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"""
    # Example of pre-measurement design

    ## Pressure transducer choice of parameters

    We require to choose a pressure transduced such that we could measure a signal up to 100 Hz with a dynamic
    error of up to 5%.

    The pressure transducers available in the lab is measured to have damping of $\zeta = 0.5$ and ringing frequency of 1200 Hz.
    """)
    return


@app.cell
def _():
    from pylab import figure, plot, subplots, title, xlabel, ylabel
    from scipy import signal
    import numpy as np

    return figure, np, plot, signal, subplots, title, xlabel, ylabel


@app.cell
def _(figure, np, plot, signal, title, xlabel, ylabel):
    # Define transfer function
    fd = 1200 # Hz
    fn = fd/(np.sqrt(1-0.5**2))
    wn = fn/(2*np.pi) # rad/s
    z=0.5     # damping
    k = 1 		# sensitivity


    sys = signal.lti(k*wn**2,[1,2*z*wn, wn**2])

    # step function output
    t,y = sys.step(N=1000)

    figure(figsize=(8,6))
    plot(t,y)
    title('Step response of a pressure transducer')
    xlabel('$t$ [sec]')
    ylabel('E [V]')
    return sys, wn


@app.cell
def _():
    # note that sampling is sufficient, if not we need to apply the D/A reconstruction
    # or interpolations, which will add more noise and uncertainty to the system identification
    return


@app.cell
def _(signal, subplots, sys, wn):
    # Create Bode plot
    w, mag, phase = signal.bode(sys)

    fig,ax = subplots(2,1,figsize=(8,10))
    ax[0].semilogx(w/wn, mag)    # Bode magnitude plot
    # ax[0].plot(w/wn,mag)
    ax[0].set_ylabel('Magnitude (dB)',fontsize=16)
    ax[1].semilogx(w/wn, phase)  # Bode phase plot
    # ax[1].plot(w/wn, phase)  # Bode phase plot
    ax[1].set_ylabel('Phase (deg)',fontsize=16)
    ax[1].set_xlabel('$\omega/\omega_n$',fontsize=16)
    # fig.savefig('bode_pressure_transducer.png',dpi=200)
    return


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