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Details for: "design of a full state feedback controller to control position of the both balls"

Name: design of a full state feedback controller to control position of the both balls (Key: SN5NK)
Path: ackrep_data/problem_specifications/full_state_feedback_two_mass_floating_bodies View on GitHub
Type: problem_specification
Short Description: to be done
Created: 2020-12-30
Source Code [ / ]
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
system description: a two-body floating system is considered. A magnetic force generated by a current
is applied to a iron ball, which is located directly under the magnet. A CuZn ball below is attached
to that iron ball by a spring with the spring constant kf.

problem specification for control problem: design of a full state feedback controller to control
position of the both balls.
import numpy as np
import sympy as sp
from ackrep_core import ResultContainer
from system_models.two_mass_floating_bodies_system.system_model import Model

j = 1j  # imaginary unit

class ProblemSpecification(object):
    # system symbols for setting up the equation of motion
    model = Model()
    x1, x2, x3, x4 = model.xx_symb
    xx = sp.Matrix(model.xx_symb)  # states of system
    u1 = model.uu_symb[0]  # input of system
    u = [u1]

    # equilibrium points for linearization of the nonlinear system
    eqrt = [(x1, 0.01), (x2, 0.049), (x3, 0), (x4, 0), (u1, 5)]
    xx0 = np.array([0.02, 0.05, 0, 0])  # initial condition
    tt = np.linspace(0, 10, 1000)  # vector for the time axis for simulating
    yr = 0  # reference output

    # desired poles of closed system
    poles_cl = [-60, -40, -1 + 16 * j, -1 - 16 * j]

    # plotting parameters
    titles_state = ["x1", "x2", "x1_dot", "x2_dot"]
    titles_output = ["y"]
    x_label = "time [s]"
    y_label_state = ["position [m]", "position [m]", "velocity [m/s]", "velocity [m/s]"]
    y_label_output = ["position [m]"]
    graph_color = "r"
    row_number = 2  # the number of images in each row

    def rhs(cls):
        """Right hand side of the equation of motion in nonlinear state space form
        :return:     nonlinear state space

        return sp.Matrix(cls.model.get_rhs_symbolic_num_params())

    def output_func(cls):
        """output equation of the system
        :return:     output equation y = x1
        x1, x2, x3, x4 = cls.xx
        u = cls.u

        return sp.Matrix([x1])

def evaluate_solution(solution_data):
    Condition: the both balls return to their original position at least after 4 seconds.
    :param solution_data: solution data of problem of solution
    P = ProblemSpecification
    success = all(abs(solution_data.res[800:, 0] - [P.eqrt[0][1]] * 200) < 1e-2) and all(
        abs(solution_data.res[800:, 1] - [P.eqrt[1][1]] * 200) < 1e-2

    return ResultContainer(success=success, score=1.0)

Available solutions:
controller design via full state feedback
Related System Models:
two mass floating bodies