def set_aw(sys,poles):
"""
Divide in controller in input and feedback part
for anti-windup
Usage
=====
[sys_in,sys_fbk] = set_aw(sys,poles)
Inputs
------
sys: controller
poles : poles for the anti-windup filter
Outputs
-------
sys_in, sys_fbk: controller in input and feedback part
"""
sys = ct.ss(sys)
Ts = sys.dt
den_old = sp.poly(la.eigvals(sys.A))
sys = ct.tf(sys)
den = sp.poly(poles)
tmp = ct.tf(den_old,den,sys.dt)
sys_in = tmp*sys
sys_in = sys_in.minreal()
sys_in = ct.ss(sys_in)
sys_fbk = 1-tmp
sys_fbk = sys_fbk.minreal()
sys_fbk = ct.ss(sys_fbk)
return sys_in, sys_fbk
def set_aw(sys, poles):
"""Divide in controller in input and feedback part
for anti-windup
Usage
=====
[sys_in,sys_fbk]=set_aw(sys,poles)
Inputs
------
sys: controller
poles : poles for the anti-windup filter
Outputs
-------
sys_in, sys_fbk: controller in input and feedback part
"""
# sys=StateSpace(sys);
sys = ss(sys)
den_old = poly(eigvals(sys.A))
den = poly(poles)
tmp = tf(den_old, den, sys.dt)
tmpss = tf2ss(tmp)
# sys_in=StateSpace(tmp*sys)
sys_in = ss(tmp * sys)
sys_in.dt = sys.dt
# sys_fbk=StateSpace(1-tmp)
sys_fbk = ss(1 - tmp)
sys_fbk.dt = sys.dt
return sys_in, sys_fbk
def set_aw(sys,poles):
"""Divide in controller in input and feedback part
for anti-windup
Usage
=====
[sys_in,sys_fbk]=set_aw(sys,poles)
Inputs
------
sys: controller
poles : poles for the anti-windup filter
Outputs
-------
sys_in, sys_fbk: controller in input and feedback part
"""
sys = ss(sys)
den_old=poly(eigvals(sys.A))
sys=tf(sys)
den = poly(poles)
tmp= tf(den_old,den,sys.dt)
sys_in=tmp*sys
sys_in = sys_in.minreal()
sys_in = ss(sys_in)
sys_fbk=1-tmp
sys_fbk = sys_fbk.minreal()
sys_fbk = ss(sys_fbk)
return sys_in, sys_fbk
def set_aw(sys,poles):
"""Divide in controller in input and feedback part
for anti-windup
Usage
=====
[sys_in,sys_fbk]=set_aw(sys,poles)
Inputs
------
sys: controller
poles : poles for the anti-windup filter
Outputs
-------
sys_in, sys_fbk: controller in input and feedback part
"""
sys=ss(sys);
den_old=poly(eigvals(sys.A))
den = poly(poles)
tmp= tf(den_old,den,sys.Tsamp)
tmpss=tf2ss(tmp)
sys_in=ss(tmp*sys)
sys_in.Tsamp=sys.Tsamp
sys_fbk=ss(1-tmp)
sys_fbk.Tsamp=sys.Tsamp
return sys_in, sys_fbk
def set_aw(sys, poles):
"""Divide in controller in input and feedback part
for anti-windup
Usage
=====
[sys_in,sys_fbk]=set_aw(sys,poles)
Inputs
------
sys: controller
poles : poles for the anti-windup filter
Outputs
-------
sys_in, sys_fbk: controller in input and feedback part
"""
den_old = poly(eigvals(sys.A))
den = poly(poles)
tmp = tf(den_old, den, sys.Tsamp)
tmpss = tf2ss(tmp)
sys_in = minreal(series(sys, tmp))
sys_in.Tsamp = sys.Tsamp
sys_fbk = tf2ss(1 - tmp)
sys_fbk.Tsamp = sys.Tsamp
return sys_in, sys_fbk
def notch(fcut, Fs=2.0, nwid=3.0, npo=None, nzo=3):
f0 = fcut * 2 / Fs
fw = nwid * 2 / Fs
z = [np.exp(1j * np.pi * f0), np.exp(-1j * np.pi * f0)]
# find the polynomial with the specified (multiplicity of) zeros
b = poly(np.array(z * int(nzo)))
# the polynomial with the specified (multiplicity of) poles
if npo is None:
npo = nzo
a = poly((1 - fw) * np.array(z * int(npo)))
return (b, a)
def acker(A,B,poles):
"""Pole placemenmt using Ackermann method
Call:
k=acker(A,B,poles)
Parameters
----------
A, B : State and input matrix of the system
poles: desired poles
Returns
-------
k: matrix
State feedback gains
"""
a=mat(A)
b=mat(B)
p=real(poly(poles))
ct=ctrb(A,B)
if det(ct)==0:
k=0
print "Pole placement invalid"
else:
n=size(p)
pmat=p[n-1]*a**0
for i in arange(1,n):
pmat=pmat+p[n-i-1]*a**i
k=inv(ct)*pmat
k=k[-1][:]
return k
def acker(A,B,poles):
"""Pole placemenmt using Ackermann method
Call:
k=acker(A,B,poles)
Parameters
----------
A, B : State and input matrix of the system
poles: desired poles
Returns
-------
k: matrix
State feedback gains
"""
a=mat(A)
b=mat(B)
p=real(poly(poles))
ct=ctrb(A,B)
if det(ct)==0:
k=0
print "Pole placement invalid"
else:
n=size(p)
pmat=p[n-1]*a**0
for i in arange(1,n):
pmat=pmat+p[n-i-1]*a**i
k=inv(ct)*pmat
k=k[-1][:]
return k
def Weights(yCor,x,ind):
ww = sp.zeros(4)
base = 1
extx = sp.concatenate(([x[-2]-1],x,[x[1]+1]))
if yCor == x[ind]:
ww[2] = 1
else:
for k in range(0,4):
poly = sp.poly1d(sp.poly(extx[[i for i in range(base+ind-2,base+ind+2) if i != base+ind+k-2]]))
ww[k] = poly(yCor)/poly(extx[base+ind+k-2])
return ww
def funcionNewton( f, a ):
Ai = 0
polyDef = []
for i in range( len(a) ):
Ai = AiNewt( f, i, a, Ai)
b = []
for j in range( len(a) ):
b.append(a[i]) if j!=i
lista = np.poly(b)
pol = [ Ai*x for x in lista]
polyDef = P.polyadd(poly, polyDef);
return polyDef
# Test the magToDb <-> dbToMag i = scipy.arange(1, 7, dtype = 'f4') a = loudia.magToDb(i) o = loudia.dbToMag(a) print 'magToDb/dbToMag:', scipy.allclose(i, o) # Test the transform of windows transf = loudia.hammingTransform(24, 10, 1024, 4096) # Test the poly function a = scipy.array([1, 2, 3, 4, 5]) rr = loudia.poly( a ) rs = scipy.poly( a ) print 'poly:', scipy.allclose(rr, rs) a = scipy.array([2, 0]) rr = loudia.poly( a ) rs = scipy.poly( a[:-1] ) print 'poly, plus zero:', scipy.allclose(rr[0,:-1], rs) # Test the zpk <--> coeffs functions z = scipy.array([1, -0.96, 0.80]) p = scipy.array([1, 0.5, 0.5]) k = 1.2
# Test the magToDb <-> dbToMag i = scipy.arange(1, 7, dtype='f4') a = loudia.magToDb(i) o = loudia.dbToMag(a) print 'magToDb/dbToMag:', scipy.allclose(i, o) # Test the transform of windows transf = loudia.hammingTransform(24, 10, 1024, 4096) # Test the poly function a = scipy.array([1, 2, 3, 4, 5]) rr = loudia.poly(a) rs = scipy.poly(a) print 'poly:', scipy.allclose(rr, rs) a = scipy.array([2, 0]) rr = loudia.poly(a) rs = scipy.poly(a[:-1]) print 'poly, plus zero:', scipy.allclose(rr[0, :-1], rs) # Test the zpk <--> coeffs functions z = scipy.array([1, -0.96, 0.80]) p = scipy.array([1, 0.5, 0.5]) k = 1.2
#!/usr/bin/env python # Create input import scipy import loudia a = scipy.array([1, 2, 3, 4, 5]) rr = loudia.poly( a ) rs = scipy.poly( a ) print rr[0] print rs print scipy.allclose(rr[0], rs, rtol = 1e1)
