import marimo

__generated_with = "0.25.1"
app = marimo.App()


@app.cell
def _():
    import marimo as mo

    return (mo,)


@app.cell(hide_code=True)
def _(mo):
    mo.md(r"""
    # Step responses of dynamical systems
    """)
    return


@app.cell
def _():
    #!/usr/bin/env python
    from numpy import arange
    from matplotlib import pyplot as plt
    from scipy import signal
    import matplotlib as mpl
    mpl.rcParams['lines.linewidth'] = 2
    mpl.rcParams['lines.color'] = 'r'
    mpl.rcParams['figure.figsize'] = (10, 10)
    mpl.rcParams['font.size'] = 14
    mpl.rcParams['axes.labelsize'] = 20
    _tau = 5.0 * 60
    _h_times = arange(0.0, 10 * _tau, 0.1)
    _sys = signal.lti(1, [1, 1.0 / _tau])  # 5 minutes
    _step_response = _sys.step(T=_h_times)[1]
    plt.plot(_h_times, _step_response / _step_response[-1])
    plt.axhline(1.0, color='brown')
    plt.axhline(0.63, color='red')
    plt.axvline(_tau, color='red')
    # plt.title('Step response')
    # plt.show()
    plt.xlabel('$t$ (sec)')  # normalized
    return arange, plt, signal


@app.cell
def _(arange, plt, signal):
    _tau = 5.0  # 5 sec
    _h_times = arange(0.0, 5 * _tau, 0.01)
    omega_n = 1
    for zeta in [0.001, 0.3, 0.7, 1, 1.8]:  # rad/s
        _sys = signal.lti(1, [1, 2 * zeta / omega_n, 1.0 / omega_n ** 2])
        _step_response = _sys.step(T=_h_times)[1]
        plt.plot(_h_times, _step_response / _step_response[-2])  # zeta = 0.1  # damping
    plt.axhline(0.63, color='red')
    plt.axvline(_tau, color='red')
    plt.xlabel('$t$ (sec)')  # normalized
    plt.title('Step response')
    plt.ylim([0, 1.5])
    plt.show()
    return


if __name__ == "__main__":
    app.run()