```
#!/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
@classmethod
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())
@classmethod
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
:return:
"""
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)
```

controller design via full state feedback

two mass floating bodies