[SciPy-user] Fwd: signal.lti(A,B,C,D) with D=0
flyeng4
williamhpurcell@gmail....
Tue Feb 17 14:25:54 CST 2009
I am getting back to using signal.lti for state-space representation.
This is a post and a reply that I had received a while back, but there
was no follow up. Any thoughts on a solution for representing MIMO or
SIMO systems with signal.lti, with the issue described below with
ss2zpk?
-Bill
---------- Forwarded message ----------
From: "Ryan Krauss" <ryanli...@gmail.com>
Date: Jul 14 2008, 7:41 am
Subject: signal.lti(A,B,C,D) with D=0
To: SciPy-user
This seems like a bug in ltisys. I think this line
149 type_test = A[:,0] + B[:,0] + C[0,:] + D
should be
149 type_test = A[:,0] + B[:,0] + C[0,:] + D[0,:]
for a multipe-input/multiple-output system with i inputs, n states,
and m outputs, A should be n by n, B should be n by i, C should be m
by n, and D should be m by i.
(actually, because of this code a few lines above:
# make MOSI from possibly MOMI system.
if B.shape[-1] != 0:
B = B[:,input]
B.shape = (B.shape[0],1)
if D.shape[-1] != 0:
D = D[:,input]
I guess line 149 should be
149 type_test = A[:,0] + B[:,0] + C[0,:] + D[0]
)
But making this change exposes another problem:
/usr/lib/python2.5/site-packages/scipy/signal/ltisys.py in
__init__(self, *args, **kwords)
224 self.__dict__['D'] =
abcd_normalize(*args)
225 self.__dict__['zeros'], self.__dict__['poles'], \
--> 226 self.__dict__['gain'] =
ss2zpk(*args)
227 self.__dict__['num'], self.__dict__['den'] = ss2tf
(*args)
228 self.inputs = self.B.shape[-1]
/usr/lib/python2.5/site-packages/scipy/signal/ltisys.py in ss2zpk(A,
B, C, D, input)
183 """
184 Pdb().set_trace()
--> 185 return tf2zpk(*ss2tf(A,B,C,D,input=input))
186
187 class lti(object):
/usr/lib/python2.5/site-packages/scipy/signal/filter_design.py in
tf2zpk(b, a)
128 k = b[0]
129 b /= b[0]
--> 130 z = roots(b)
131 p = roots(a)
132 return z, p, k
/usr/lib/python2.5/site-packages/numpy/lib/polynomial.py in roots(p)
98 p = atleast_1d(p)
99 if len(p.shape) != 1:
--> 100 raise ValueError,"Input must be a rank-1 array."
101
102 # find non-zero array entries
<type 'exceptions.ValueError'>: Input must be a rank-1 array.
WARNING: Failure executing file: <proj2.py>
In [2]: %debug> /usr/lib/python2.5/site-packages/numpy/lib/
polynomial.py(100)roots()
99 if len(p.shape) != 1:
--> 100 raise ValueError,"Input must be a rank-1 array."
101
ipdb> print p
[[ 1.00000000e+00 1.00000000e+00 1.00000000e+00 1.00000000e+00
1.00000000e+00 1.00000000e+00]
[ 1.81898940e-11 -3.06222400e+00 -2.79196150e+02 -5.87518033e+03
-1.59843721e+04 1.91386789e-07]
[ 1.75910240e+01 1.60479206e+03 3.37698682e+04 9.12618857e+04
-1.23219975e+04 -3.29828641e+04]]
ss2tf seems to correctly handle MIMO (or at least SIMO systems)
correctly and returns one denominator polynomial with several (m)
numerator polynomials. But tf2zpk in filter_design.py does not seem
able to handle more than siso systems (which makes sense, it is
expecting a transfer function which is just a SISO system).
How should this be fixed?
I understand why ss2tf converts a MIMO system to SIMO - trying to
represent a mulitple input, multiple output system with a transfer
function has some limitations. I think the real offender is in the
__init__ method of signal.lti:
elif N == 4:
...
self.__dict__['zeros'], self.__dict__['poles'], \
self.__dict__['gain'] = ss2zpk
(*args)
For a MIMO system, what should the zpk representation be? For a SIMO
system, I would expect a vector of poles and a matrix of zeros. This
seems to be in line with what ss2tf does.
It seems like the init method could find the pole by passing C[0,:]
and D[0,:] to ss2zpk. The zeros and gains could then be found by
calling ss2zpk in some vectorized way or simply in a for loop for each
row of C and D. But there may well be a more elegant solution.
Any thoughts?
Ryan
On Sun, Jul 13, 2008 at 2:59 PM, William Purcell
<williamhpurc...@gmail.com> wrote:
> I am trying to set up state space representation of a system using
> signal.lti. The system has no feedforward so D = 0. I've tried the three
> options listed in the code below to represent D.
> The only way I can get it to work is option 2 if C has 1 row. If C has more
> than 1 row it won't work.
> Any thoughts?
> -Bill
> Code
> ---------------------------------------------------------------
> from numpy import ones,matrix
> from scipy import signal
> r = ones(3)
> A = matrix([r,r,r])
> B = matrix([r]).T
> C = matrix([r,r])
> #three options of D to make it 0
> #1) D=0
> #2) D = matrix([0,0]).T
> #3) D = None
> D = 0
> #D = None
> #D = matrix([0,0]).T
> Gss = signal.lti(A,B,C,D)
> -----------------------------------------------------------
> Tracebacks
> -----------------------------------------------------------
> Option 1
> /usr/lib/python2.5/site-packages/scipy/signal/ltisys.py in abcd_normalize(A,
> B, C, D)
> 101 raise ValueError, "A and C must have the same number of
> columns."
> 102 if MD != MC:
> --> 103 raise ValueError, "C and D must have the same number of
> rows."
> 104 if ND != NB:
> 105 raise ValueError, "B and D must have the same number of
> columns."
> <type 'exceptions.ValueError'>: C and D must have the same number of rows.
> WARNING: Failure executing file: <testlti.py>
> Option 2 (with C as two rows...if C is a single row I do not get this
> traceback)
> /usr/lib/python2.5/site-packages/scipy/signal/ltisys.py in ss2tf(A, B, C, D,
> input)
> 147
> 148 num_states = A.shape[0]
> --> 149 type_test = A[:,0] + B[:,0] + C[0,:] + D
> 150 num = numpy.zeros((nout, num_states+1), type_test.dtype)
> 151 for k in range(nout):
> <type 'exceptions.ValueError'>: shape mismatch: objects cannot be broadcast
> to a single shape
> WARNING: Failure executing file: <testlti.py>
> Option 3
> same as 1
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