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#!/usr/bin/python
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# 10.9
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import os, sys
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sys.path += [os.getcwdu() + os.sep + ".." + os.sep + "python"]
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import scipy as sp
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from imcsplit import imcsplit
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from polyfuncs import poladd
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from zpowk import zpowk
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def imc_stable(B, A, k, alpha):
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""" Designs Discrete Internal Model Controller
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for transfer function z^{-k}B(z^{-1})/A(z^{-1})
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Numerator and Denominator of IMC HQ are outputs
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Controller is also given in R,S form. """
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Kp, d, Bg, Bnmp, Bm = imcsplit(B, 1)
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Bg = Kp * Bg
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Bnmpr = Bnmp[::-1]
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Bms = sum(Bm)
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HiN = A
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HiD = Bms * sp.convolve(Bg, Bnmpr)
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k = k+d
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zk, dzk = zpowk(k)
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zk = sp.squeeze(zk)
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Bf = 1-alpha
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Af = sp.array([1, -alpha])
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S = sp.convolve(Bf, A)
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R1 = sp.convolve(Af, sp.convolve(Bnmpr, Bms))
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R2 = sp.convolve(zk, sp.convolve(Bf, sp.convolve(Bnmp, Bm)))
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R, dR = poladd(R1, len(R1)-1, -R2, len(R2)-1)
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R = sp.squeeze(R)
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R = sp.convolve(Bg, R)
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return k, HiN, HiD, R, S
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