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 Qxx, Qyy, or Qxy. 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. Qyy has matrix
dimensions equal to the number of plant outputs and must be positive
definite, while Qxx 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 Qxy =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()()Qyyδtτ–()=
EGωt()ω′τ()G'()Qxxδtτ–()=
EGωt()v′τ()()Qxyδtτ–()=