"metadata": {},

"outputs": [],

"source": [

"import numpy as np\n",

"import scipy as sp\n",

"import matplotlib.pyplot as plt\n",

"import control as ct"

"w001rad = 1. # 1 rad/s\n",

"w010rad = 10. # 10 rad/s\n",

"w100rad = 100. # 100 rad/s\n",

"w001hz = 2*sp.pi*1. # 1 Hz\n",

"w010hz = 2*sp.pi*10. # 10 Hz\n",

"w100hz = 2*sp.pi*100. # 100 Hz\n",

"w001hz = 2*np.pi*1. # 1 Hz\n",

"w010hz = 2*np.pi*10. # 10 Hz\n",

"w100hz = 2*np.pi*100. # 100 Hz\n",

"# First order systems\n",

"pt1_w001rad = ct.tf([1.], [1./w001rad, 1.], name='pt1_w001rad')\n",

"display(pt1_w001rad)\n",

],

"source": [

"sampleTime = 0.001\n",

"display('Nyquist frequency: {:.0f} Hz, {:.0f} rad/sec'.format(1./sampleTime /2., 2*sp.pi*1./sampleTime /2.))"

"display('Nyquist frequency: {:.0f} Hz, {:.0f} rad/sec'.format(1./sampleTime /2., 2*np.pi*1./sampleTime /2.))"

]

},

{

plt.axis([0,25,0,5])

plt.xlabel('Time {\itt} [scaled]')

plt.xlabel('Time {\\itt} [scaled]')

plt.ylabel('Protein concentrations [scaled]')

plt.legend(('z1 (A)','z2 (B)'))# 'Orientation', 'horizontal')

plt.subplot(2,4,8)

plt.plot(t,ud[1])

plt.xlabel('Ttime t [sec]')

plt.ylabel('$\delta$ [rad]')

plt.xlabel('Time t [sec]')

plt.ylabel('$\\delta$ [rad]')

plt.tight_layout()

],

"source": [

"sampleTime = 10\n",

"display('Nyquist frequency: {:.4f} Hz, {:.4f} rad/sec'.format(1./sampleTime /2., 2*sp.pi*1./sampleTime /2.))"

"display('Nyquist frequency: {:.4f} Hz, {:.4f} rad/sec'.format(1./sampleTime /2., 2*np.pi*1./sampleTime /2.))"

]

},

{

importmatplotlib.pyplotasplt# Grab MATLAB plotting functions

fromcontrol.matlabimport*# MATLAB-like functions

integrator=tf([0,1], [1,0])# 1/s