def step_response_plot(Y,
U,
t_end=50,
initial_val=0,
timedim='sec',
axlim=None,
points=1000,
constraint=None,
method='numeric'):
'''
A plot of the step response of a transfer function
Parameters
----------
Y : tf
Output transfer function.
U : tf
Input transfer function.
t_end : integer
Time period which the step response should occur (optional).
initial_val : integer
Starting value to evalaute step response (optional).
constraint : float
The upper limit the step response cannot exceed. is only calculated
if a value is specified (optional).
method : ['numeric','analytic']
The method that is used to calculate a constrainted response. A
constraint value is required (optional).
Returns
-------
Plot : matplotlib figure
'''
if axlim is None:
axlim = [None, None, None, None]
plt.gcf().set_facecolor('white')
[t, y] = utils.tf_step(Y, t_end, initial_val)
plt.plot(t, y)
[t, y] = utils.tf_step(U, t_end, initial_val)
plt.plot(t, y)
if constraint is None:
plt.legend(['$y(t)$', '$u(t)$'])
else:
[t, y] = utils.tf_step(U, t_end, initial_val, points, constraint, Y,
method)
plt.plot(t, y[0])
plt.plot(t, y[1])
plt.legend(['$y(t)$', '$u(t)$', '$u(t) const$',
'$y(t) const$']) #con = constraint
plt.plot([0, t_end], numpy.ones(2), '--')
plt.axis(axlim)
plt.xlabel('Time [' + timedim + ']')
def step_response_plot(Y, U, t_end=50, initial_val=0, timedim='sec',
axlim=None, points=1000, constraint=None,
method='numeric'):
"""
A plot of the step response of a transfer function
Parameters
----------
Y : tf
Output transfer function.
U : tf
Input transfer function.
t_end : integer
Time period which the step response should occur (optional).
initial_val : integer
Starting value to evaluate step response (optional).
constraint : float
The upper limit the step response cannot exceed. is only calculated
if a value is specified (optional).
method : ['numeric','analytic']
The method that is used to calculate a constrained response. A
constraint value is required (optional).
Returns
-------
Plot : matplotlib figure
"""
axlim = df.frequency_plot_setup(axlim)
[t, y] = utils.tf_step(Y, t_end, initial_val)
plt.plot(t, y)
[t, y] = utils.tf_step(U, t_end, initial_val)
plt.plot(t, y)
if constraint is None:
plt.legend(['$y(t)$', '$u(t)$'])
else:
[t, y] = utils.tf_step(U, t_end, initial_val,
points, constraint, Y, method)
plt.plot(t, y[0])
plt.plot(t, y[1])
# con = constraint
plt.legend(['$y(t)$', '$u(t)$', '$u(t) const$', '$y(t) const$'])
plt.plot([0, t_end], numpy.ones(2), '--')
plt.axis(axlim)
plt.xlabel('Time [' + timedim + ']')
# First example in reference to demonstrate working of tf object # Define s as tf to enable its use as a variable s = tf([1, 0]) # Define the transfer functions F = tf(1, [1, 1]) G = tf(100, [1, 5, 100]) C = 20*(s**2 + s + 60) / s / (s**2 + 40*s + 400) S = tf(10, [1, 10]) T = F * feedback(G*C, S) # This is the same figure as in the reference tf_step(T, 6) # Assign names to lines as in second example F.u = 'r'; F.y = 'uF' C.u = 'e'; C.y = 'uC' G.u = 'u'; G.y = 'ym' S.u = 'ym'; S.y = 'y' # There must be a better way to call the name of an object if the object has # already been assigned a name.... F.name = 'F' C.name = 'C'
S = 1/(1+L)
mT = maxpeak(T)
mS = maxpeak(S)
GM, PM, wc, wb, wbt, valid = marginsclosedloop(L)
GM, PM, wc, w_180 = margins(L)
print('GM = ', np.round(GM, 1))
print('PM = ', np.round(PM, 1), 'rad')
print('wB = ', np.round(wb, 3))
print('wC = ', np.round(wc, 3))
print('wBT = ', wbt)
print('w180 = ', np.round(w_180, 3))
print('Ms = ', np.round(mS, 2))
print('Mt = ', np.round(mT, 1))
[t, y] = tf_step(T, 50)
plt.figure('Figure 2.17')
plt.plot(t, y)
plt.xlabel('time (s)')
plt.ylabel('y(t)')
plt.show()
w = np.logspace(-2, 2, 1000)
s = 1j*w
gain_T = np.abs(T(s))
gain_S = np.abs(S(s))
plt.figure('Figure 2.18')
plt.loglog(w, gain_T)
plt.loglog(w, gain_S)
yrange = np.logspace(-2, 2)
import matplotlib.pyplot as plt
import numpy as np
s = tf([1,0], 1)
G = 200/((10*s + 1)*(0.05*s + 1)**2)
Gd = 100/(10*s + 1)
wc = 10
K = wc*(10*s + 1)*(0.1*s + 1)/(200*s*(0.01*s + 1))
L = G*K
t = np.linspace(0, 3)
Sd = (1/(1 + G*K))*Gd
T = feedback(L, 1)
[t,y] = tf_step(T, 3)
plt.figure('Figure 2.22')
plt.subplot(1, 2, 1)
plt.plot(t, y)
plt.title('Tracking Response')
plt.ylabel('y(t)')
plt.xlabel('Time (s)')
plt.ylim([0, 1.5])
[t,yd] = Sd.step(0, t)
plt.subplot(1, 2, 2)
plt.plot(t, yd)
plt.ylabel('y(t)')
plt.xlabel('Time (s)')
plt.title('Disturbance Response')
plt.ylim([0, 1.5])
"""
# First example in reference to demonstrate working of tf object
# Define s as tf to enable its use as a variable
s = tf([1, 0])
# Define the transfer functions
F = tf(1, [1, 1])
G = tf(100, [1, 5, 100])
C = 20*(s**2 + s + 60) / s / (s**2 + 40*s + 400)
S = tf(10, [1, 10])
T = F * feedback(G*C, S)
# This is NOT the same figure as in the reference
t, y = tf_step(T, 6)
plt.plot(t, y)
plt.xlabel('Time')
plt.ylabel('y(t)')
plt.show()
#utilsplot.step(T, t_end = 6)
# Assign names to lines as in second example
F.u = 'r'; F.y = 'uF'
C.u = 'e'; C.y = 'uC'
G.u = 'u'; G.y = 'ym'
S.u = 'ym'; S.y = 'y'
# There must be a better way to call the name of an object if the object has
# already been assigned a name....
F.name = 'F'
"""
# First example in reference to demonstrate working of tf object
# Define s as tf to enable its use as a variable
s = tf([1, 0])
# Define the transfer functions
F = tf(1, [1, 1])
G = tf(100, [1, 5, 100])
C = 20 * (s**2 + s + 60) / s / (s**2 + 40 * s + 400)
S = tf(10, [1, 10])
T = F * feedback(G * C, S)
# This is NOT the same figure as in the reference
t, y = tf_step(T, 6)
plt.plot(t, y)
plt.xlabel('Time')
plt.ylabel('y(t)')
plt.show()
#utilsplot.step(T, t_end = 6)
# Assign names to lines as in second example
F.u = 'r'
F.y = 'uF'
C.u = 'e'
C.y = 'uC'
G.u = 'u'
G.y = 'ym'
S.u = 'ym'
S.y = 'y'
S = 1/(1 + L)
mT = maxpeak(T)
mS = maxpeak(S)
GM, PM, wc, wb, wbt, valid = marginsclosedloop(L)
GM, PM, wc, w_180 = margins(L)
print('GM = ', np.round(GM, 1))
print('PM = ', np.round(PM, 1), 'rad')
print('wB = ', np.round(wb, 3))
print('wC = ', np.round(wc, 3))
print('wBT = ', wbt)
print('w180 = ', np.round(w_180, 3))
print('Ms = ', np.round(mS, 2))
print('Mt = ', np.round(mT, 1))
[t, y] = tf_step(T, 50)
plt.figure('Figure 2.17')
plt.title('Step response for system T')
plt.plot(t, y)
plt.xlabel('time (s)')
plt.ylabel('y(t)')
# Calculate rise time tr
y90 = y[y<=0.9]
tr = t[len(y90)]
print('rise time = ',np.round(tr, 1) ,'s')
plt.axhline(0.9, color='black', linestyle='--',linewidth=0.5)
plt.axvline(tr, color='black', linestyle='--',linewidth=0.5)
plt.show()
w = np.logspace(-2, 2, 1000)
s = 1j*w
# First example in reference to demonstrate working of tf object # Define s as tf to enable its use as a variable s = tf([1, 0]) # Define the transfer functions F = tf(1, [1, 1]) G = tf(100, [1, 5, 100]) C = 20 * (s**2 + s + 60) / s / (s**2 + 40 * s + 400) S = tf(10, [1, 10]) T = F * feedback(G * C, S) # This is the same figure as in the reference tf_step(T, 6) # Assign names to lines as in second example F.u = 'r' F.y = 'uF' C.u = 'e' C.y = 'uC' G.u = 'u' G.y = 'ym' S.u = 'ym' S.y = 'y' # There must be a better way to call the name of an object if the object has # already been assigned a name.... F.name = 'F'
