def _tc2tf(zeros, poles, K=1, var=None):
"""Create a transfer function in time-constant form from lists (or
dictionaries) of zeros and poles, and from a constant gain
"""
K = sympify(K)
zeros = sympify(zeros)
poles = sympify(poles)
zz = []
pp = []
if isinstance(zeros, (tuple, list)):
for z in zeros:
if z == 0:
zz.append(var)
else:
zz.append((var / -z + 1))
K *= z
else:
for z, o in zeros.items():
if z == 0:
zz.append(var**o)
else:
zz.append((var / -z + 1)**zeros[z])
K *= z**o
if isinstance(zeros, (tuple, list)):
for p in poles:
if p == 0:
pp.append(p)
else:
pp.append(1 / (var / -p + 1))
K /= p
else:
for p, o in poles.items():
if p == 0:
pp.append(var**o)
else:
pp.append(1 / (var / -p + 1)**o)
K /= p**o
K = K.simplify()
return uMul(K, *(zz + pp))
def _zp2tf(zeros, poles, K=1, var=None):
"""Create a transfer function from lists of zeros and poles,
and from a constant gain"""
K = sym.sympify(K)
zeros = sym.sympify(zeros)
poles = sym.sympify(poles)
if isinstance(zeros, (tuple, list)):
zz = [(var - z) for z in zeros]
else:
zz = [(var - z)**zeros[z] for z in zeros]
if isinstance(zeros, (tuple, list)):
pp = [1 / (var - p) for p in poles]
else:
pp = [1 / (var - p)**poles[p] for p in poles]
return uMul(K, *(zz + pp))
def _zp2tf(zeros, poles, K=1, var=None):
"""Create a transfer function from lists of zeros and poles,
and from a constant gain"""
K = sympify(K)
zeros = sympify(zeros)
poles = sympify(poles)
if isinstance(zeros, (tuple, list)):
zz = [(var - z) for z in zeros]
else:
zz = [(var - z) ** zeros[z] for z in zeros]
if isinstance(zeros, (tuple, list)):
pp = [1 / (var - p) for p in poles]
else:
pp = [1 / (var - p) ** poles[p] for p in poles]
return uMul(K, *(zz + pp))