Module « scipy.signal »

Fonction lsim2 - module scipy.signal

Signature de la fonction lsim2

def lsim2(system, U=None, T=None, X0=None, **kwargs) 

Description

lsim2.__doc__

    Simulate output of a continuous-time linear system, by using
    the ODE solver `scipy.integrate.odeint`.

    Parameters
    ----------
    system : an instance of the `lti` class or a tuple describing the system.
        The following gives the number of elements in the tuple and
        the interpretation:

        * 1: (instance of `lti`)
        * 2: (num, den)
        * 3: (zeros, poles, gain)
        * 4: (A, B, C, D)

    U : array_like (1D or 2D), optional
        An input array describing the input at each time T.  Linear
        interpolation is used between given times.  If there are
        multiple inputs, then each column of the rank-2 array
        represents an input.  If U is not given, the input is assumed
        to be zero.
    T : array_like (1D or 2D), optional
        The time steps at which the input is defined and at which the
        output is desired.  The default is 101 evenly spaced points on
        the interval [0,10.0].
    X0 : array_like (1D), optional
        The initial condition of the state vector.  If `X0` is not
        given, the initial conditions are assumed to be 0.
    kwargs : dict
        Additional keyword arguments are passed on to the function
        `odeint`.  See the notes below for more details.

    Returns
    -------
    T : 1D ndarray
        The time values for the output.
    yout : ndarray
        The response of the system.
    xout : ndarray
        The time-evolution of the state-vector.

    Notes
    -----
    This function uses `scipy.integrate.odeint` to solve the
    system's differential equations.  Additional keyword arguments
    given to `lsim2` are passed on to `odeint`.  See the documentation
    for `scipy.integrate.odeint` for the full list of arguments.

    If (num, den) is passed in for ``system``, coefficients for both the
    numerator and denominator should be specified in descending exponent
    order (e.g. ``s^2 + 3s + 5`` would be represented as ``[1, 3, 5]``).

    See Also
    --------
    lsim

    Examples
    --------
    We'll use `lsim2` to simulate an analog Bessel filter applied to
    a signal.

    >>> from scipy.signal import bessel, lsim2
    >>> import matplotlib.pyplot as plt

    Create a low-pass Bessel filter with a cutoff of 12 Hz.

    >>> b, a = bessel(N=5, Wn=2*np.pi*12, btype='lowpass', analog=True)

    Generate data to which the filter is applied.

    >>> t = np.linspace(0, 1.25, 500, endpoint=False)

    The input signal is the sum of three sinusoidal curves, with
    frequencies 4 Hz, 40 Hz, and 80 Hz.  The filter should mostly
    eliminate the 40 Hz and 80 Hz components, leaving just the 4 Hz signal.

    >>> u = (np.cos(2*np.pi*4*t) + 0.6*np.sin(2*np.pi*40*t) +
    ...      0.5*np.cos(2*np.pi*80*t))

    Simulate the filter with `lsim2`.

    >>> tout, yout, xout = lsim2((b, a), U=u, T=t)

    Plot the result.

    >>> plt.plot(t, u, 'r', alpha=0.5, linewidth=1, label='input')
    >>> plt.plot(tout, yout, 'k', linewidth=1.5, label='output')
    >>> plt.legend(loc='best', shadow=True, framealpha=1)
    >>> plt.grid(alpha=0.3)
    >>> plt.xlabel('t')
    >>> plt.show()

    In a second example, we simulate a double integrator ``y'' = u``, with
    a constant input ``u = 1``.  We'll use the state space representation
    of the integrator.

    >>> from scipy.signal import lti
    >>> A = np.array([[0, 1], [0, 0]])
    >>> B = np.array([[0], [1]])
    >>> C = np.array([[1, 0]])
    >>> D = 0
    >>> system = lti(A, B, C, D)

    `t` and `u` define the time and input signal for the system to
    be simulated.

    >>> t = np.linspace(0, 5, num=50)
    >>> u = np.ones_like(t)

    Compute the simulation, and then plot `y`.  As expected, the plot shows
    the curve ``y = 0.5*t**2``.

    >>> tout, y, x = lsim2(system, u, t)
    >>> plt.plot(t, y)
    >>> plt.grid(alpha=0.3)
    >>> plt.xlabel('t')
    >>> plt.show()