def tb03ad_example():
A = array([ [1, 2, 0],
[4,-1, 0],
[0, 0, 1]])
B = array([ [1, 0],
[0, 0],
[1, 0]])
C = array([ [0, 1,-1],
[0, 0, 1]])
D = array([ [0, 1],
[0, 0]])
n = 3
m = 1
p = 2
out = slycot.tb03ad(n,m,p,A,B,C,D,'R')
#out = slycot.tb03ad_l(n,m,p,A,B,C,D)
print('--- Example for tb03ad ...')
print('The right polynomial representation of' )
print(' W(z) = C(zI-A)^-1B + D')
print('is the following:' )
print('index', out[4])
k_max = max(out[4]) + 1
for k in range(0,k_max):
print('P_%d =' %(k))
print(out[5][0:m,0:m,k])
for k in range(0,k_max):
print('Q_%d =' %(k))
print(out[6][0:m,0:p,k])
def tc04ad_example():
from numpy import shape,zeros
A = array([ [1, 2, 0],
[4,-1, 0],
[0, 0, 1]])
B = array([ [1, 0],
[0, 0],
[1, 0]])
C = array([ [0, 1,-1],
[0, 0, 1]])
D = array([ [0, 1],
[0, 0]])
n = 3
m = 1
p = 2
out = slycot.tb03ad(n,m,p,A,B,C,D,'R')
qcoeff = zeros((max(m,p),max(m,p),shape(out[6])[2]))
qcoeff[0:shape(out[6])[0],0:shape(out[6])[1],0:shape(out[6])[1]]
out2 = slycot.tc04ad(m,p,out[4],out[5][0:m,0:m,:],qcoeff,'R')
print('--- Example for tb04ad ...')
print('The system has a state space realization (A,B,C,D) where')
print('A =')
print(out2[1])
print('B =')
print(out2[2])
print('C =')
print(out2[3])
print('D =')
print(out2[4])
def tc04ad_example():
from numpy import shape,zeros
A = array([ [1, 2, 0],
[4,-1, 0],
[0, 0, 1]])
B = array([ [1, 0],
[0, 0],
[1, 0]])
C = array([ [0, 1,-1],
[0, 0, 1]])
D = array([ [0, 1],
[0, 0]])
n = 3
m = 1
p = 2
out = slycot.tb03ad(n,m,p,A,B,C,D,'R')
qcoeff = zeros((max(m,p),max(m,p),shape(out[6])[2]))
qcoeff[0:shape(out[6])[0],0:shape(out[6])[1],0:shape(out[6])[1]]
out2 = slycot.tc04ad(m,p,out[4],out[5][0:m,0:m,:],qcoeff,'R')
print('--- Example for tb04ad ...')
print('The system has a state space realization (A,B,C,D) where')
print('A =')
print(out2[1])
print('B =')
print(out2[2])
print('C =')
print(out2[3])
print('D =')
print(out2[4])
def tb03ad_example():
A = array([ [1, 2, 0],
[4,-1, 0],
[0, 0, 1]])
B = array([ [1, 0],
[0, 0],
[1, 0]])
C = array([ [0, 1,-1],
[0, 0, 1]])
D = array([ [0, 1],
[0, 0]])
n = 3
m = 1
p = 2
out = slycot.tb03ad(n,m,p,A,B,C,D,'R')
#out = slycot.tb03ad_l(n,m,p,A,B,C,D)
print('--- Example for tb03ad ...')
print('The right polynomial representation of' )
print(' W(z) = C(zI-A)^-1B + D')
print('is the following:' )
print('index', out[4])
k_max = max(out[4]) + 1
for k in range(0,k_max):
print('P_%d =' %(k))
print(out[5][0:m,0:m,k])
for k in range(0,k_max):
print('Q_%d =' %(k))
print(out[6][0:m,0:p,k])
def minreal(sys):
"""Minimal representation for state space systems
Usage
=====
[sysmin]=minreal[sys]
Inputs
------
sys: system in ss or tf form
Outputs
-------
sysfin: system in state space form
"""
a=mat(sys.A)
b=mat(sys.B)
c=mat(sys.C)
d=mat(sys.D)
nx=shape(a)[0]
ni=shape(b)[1]
no=shape(c)[0]
out=tb03ad(nx,no,ni,a,b,c,d,'R')
nr=out[3]
A=out[0][:nr,:nr]
B=out[1][:nr,:ni]
C=out[2][:no,:nr]
sysf=ss(A,B,C,sys.D,sys.Tsamp)
return sysf
def minreal(sys):
"""Minimal representation for state space systems
Usage
=====
[sysmin]=minreal[sys]
Inputs
------
sys: system in ss or tf form
Outputs
-------
sysfin: system in state space form
"""
sys=ss(sys)
a=mat(sys.A)
b=mat(sys.B)
c=mat(sys.C)
d=mat(sys.D)
nx=shape(a)[0]
ni=shape(b)[1]
no=shape(c)[0]
if no<ni:
c=vstack((c,zeros((ni-no,nx))))
d=vstack((d,zeros((ni-no,ni))))
if ni<no:
b=hstack((b,zeros((nx,no-ni))))
d=hstack((d,zeros((no,no-ni))))
print nx
print ni
print no
print a
print b
print c
print d
out=tb03ad(nx,ni,no,a,b,c,d,'R')
nr=out[3]
A=out[0][:nr,:nr]
B=out[1][:nr,:ni]
C=out[2][:no,:nr]
sysf=ss(A,B,C,sys.D,sys.Tsamp)
return sysf
def minreal(sys):
"""Minimal representation for state space systems
Usage
=====
[sysmin]=minreal[sys]
Inputs
------
sys: system in ss or tf form
Outputs
-------
sysfin: system in state space form
"""
a = mat(sys.A)
b = mat(sys.B)
c = mat(sys.C)
d = mat(sys.D)
nx = shape(a)[0]
ni = shape(b)[1]
no = shape(c)[0]
if no < ni:
c = vstack((c, zeros((ni - no, nx))))
d = vstack((d, zeros((ni - no, ni))))
if ni < no:
b = hstack((b, zeros((nx, no - ni))))
d = hstack((d, zeros((no, no - ni))))
out = tb03ad(nx, ni, no, a, b, c, d, 'R')
nr = out[3]
A = out[0][:nr, :nr]
B = out[1][:nr, :ni]
C = out[2][:no, :nr]
sysf = ss(A, B, C, sys.D, sys.Tsamp)
return sysf
