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Chapter 6 State-Space Design
© National Instruments Corporation 6-17 Xmath Control Design Module
Figure 6-5. Diagram of the Estimator Representation
estimator( )
inputs include the dynamic system Sys, and the noise
intensity matrices Q
xx
, Q
yy
, or Q
xy
. For a linear–time–invariant process
described by:
Sys = system(A,B,C,D)
The following equation describes the complete plant:
A, B, C, and D are directly from the previous state-space system
representation where ω is the input disturbance, G is the input disturbance
matrix and ν is the measurement noise. The noise intensity matrices are
defined as,
where E is the expectation operator and δ is the delta function.
The noises ω and ν are assumed to be white and zero mean. Q
yy
has matrix
dimensions equal to the number of plant outputs and must be positive
definite, while Q
xx
has matrix dimensions equal to the number of plant
states and must be positive semi-definite. In many cases the input
disturbances and output noises are uncorrelated so that Q
xy
=0. If
uy
Cx + Du
+
+
+
–
x = Ax + Bu + Gw
x
y
Cx + Du
K
e
x
x = Ax + Bu + K
e
(y – y)
e = y – y
x
·
Ax Bu Gw++=
yCxDun++=
Evt()v′τ()()Q
yy
δ t τ–()=
EGω t()ω′τ()G'()Q
xx
δ t τ–()=
EGω t()v′τ()()Q
xy
δ t τ–()=