQ[0], QQ_expr[0]), (QQ[1], QQ_expr[1]), (QQ[2], QQ_expr[2]), (QQ[3], QQ_expr[3]), (QQ[4], QQ_expr[4])]
)
mod.calc_state_eq(simplify=False)
self.dxx_dt_symb = mod.state_eq.subs([(xdot1, x6), (xdot2, x7), (xdot3, x8), (xdot4, x9), (xdot5, x10)])
return self.dxx_dt_symb
parameters.py
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 = "overhead crane"
# ---------- create symbolic parameters
pp_symb = [s2, m1, m2, m3, J2, l0, l1, l2, g] = sp.symbols("s2, m1, m2, m3, J2, l0, l1, l2, g", real=True)
# ---------- create symbolic parameter functions
# parameter values can be constant/fixed values OR set in relation to other parameters (for example: a = 2*b)
s2_sf = 0.15
m1_sf = 0.45
m2_sf = 0.557
m3_sf = 0.45
J2_sf = 0.000221
l0_sf = 0.5
l1_sf = 0.4
l2_sf = 0.3
g_sf = 9.81
# list of symbolic parameter functions
# tailing "_sf" stands for "symbolic parameter function"
pp_sf = [s2_sf, m1_sf, m2_sf, m3_sf, J2_sf, l0_sf, l1_sf, l2_sf, g_sf]
# ---------- 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 = ["Parameter Name", "Symbol", "Value", "Unit"]
# Define column text alignments
col_alignment = ["left", "center", "left", "center"]
# Define Entries of all columns before the Symbol-Column
# --- Entries need to be latex code
col_1 = [
"center of gravity distance of the load",
"mass of trolley 1",
"mass of load",
"mass of trolley 2",
"moment of inertia of the load",
"initial distance between the trolleys",
"length of rope 1",
"length of rope 2",
"acceleration due to gravity",
]
# contains all lists of the columns before the "Symbol" Column
# --- Empty list, if there are no columns before the "Symbol" Column
start_columns_list = [col_1]
# Define Entries of the columns after the Value-Column
# --- Entries need to be latex code
col_4 = ["m", "kg", "kg", "kg", r"$kg \cdot m^2$", "m", "m", "m", r"$\frac{m}{s^2}$"]
# contains all lists of columns after the FIX ENTRIES
# --- Empty list, if there are no columns after the "Value" column
end_columns_list = [col_4]