Page 321 - Electrical Engineering Dictionary

0 x 0q
+ T i−p,j−q−1 u pq + T i−1,j−q−1 [A 0 ,B 0 ]
B 2 u 0q

x 00
h
v
where x ∈ R n 1 and x ∈ R n 2 are the hori- + T i−1,j−1 [A 0 ,B 0 ] + (2)
ij ij u 00
m
zontal and vertical state vectors, u ij ∈ R is
n
p
the input vector, y ij ∈ R is the output vec- where x i,j ∈ R is the semistate local vector,
tor, A 1 , A 2 , A 3 , A 4 , B 1 , B 2 , C 1 , C 2 , D are u i,j ∈ R m is the input vector, E, A k , B k
given real matrices, and the transition matrix (k = 0, 1, 2)C, D are given real matrices
T pq is defined by with E possibly singular and the transition
matrices T p q are defined by

 I n for p = q = 0 


  A 0 T −1,−1 + A 1 T 0,−1
 A 1 A 2 
 for p = 1,q = 0 

  +A 2 T −1,0 + I for p = q = 0
 00


 ET pq = A 0 T p−1,q−1 + A 1 T p,q−1
00
T pq = for p = 0,q = 1 and 

 A 3 A 4  +A 2 T p−1,q

 
 for p 6= 0 and/or q 6= 0
 T 10 T i−1,j + T 01 T i,j−1 for



 i, j ∈ Z + (i + j> 0)

 and

0 for p< 0 or/and q< 0
−1
[Ez 1 z 2 − A 0 − A 1 z 1 − A 2 z 2 ]
Substitution of (2) into (1b) yields the re- ∞ ∞
X X −(p+1) −(q+1)
sponse formula. = T pq z z
1 2
p=−n 1 q=−n 2
general response formula for generalized
pair (n 1 ,n 2 ) of positive integers n 1 ,n 2 such
2-D model the solution x ij to the gener-
alized 2-D model that T pq = 0 for p< −n 1 and/or q< −n 2
is called the index of the model. Substitution
of (2) into (1b) yields the response formula.
Ex i+1,j+1 = A 0 x ij + A 1 x i+1,j + A 2 x i,j+1
+ B 0 u ij + B 1 u i+1,j
general-purpose motor term often used
(1a)
+ B 2 u i,j+1 to describe National Electrical Manufactur-
(1b) ers Association (NEMA) class B, and less
y ij = Cx ij + Du ij
often class B, induction motors. General-
i, j ∈ Z + (the set of nonnegative integers) purpose motors are those typically used when
with admissible boundary conditions x i0 , i ∈ relatively low starting currents, low slip,
Z + and x 0j , j ∈ Z + is given by good speed regulation, moderate starting
torque, and high efficiency are the predomi-
i+n 1 j+n 2 nant concerns.
X X
x ij = T i−p−1,j−q−1 B 0
p=1 q=1 general-purpose register a register that
is not assigned to a specific purpose, such
+ T i−p,j−q−1 B 1
as holding condition codes or a stack pointer,

+ T i−p−1,j−q B 2 u pq
but that may be used to hold any sort of value.
i+n 1
X General-purpose registers are typically not
+ T i−p,j−1 [A 1 ,B 1 ]
equipped with any dedicated logic to oper-
p=1
ate on the data stored in the register.

x p0
+ T i−p−1,j−1 [A 0 ,B 0 ]
u p0 general-use switch a manually operated
switching device designed for general use. It
i+n 2
X
+ T i−1,j−q [A 2 ,B 2 ] is designed to interrupt rated current at rated
voltage.
q=1
c
2000 by CRC Press LLC