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Re: lsim vs. filter for simulation in Octave 2.1.50


From: Geraint Paul Bevan
Subject: Re: lsim vs. filter for simulation in Octave 2.1.50
Date: Fri, 17 Oct 2003 13:34:03 -0500
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E. Joshua Rigler wrote:

|>If I have numerator and denominator filter coefficients:
|>
|> A = [1.0  .33]
|> B = [0.2  .10]
|> lag = [0 1] ;; not necessary for anything
|>
|>
|>...or if I have a system derived from a state-space description with:
|>
|>
|> A = -.33
|> B = .10
|> C = 1
|> D = 0.2
|> sys = ss2sys (A,B,C,D,1,0,1)
|>


I think the problem here is with your conversion from your ARMAX model
to a state space representation. Try this instead

Problem:
A = [1, 0.33]
B = [0.2, 0.1]

Y1 + 0.33 Y0 = 0.2 U1 + 0.1 U0

Let:
Y  = Y1
X1 = Y0
X2 = U0
U  = U1

Y   = -0.33 X1 + 0.1 X2 + 0.2 U
dX1 = Y - X1
~    = -1.33 X1 + 0.1 X2 + 0.2 U
dX2 = U - X2

State space:
A = [ -1.33, 0.1 ; 0, -1 ];
B = [ 0.2; 1 ];
C = [ -0.33, 0.1 ];
D = [ 0.2 ];

sysd = ss2sys(A,B,C,D,1)
sysc = d2c(sysd)


- --
Geraint Bevan
http://homepage.ntlworld.com/geraint.bevan

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