Basic calculations - quangounet/open-control-theory GitHub Wiki
Before starting, make sure to load the required packages.
Type (or copy-paste) the following code into the ipython
command prompt
s = -3 + 4j # Define a complex number s
print s*s
print abs(s) # Print the norm of s
print angle(s) # Print the angle of s in radians
print angle(s) * 180/pi # Print the angle of s in degreesThe output should look like this
(-7-24j) 5.0 2.21429743559 126.869897646
Type (or copy-paste) the following code into the ipython
command prompt
D1 = poly1d([1, 2, 5]) # Define a polynomial D1 = s^2+2s+5
D2 = poly1d([1, 3, 20]) # Define a polynomial D2 = s^2+3s+20
D = D1*D2 # Define a polynomial D = (s^2+2s+5)(s^2+3s+20)
N = poly1d([1, 0.5]) # Define a polynomial N = s+0.5
print D.r # Print the roots of D
P = D*N.deriv() - N*D.deriv() # Compute P = DN'-ND'
print P.r # Print the roots of PThe output should look like this
[-1.5+4.21307489j -1.5-4.21307489j -1.0+2.j -1.0-2.j] [-1.29900707+3.10442853j -1.29900707-3.10442853j -2.32128078+0.j 0.91929492+0.j]
One can see that the polynomial P has four roots: -1.299 +- 3.104j, -2.321 +- 0.919.