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Details for: "design of a full state feedback controller to control the x-position of the load to 1.5m"

Name: design of a full state feedback controller to control the x-position of the load to 1.5m (Key: LAQJB)
Path: ackrep_data/problem_specifications/full_state_feedback_cartpole_system 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 cartpole system is considered, which consists of a wagon with the mass M,
a rope with the constant length l, which is attached to the wagon, and a load,
which is located at the free end of the rope. The force that can be applied to the wagon
is available as a manipulated variable.

problem specification for control problem: design of a full state feedback controller to control
the x-position of the load to 1.5m.

import numpy as np
import sympy as sp
from sympy import cos, sin
from math import pi
from ackrep_core import ResultContainer
from system_models.cartpole_system.system_model import Model

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
    u = [model.uu_symb[0]]  # input of system

    # equilibrium point for linearization of the nonlinear system
    eqrt = [(x1, 0), (x2, 0), (x3, 0), (x4, 0), (u, 0)]
    xx0 = np.array([0.2, pi / 6, 1, 0.2])  # initial condition for simulation
    tt = np.linspace(0, 5, 1000)  # vector for the time axis for simulating
    poles_cl = [-3, -3, -3, -3]  # desired poles of closed loop
    yr = 1.5  # reference output

    # plotting parameters
    titles_state = ["x1", "x2", "x1_dot", "x2_dot"]
    titles_output = ["y"]
    x_label = "time [s]"
    y_label_state = ["position [m]", "angular position [rad]", "velocity [m/s]", "angular velocity [rad/s]"]
    y_label_output = ["x-position of pendulum 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: x-position of the load
        :return:     output equation y = x1
        x1, x2, x3, x4 = cls.xx
        u = cls.u
        l = cls.model.pp_str_dict["l"]  # geometry constant

        return sp.Matrix([x1 + l * sin(x2)])

def evaluate_solution(solution_data):
    Condition: the x-position of the load reaches 1.5m after at least 4 seconds
    :param solution_data: solution data of problem of solution
    P = ProblemSpecification
    success = all(abs(solution_data.yy[800:] - [P.yr] * 200) < 1e-2)
    return ResultContainer(success=success, score=1.0)

Available solutions:
controller design via full state feedback
Related System Models:
cartpole system