コード例 #1
0
ファイル: Project.py プロジェクト: pdawsonsa/CBT700Project
def distRej():
    w = np.logspace(-3,0,1000)
    S1 = np.zeros((len(w)))
    S2 = np.zeros((len(w)))
    Gd1 = np.zeros((len(w)))
    distCondNum = np.zeros((len(w)))
    condNum = np.zeros((len(w)))
    for i in range(len(w)):
        U, Sv, V = utils.SVD(S(w[i]*1j))
        S1[i] = Sv[0]                      #S = 1/|L + 1| 
        S2[i] = Sv[2]
        Gd1[i], distCondNum[i] = utils.distRej(G(w[i]*1j), Gd(w[i]*1j))
        condNum[i] = utils.sigmas(G(w[i]*1j),)[0]*utils.sigmas(la.inv(G(w[i]*1j)))[0]
    plt.figure(5)
    plt.clf()
    plt.subplot(211)
    plt.loglog(w, S1, 'r-', label = 'max $\sigma$S')
    plt.loglog(w, S2, 'r-', alpha = 0.4, label = 'min $\sigma$S')
    plt.loglog(w, Gd1, 'k-', label = '1/||Gd||$_2$')
    plt.axvline(wB, color='green')
    plt.ylabel('Magnitude')
    plt.xlabel('Frequency [rad/s)]')
    plt.text(wB*1.1, 0.015, 'wB = %s rad/s'%(np.round(wB,3)), color='green')
    plt.axis([None, None, None, 10])
    plt.grid(True)
    plt.legend(loc='upper left', fontsize = 12, ncol=5)
    fig = plt.gcf()
    BG = fig.patch
    BG.set_facecolor('white')
    plt.subplot(212)
    plt.semilogx(w, distCondNum, 'r-', label = 'Dist CondNum')
    plt.semilogx(w, condNum, 'k-', label = 'CondNum')
    plt.axvline(wB, color='green')
    plt.ylabel('Disturbance condtion number')
    plt.xlabel('Frequency [rad/s)]')
    plt.text(wB*1.1, 0.2, 'wB = %s rad/s'%(np.round(wB,3)), color='green')
    plt.axis([None, None, 0, None])
    plt.legend(loc='upper left', fontsize = 12, ncol=5)
    plt.grid(True)
    fig = plt.gcf()
    BG = fig.patch
    BG.set_facecolor('white')
    fig.subplots_adjust(bottom=0.2) 
    fig.subplots_adjust(top=0.9) 
    fig.subplots_adjust(left=0.2) 
    fig.subplots_adjust(right=0.9)
コード例 #2
0
ファイル: utilsplot.py プロジェクト: wakum/Skogestad-Python
def dis_rejctn_plot(G, Gd, S, axlim=None, w_start=-2, w_end=2, points=100):
    '''
    A subplot of disturbance conditition number to check for input saturation
    and a subplot of  to see if the disturbances fall withing the bounds on
    the singular values of S.
    Parameters
    ----------
    G : numpy array
        plant model
    
    Gd : numpy array
        plant disturbance model

    S : numpy array
        Sensitivity function
              
              
    Returns
    -------
    fig(Condition number and performance objective) : figure
        A figure of the disturbance condition number and the bounds imposed
        by the singular values.
    
    Note
    ----
    The disturbance condition number provides a measure of how a disturbance gd
    is aligned with the plant G. Alignment can vary between 1 and the condition
    number.
    
    For acceptable performance the singular values of S must fall below the
    inverse 2-norm of gd.
    '''

    if axlim is None:
        axlim = [None, None, None, None]

    w = numpy.logspace(w_start, w_end, points)
    s = w * 1j

    dim = numpy.shape(G(0))
    inv_norm_gd = numpy.zeros((dim[1], points))
    condtn_nm_gd = numpy.zeros((dim[1], points))
    for i in range(dim[1]):
        for k in range(points):
            inv_norm_gd[i, k], condtn_nm_gd[i, k] = utils.distRej(
                G(s[k]),
                Gd(s[k])[:, i])

    s_min = [utils.sigmas(S(s[i]))[-1] for i in range(points)]
    s_max = [utils.sigmas(S(s[i]))[0] for i in range(points)]

    plt.figure('Condition number and performance objective')
    plt.clf()
    plt.gcf().set_facecolor('white')

    plt.subplot(2, 1, 1)
    for i in range(dim[1]):
        plt.loglog(w,
                   condtn_nm_gd[i],
                   label=('$\gamma$$_{d%s}$(G)' % (i + 1)),
                   color='blue',
                   alpha=((i + 1.) / dim[1]))
    plt.axhline(1., color='red', ls=':')
    plt.axis(axlim)
    plt.ylabel('$\gamma$$_d$(G)')
    plt.axhline(1., color='red', ls=':')
    plt.legend()

    plt.subplot(2, 1, 2)
    for i in range(dim[1]):
        plt.loglog(w,
                   inv_norm_gd[i],
                   label=('1/||g$_{d%s}$||$_2$' % (i + 1)),
                   color='blue',
                   alpha=((i + 1.) / dim[1]))
    plt.loglog(w, s_min, label=('$\sigma$$_{MIN}$'), color='green')
    plt.loglog(w, s_max, label=('$\sigma$$_{MAX}$'), color='green', alpha=0.5)
    plt.xlabel('Frequency (rad/unit time)')
    plt.ylabel('1/||g$_d$||$_2$')
    plt.axhline(1., color='red', ls=':')
    plt.legend()

    plt.show()
    return
コード例 #3
0
def dis_rejctn_plot(G,
                    Gd,
                    S=None,
                    w_start=-2,
                    w_end=2,
                    axlim=None,
                    points=1000):
    """
    A subplot of disturbance condition number to check for input saturation
    (equation 6.43, p238). Two more subplots indicate if the disturbances fall
    withing the bounds of S, applying equations 6.45 and 6.46 (p239).

    Parameters
    ----------
    G : numpy matrix
        Plant model.
    Gd : numpy matrix
        Plant disturbance model.
    S : numpy matrix
        Sensitivity function (optional, if available).
    # TODO test S condition
    Returns
    -------
    Plot : matplotlib figure

    Note
    ----
    The disturbance condition number provides a measure of how a disturbance gd
    is aligned with the plant G. Alignment can vary between 1 and the condition
    number.

    For acceptable performance the singular values of S must fall below the
    inverse 2-norm of gd.
    """

    s, w, axlim = df.frequency_plot_setup(axlim, w_start, w_end, points)

    dim = numpy.shape(Gd(0))[1]  # column count
    inv_norm_gd = numpy.zeros((dim, points))
    # row count
    yd = numpy.zeros((dim, points, numpy.shape(Gd(0))[0]), dtype=complex)
    condtn_nm_gd = numpy.zeros((dim, points))
    for i in range(dim):
        for k in range(points):
            inv_norm_gd[i, k], yd[i, k, :], condtn_nm_gd[i, k] = utils.distRej(
                G(s[k]),
                Gd(s[k])[:, i])

    if S is None:
        sub = 2
    else:
        sub = 3

    # Equation 6.43
    plt.subplot(sub, 1, 1)
    for i in range(dim):
        plt.loglog(w, condtn_nm_gd[i], label=('$\gamma_{d%s} (G)$' % (i + 1)))
    plt.axhline(1., color='red', ls=':')
    plt.axis(axlim)
    plt.xlabel('Frequency [rad/unit time]')
    plt.ylabel('$\gamma$$_d (G)$')
    plt.axhline(1., color='red', ls=':')
    plt.legend()

    # Equation 6.44
    plt.subplot(sub, 1, 2)
    for i in range(dim):
        plt.loglog(w, inv_norm_gd[i], label=('$1/||g_{d%s}||_2$' % (i + 1)))
        if S is not None:
            S_yd = numpy.array([
                numpy.linalg.norm(S(p) * yd[i, p, :].T, 2)
                for p in range(points)
            ])
            plt.loglog(w, S_yd, label='$||Sy_d||_2$')
    plt.axis(axlim)
    plt.xlabel('Frequency [rad/unit time]')
    plt.legend()

    if S is not None:  # subplot should not be repeated with S is not available
        # Equation 6.45
        plt.subplot(3, 1, 3)
        for i in range(dim):
            plt.loglog(w,
                       inv_norm_gd[i],
                       label=('$1/||g_{d%s}||_2$' % (i + 1)))
            s_min = numpy.array(
                [utils.sigmas(S(s[p]), 'min') for p in range(points)])
            s_max = numpy.array(
                [utils.sigmas(S(s[p]), 'max') for p in range(points)])
            plt.loglog(w, s_min, label='$\sigma_{min}$')
            plt.loglog(w, s_max, label='$\sigma_{max}$')
        plt.axis(axlim)
        plt.xlabel('Frequency [rad/unit time]')
        plt.legend()
コード例 #4
0
ファイル: utilsplot.py プロジェクト: Mvuyiso/Skogestad-Python
def dis_rejctn_plot(G, Gd, S=None, w_start=-2, w_end=2, axlim=None, points=1000):
    """
    A subplot of disturbance condition number to check for input saturation
    (equation 6.43, p238). Two more subplots indicate if the disturbances fall
    withing the bounds of S, applying equations 6.45 and 6.46 (p239).

    Parameters
    ----------
    G : numpy matrix
        Plant model.
    Gd : numpy matrix
        Plant disturbance model.
    S : numpy matrix
        Sensitivity function (optional, if available).
    # TODO test S condition
    Returns
    -------
    Plot : matplotlib figure

    Note
    ----
    The disturbance condition number provides a measure of how a disturbance gd
    is aligned with the plant G. Alignment can vary between 1 and the condition
    number.

    For acceptable performance the singular values of S must fall below the
    inverse 2-norm of gd.
    """

    s, w, axlim = df.frequency_plot_setup(axlim, w_start, w_end, points)

    dim = numpy.shape(Gd(0))[1]  # column count
    inv_norm_gd = numpy.zeros((dim, points))
    yd = numpy.zeros((dim, points, numpy.shape(Gd(0))[0]), dtype=complex)  # row count
    condtn_nm_gd = numpy.zeros((dim, points))
    for i in range(dim):
        for k in range(points):
            inv_norm_gd[i, k], yd[i, k, :], condtn_nm_gd[i, k] = utils.distRej(G(s[k]), Gd(s[k])[:, i])

    if S is None:
        sub = 2
    else:
        sub = 3

    # Equation 6.43
    plt.subplot(sub, 1, 1)
    for i in range(dim):
        plt.loglog(w, condtn_nm_gd[i], label=('$\gamma_{d%s} (G)$' % (i+1)))
    plt.axhline(1., color='red', ls=':')
    plt.axis(axlim)
    plt.xlabel('Frequency [rad/unit time]')
    plt.ylabel('$\gamma$$_d (G)$')
    plt.axhline(1., color='red', ls=':')
    plt.legend()

    # Equation 6.44
    plt.subplot(sub, 1, 2)
    for i in range(dim):
        plt.loglog(w, inv_norm_gd[i], label=('$1/||g_{d%s}||_2$' % (i+1)))
        if not S is None:
            S_yd = numpy.array([numpy.linalg.norm(S(p) * yd[i, p, :].T, 2) for p in range(points)])
            plt.loglog(w, S_yd, label='$||Sy_d||_2$')
    plt.axis(axlim)
    plt.xlabel('Frequency [rad/unit time]')
    plt.legend()

    if S is not None:  # this subplot should not be repeated with S is not available
        # Equation 6.45
        plt.subplot(3, 1, 3)
        for i in range(dim):
            plt.loglog(w, inv_norm_gd[i], label=('$1/||g_{d%s}||_2$' % (i+1)))
            s_min = numpy.array([utils.sigmas(S(s[p]), 'min') for p in range(points)])
            s_max = numpy.array([utils.sigmas(S(s[p]), 'max') for p in range(points)])
            plt.loglog(w, s_min, label='$\sigma_{min}$')
            plt.loglog(w, s_max, label='$\sigma_{max}$')
        plt.axis(axlim)
        plt.xlabel('Frequency [rad/unit time]')
        plt.legend()
コード例 #5
0
def dis_rejctn_plot(G, Gd, S, axlim=[None, None, None, None], w_start=-2, w_end=2, points=100):
    '''
    A subplot of disturbance conditition number to check for input saturation
    and a subplot of  to see if the disturbances fall withing the bounds on
    the singular values of S.
    Parameters
    ----------
    G : numpy array
        plant model
    
    Gd : numpy array
        plant disturbance model

    S : numpy array
        Sensitivity function
              
              
    Returns
    -------
    fig(Condition number and performance objective) : figure
        A figure of the disturbance condition number and the bounds imposed
        by the singular values.
    
    Note
    ----
    The disturbance condition number provides a measure of how a disturbance gd
    is aligned with the plant G. Alignment can vary between 1 and the condition
    number.
    
    For acceptable performance the singular values of S must fall below the
    inverse 2-norm of gd.
    '''
    w = numpy.logspace(w_start, w_end, points)
    s = w*1j
    
    dim = numpy.shape(G(0))    
    inv_norm_gd = numpy.zeros((dim[1],points))
    condtn_nm_gd = numpy.zeros((dim[1],points))
    for i in range(dim[1]):
        for k in range(points):
            inv_norm_gd[i,k], condtn_nm_gd[i,k] = utils.distRej(G(s[k]), Gd(s[k])[:,i])
                      
    s_min = [utils.sigmas(S(s[i]))[-1] for i in range(points)]
    s_max = [utils.sigmas(S(s[i]))[0] for i in range(points)]
    
    plt.figure('Condition number and performance objective')
    plt.clf()
    plt.gcf().set_facecolor('white')
    
    plt.subplot(2,1,1)
    for i in range(dim[1]):
        plt.loglog(w, condtn_nm_gd[i], label=('$\gamma$$_{d%s}$(G)' % (i+1)), color='blue', alpha=((i+1.)/dim[1]))
    plt.axhline(1., color='red', ls=':')  
    plt.axis(axlim)
    plt.ylabel('$\gamma$$_d$(G)')
    plt.axhline(1., color='red', ls=':')
    plt.legend()
    
    plt.subplot(2,1,2)
    for i in range(dim[1]):
        plt.loglog(w, inv_norm_gd[i], label=('1/||g$_{d%s}$||$_2$' % (i+1)), color='blue', alpha=((i+1.)/dim[1]))   
    plt.loglog(w, s_min, label=('$\sigma$$_{MIN}$'), color='green')
    plt.loglog(w, s_max, label=('$\sigma$$_{MAX}$'), color='green', alpha = 0.5)  
    plt.xlabel('Frequency (rad/unit time)')
    plt.ylabel('1/||g$_d$||$_2$')
    plt.axhline(1., color='red', ls=':')
    plt.legend()    
    
    plt.show()
    return