1 #!/usr/bin/env python

     2 

     3 # function [phi,psi] = ch_pol(N,epsilon)

     4 # Returns desired characteristic polynomial and numerator

     5 # N = rise time in number of sample times

     6 # epsilon = overshoot as a fraction of ss gain

     7 

     8 import pylab as pl

     9 

    10 def ch_pol(N,epsilon):

    11     omega = pl.pi/2/N

    12     r = epsilon**(omega/pl.pi)

    13     phi = pl.array([1, -2*r*pl.cos(omega), r**2])

    14     psi = pl.array([1-r*pl.cos(omega), r**2-r*pl.cos(omega)])

    15     return phi, psi