Module « scipy.signal »

Fonction lsim - module scipy.signal

Signature de la fonction lsim

def lsim(system, U, T, X0=None, interp=True) 

Description

lsim.__doc__

    Simulate output of a continuous-time linear system.

    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
        An input array describing the input at each time `T`
        (interpolation is assumed between given times).  If there are
        multiple inputs, then each column of the rank-2 array
        represents an input.  If U = 0 or None, a zero input is used.
    T : array_like
        The time steps at which the input is defined and at which the
        output is desired.  Must be nonnegative, increasing, and equally spaced.
    X0 : array_like, optional
        The initial conditions on the state vector (zero by default).
    interp : bool, optional
        Whether to use linear (True, the default) or zero-order-hold (False)
        interpolation for the input array.

    Returns
    -------
    T : 1D ndarray
        Time values for the output.
    yout : 1D ndarray
        System response.
    xout : ndarray
        Time evolution of the state vector.

    Notes
    -----
    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]``).

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

    >>> from scipy.signal import bessel, lsim
    >>> 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 `lsim`.

    >>> tout, yout, xout = lsim((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([[0.0, 1.0], [0.0, 0.0]])
    >>> B = np.array([[0.0], [1.0]])
    >>> C = np.array([[1.0, 0.0]])
    >>> D = 0.0
    >>> 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 = lsim(system, u, t)
    >>> plt.plot(t, y)
    >>> plt.grid(alpha=0.3)
    >>> plt.xlabel('t')
    >>> plt.show()