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Details for: "Helicopter control"

Name: Helicopter control (Key: COM22)
Path: ackrep_data/system_models/compleib_models/HE4 View on GitHub
Type: system_model
Short Description: 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
Created: 2022-10-10 15:53:25
Compatible Environment: default_conda_environment (Key: CDAMA)
Source Code [ / ] 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 = []

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