Automatic Control Knowledge Repository

You currently have javascript disabled. Some features will be unavailable. Please consider enabling javascript.

Details for: "controller design via full state feedback"

Name: controller design via full state feedback (Key: ZPPRG)
Path: ackrep_data/problem_solutions/full_state_feedback View on GitHub
Type: problem_solution
Short Description:
Created: 2020-12-30
Compatible Environment: default_conda_environment (Key: CDAMA)
Source Code [ / ]
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
problem solution for control problem: design a controller by using full state feedback.
    import method_full_state_feedback as ftf  # noqa
    import method_system_property as msp  # noqa
except ImportError:
    from method_packages.method_full_state_feedback import method_full_state_feedback as ftf
    from method_packages.method_system_property import method_system_property as msp

import symbtools as st
from scipy.integrate import odeint
import sympy as sp
import matplotlib.pyplot as plt
import os
from ackrep_core.system_model_management import save_plot_in_dir

class SolutionData:

def rhs_for_simulation(f, g, xx, controller_func):
    # calculate right hand side equation for simulation of the nonlinear system
    :param f: vector field
    :param g: input matrix
    :param xx: states of the system
    :param controller_func: input equation (trajectory)
    :return: rhs: equation that is solved

    # call the class 'SimulationModel' to build the
    # 'right hand side'equation for ode
    sim_mod = st.SimulationModel(f, g, xx)
    rhs_eq = sim_mod.create_simfunction(controller_function=controller_func)

    return rhs_eq

def solve(problem_spec):
    """solution of full state feedback
    :param problem_spec: ProblemSpecification object
    :return: solution_data: states and output values of the stabilized system, and controller gain
    sys_f_body = msp.System_Property()  # instance of the class System_Property
    sys_f_body.sys_state = problem_spec.xx  # state of the system
    sys_f_body.tau = problem_spec.u  # inputs of the system

    # original nonlinear system functions
    sys_f_body.n_state_func = problem_spec.rhs()

    # original output functions
    sys_f_body.n_out_func = problem_spec.output_func()
    sys_f_body.eqlbr = problem_spec.eqrt  # equilibrium point

    # linearize nonlinear system around the chosen equilibrium point
    tuple_system = (sys_f_body.aa,,, sys_f_body.dd)  # system tuple

    # calculate controller function
    # sfb for dataclass StateFeedbackResult
    sfb = ftf.state_feedback(
        tuple_system, problem_spec.poles_cl, problem_spec.xx, problem_spec.eqrt, problem_spec.yr, debug=False

    # simulation original nonlinear system with controller
    f = sys_f_body.n_state_func.subs(st.zip0(sys_f_body.tau))  # x_dot = f(x) + g(x) * u
    g = sys_f_body.n_state_func.jacobian(sys_f_body.tau)

    rhs = rhs_for_simulation(f, g, problem_spec.xx, sfb.input_func)
    res = odeint(rhs, problem_spec.xx0,

    output_function = sp.lambdify(problem_spec.xx, sys_f_body.n_out_func, modules="numpy")
    yy = output_function(*res.T)

    solution_data = SolutionData()
    solution_data.res = res  # states of system
    solution_data.pre_filter = sfb.pre_filter  # pre-filter
    solution_data.ff = sfb.state_feedback  # controller gain
    solution_data.input_fun = sfb.input_func  # controller function
    solution_data.yy = yy[0][0]  # system output

    save_plot(problem_spec, solution_data)

    return solution_data

def save_plot(problem_spec, solution_data):
    # plotting of the system states
    titles1 = problem_spec.titles_state
    for i in range(len(titles1)):
        plt.subplot(problem_spec.row_number, int(len(titles1) / problem_spec.row_number), i + 1)
        plt.plot(, solution_data.res[:, i], color=problem_spec.graph_color, linewidth=1)

    titles2 = problem_spec.titles_output
    for i in range(len(titles2)):
        plt.plot(, solution_data.yy)

    # save image

Solved Problems: equilibrium change of a nonlinear resistor   |   design of a full state feedback controller to control the x-position of the load to 1.5m   |   design of a full state feedback controller to control position of the both balls   |  
Used Methods: system proporty full_state_feedback_controller
Result: Success.
Last Build: Checkout CI Build
Runtime: 3.6 (estimated: 10s)

The image of the latest CI job is not available. This is a fallback image.