Automatic Control Knowledge Repository

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:
#


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("The input function only consists of the positive half wave of a sinus function. Otherwise it is zero.\n")

    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 = [0, 0, 0, 0]

    t_end = 30
    tt = np.linspace(0, t_end, 10000)
    simulation_data = solve_ivp(rhs, (0, t_end), xx0, t_eval=tt)

    u = []
    for i in range(len(simulation_data.t)):
        u.append(model.uu_func(simulation_data.t[i], xx0)[0])
    simulation_data.uu = u

    # ---------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=2, ncols=1, figsize=(12.8, 9))

    # print in axes top left
    axs[0].plot(
        simulation_data.t, simulation_data.y[0] + 1.8 * np.sin(simulation_data.y[1]), label="x position of the last"
    )
    axs[0].plot(simulation_data.t, simulation_data.y[0], label="x postion of the cart")
    axs[0].set_ylabel("x [m]")  # y-label
    axs[0].grid()
    axs[0].legend()

    axs[1].plot(simulation_data.t, simulation_data.uu)
    axs[1].set_ylabel("u [N]")  # y-label
    axs[1].set_xlabel("Time [s]")  # x-label
    axs[1].grid()

    # ---------end of edit section----------------------------------------

    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:
    """
    # ---------start of edit section--------------------------------------
    # fill in final states of simulation to check your model
    # simulation_data.y[i][-1]
    expected_final_state = [19.113936156609768, -0.0023747095479253674, 0.04470903934877705, -0.21878088945846508]

    # ---------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

import sympy as sp
import symbtools as st
import importlib
import sys, os
import numpy as np

# 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:
#


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 = 1

        # Set "sys_dim" to constant value, if system dimension is constant
        self.sys_dim = 4

        # ---------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
        """
        T = 5
        f1 = 2 * sp.sin(2 * sp.pi * self.t_symb / T)
        u_symb_func = st.piece_wise(
            (0, self.t_symb < 0),
            (f1, self.t_symb < T),
            (0, self.t_symb < 2 * T),
            (f1, self.t_symb < 3 * T),
            (0, self.t_symb < 4 * T),
            (f1, self.t_symb < 5 * T),
            (0, self.t_symb < 6 * T),
            (0, True),
        )
        u_num_func = st.expr_to_func(self.t_symb, u_symb_func)

        # ---------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
            """
            u = u_num_func(t)

            return [u]

        # ---------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

        # ---------start of edit section--------------------------------------
        x1, x2, x3, x4 = self.xx_symb  # state components
        m, M, l, g = self.pp_symb  # parameters

        u1 = self.uu_symb[0]  # inputs

        # define symbolic rhs functions
        dx1_dt = x3
        dx2_dt = x4
        dx3_dt = (u1 + (g * m * sp.sin(2 * x2)) / 2 + l * m * x4**2 * sp.sin(x2)) / (M + m * (sp.sin(x2) ** 2))
        dx4_dt = -(g * (M + m) * sp.sin(x2) + (u1 + l * m * x4**2 * sp.sin(x2)) * sp.cos(x2)) / (
            l * (M + m * (sp.sin(x2) ** 2))
        )

        # rhs functions matrix
        self.dxx_dt_symb = sp.Matrix([dx1_dt, dx2_dt, dx3_dt, dx4_dt])
        # ---------end of edit section----------------------------------------

        return self.dxx_dt_symb

import sys
import os
import numpy as np
import sympy as sp

import tabulate as tab


# link to documentation with examples:
#


# set model name
model_name = "Overhead Crane"


# ---------- create symbolic parameters
pp_symb = [m, M, l, g] = sp.symbols("m, M, l, 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)
m_sf = 0.25
M_sf = 1
l_sf = 1
g_sf = 9.81

# list of symbolic parameter functions
# tailing "_sf" stands for "symbolic parameter function"
pp_sf = [m_sf, M_sf, l_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 = ["mass of the load", "mass of the cart", "rope length", "acceleration due to gravitation"]

# 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 = ["kg", "kg", "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]