def rga_plot(G, axlim=None, w_start=-2, w_end=2, points=100):
'''
Plots the relative gain interaction between each output and input pairing
Parameters
----------
G : numpy array
plant model
Returns
-------
fig(RGA) : figure
A figure of subplots for each interaction between an output and
an input.
Example
-------
# Adapted from example 3.11 pg 86 S. Skogestad
>>> def G(s):
... G = 0.01*numpy.exp(-5*s)/((s + 1.72e-4)*(4.32*s + 1))*numpy.array([[-34.54*(s + 0.0572), 1.913], [-30.22*s, -9.188*(s + 6.95e-4)]])
... return G
>>> rga_plot(G, axlim=[None, None, 0., 1.], w_start=-5, w_end=2)
Note
----
This entry draws on and improves RGA.py.
If accepted, then RGA.py could be removed from the repository
'''
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)) # Number of rows and columns in SS transfer function
freqresp = map(G, s)
count = 0 # Arrange the individual RGA responses to be compatible with the plotting order of plt.subplot
rga = numpy.zeros([dim[0] * dim[1], points])
for i in range(dim[0]):
for k in range(dim[1]):
rga[count, :] = numpy.array(
numpy.abs(([utils.RGA(Gfr)[i, k] for Gfr in freqresp])))
count += 1
plt.figure('RGA')
plt.clf()
plt.gcf().set_facecolor('white')
plot_No = 1
for i in range(dim[0]):
for k in range(dim[1]):
plt.subplot(dim[0], dim[1], plot_No)
plt.semilogx(w, rga[plot_No - 1])
plot_No += 1
plt.ylabel('|$\lambda$$_{ %s, %s}$|' % (i + 1, k + 1))
plt.axis(axlim)
if i == dim[
0] - 1: # To avoid clutter only plot xlabel on the very bottom subplots
plt.xlabel('Frequency [rad/unit time]')
plt.title('Output %s vs. input %s' % (i + 1, k + 1))
plt.show()
return
def rga_nm_plot(G, pairing=None, axlim=None, w_start=-2, w_end=2, points=100):
'''
Plots the RGA number for a specified pairing
Parameters
----------
G : numpy array
plant model
pairing : sparse numpy array of the same shape as G
An array of zeros with a 1. at each required output-input pairing
The default is a diagonal pairing with 1.'s on the diagonal
Returns
-------
fig(RGA Number) : figure
A figure of the RGA number for a specified pairing over
a given frequency range
Example
-------
# Adapted from example 3.11 pg 86 S. Skogestad
>>> def G(s):
... G = 0.01*numpy.exp(-5*s)/((s + 1.72e-4)*(4.32*s + 1))*numpy.array([[-34.54*(s + 0.0572), 1.913], [-30.22*s, -9.188*(s + 6.95e-4)]])
... return G
>>> pairing = numpy.array([[1., 0.], [0., 1.]])
>>> rga_nm_plot(G, pairing, axlim=[None, None, 0., 1.], w_start=-5, w_end=2)
Note
----
This plotting function can only be used on square systems
'''
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)) # Number of rows and columns in SS transfer function
freqresp = map(G, s)
if pairing is None: # Setting a blank entry to the default of a diagonal comparison
diag = numpy.identity(dim[0])
print('RGA number being calculated for a diagonal pairing')
elif not all(pairing.shape == dim):
print(
'RGA_Number_Plot on plots square n by n matrices, make sure input matrix is square'
)
pass
else:
diag = pairing
plt.figure('RGA Number')
plt.clf()
plt.gcf().set_facecolor('white')
plt.semilogx(
w, [numpy.sum(numpy.abs(utils.RGA(Gfr) - diag)) for Gfr in freqresp])
plt.axis(axlim)
plt.ylabel('||$\Lambda$(G) - I||$_{sum}$', fontsize=15)
plt.xlabel('Frequency (rad/unit time)')
plt.show()
return
def rga_plot(G,
w_start=-2,
w_end=2,
axlim=None,
points=1000,
fig=0,
plot_type='elements',
input_label=None,
output_label=None):
"""
Plots the relative gain interaction between each output and input pairing
Parameters
----------
G : numpy matrix
Plant model.
plot_type : string
Type of plot.
========= ============================
plot_type Type of plot
========= ============================
all All the RGAs on one plot
output Plots grouped by output
input Plots grouped by input
element Each element has its own plot
========= ============================
Returns
-------
Plot : matplotlib figure
Example
-------
Adapted from example 3.11 pg 86 S. Skogestad
>>> def G(s):
... G = 0.01**(-5*s)/((s + 1.72e-4)*(4.32*s + 1))*numpy.matrix([[-34.54*(s + 0.0572), 1.913], [-30.22*s, -9.188*(s + 6.95e-4)]])
... return G
>>> rga_plot(G, w_start=-5, w_end=2, axlim=[None, None, 0., 1.])
"""
s, w, axlim = df.frequency_plot_setup(axlim, w_start, w_end, points)
dim = G(0).shape # Number of rows and columns in SS transfer function
freqresp = [G(si) for si in s]
plot_No = 1
if (input_label is None) and (output_label is None):
labels = False
elif numpy.shape(input_label)[0] == numpy.shape(output_label)[0]:
labels = True
else:
raise ValueError('Input and output label count is not equal')
if plot_type == 'elements':
fig = adjust_spine('Frequency [rad/unit time]', 'RGA magnitude', -0.05,
-0.03, 0.8, 0.9)
for i in range(dim[0]):
for j in range(dim[1]):
ax = fig.add_subplot(dim[0], dim[1], plot_No)
if labels:
ax.set_title('Output (%s) vs. Input (%s)' %
(output_label[i], input_label[j]))
else:
ax.set_title('Output %s vs. Input %s' % (i + 1, j + 1))
ax.semilogx(
w,
numpy.array(
numpy.abs(
([utils.RGA(Gfr)[i, j] for Gfr in freqresp]))))
plot_No += 1
ax.axis(axlim)
ax.set_ylabel('$|\lambda$$_{%s, %s}|$' % (i + 1, j + 1))
box = ax.get_position()
ax.set_position(
[box.x0, box.y0, box.width * 0.8, box.height * 0.9])
elif plot_type == 'outputs': # i
fig = adjust_spine('Frequency [rad/unit time]', 'RGA magnitude', -0.05,
-0.03, 1, 0.9)
for i in range(dim[0]):
ax = fig.add_subplot(dim[1], 1, plot_No)
ax.set_title('Output %s vs. input j' % (i + 1))
rgamax = []
for j in range(dim[1]):
rgas = numpy.array(
numpy.abs(([utils.RGA(Gfr)[i, j] for Gfr in freqresp])))
ax.semilogx(w,
rgas,
label='$\lambda$$_{%s, %s}$' % (i + 1, j + 1))
rgamax.append(max(rgas))
if j == dim[1] - 1: # self-scaling algorithm
if axlim is not None:
ax.axis(axlim)
else:
ax.axis([None, None, None, max(rgamax)])
ax.set_ylabel('$|\lambda$$_{%s, j}|$' % (i + 1))
box = ax.get_position()
ax.set_position([box.x0, box.y0, box.width, box.height * 0.9])
ax.legend()
plot_No += 1
elif plot_type == 'inputs': # j
fig = adjust_spine('Frequency [rad/unit time]', 'RGA magnitude', -0.05,
-0.03, 1, 0.9)
for j in range(dim[1]):
ax = fig.add_subplot(dim[0], 1, plot_No)
ax.set_title('Output i vs. input %s' % (j + 1))
rgamax = []
for i in range(dim[0]):
rgas = numpy.array(
numpy.abs(([utils.RGA(Gfr)[i, j] for Gfr in freqresp])))
ax.semilogx(w,
rgas,
label='$\lambda$$_{%s, %s}$' % (i + 1, j + 1))
rgamax.append(max(rgas))
if i == dim[1] - 1: # self-scaling algorithm
if axlim is not None:
ax.axis(axlim)
else:
ax.axis([None, None, None, max(rgamax)])
ax.set_ylabel('$|\lambda$$_{i, %s}|$' % (j + 1))
box = ax.get_position()
ax.set_position([box.x0, box.y0, box.width, box.height * 0.9])
ax.legend()
plot_No += 1
elif plot_type == 'all':
for i in range(dim[0]):
for j in range(dim[1]):
plt.semilogx(
w,
numpy.array(
numpy.abs([utils.RGA(Gfr)[i, j] for Gfr in freqresp])))
plt.axis(axlim)
plt.ylabel('|$\lambda$$_{i,j}$|')
plt.xlabel('Frequency [rad/unit time]')
else:
raise ValueError("Invalid plot_type parameter.")