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Chapter 7. openETCS Meta Model
In the case k = 0 for the initial calculation, the constant initial state vector s i,0 must be used
because the usage of negative calculation time points t | k=−1 = −T s < 0 would render the
system non-causal. Thus, the calculation time point must be translated about 1:
[ ]
si,k+1
= f
y i
(x i,k+1 , s i,k ); k = 0, 1, 2, 3, . . . (7.8)
i,k+1
Furthermore, not all data flow objects or rather transfer functions have inputs and outputs. If
they only have inputs (p i = 0), their transfer function equation is reduced to
s i,k+1 = f i
(x i,k+1 , s i,k ); k = 0, 1, 2, 3, . . . (7.9)
Analogously, transfer functions without any input (m i = 0) can be reduced to
[ ]
si,k+1
= f
y i
(s i,k ); k = 0, 1, 2, 3, . . . (7.10)
i,k+1
While
X ≡ { }
x j ; j = 1, 2, 3, . . . , n x
}
Y ≡
{y l
; l = 1, 2, 3, . . . , n y
S ≡ { }
s p ; p = 1, 2, 3, . . . , n s
}
≡
{s oq
; q = 1, 2, 3, . . . , n s0
S 0
(7.11)
(7.12)
(7.13)
(7.14)
are defined for a whole data flow model, the connection matrix C defines the connections
between all outputs and inputs by the connection equation:
x k = Cy k
(7.15)
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