Chapter 6 State-Space Design
Xmath Control Design Module 6-20 ni.com
this measurement update, derived in [Kal60], are shown in the following
equations.
Substituting the system and noise matrices for the steady-state case, you
solve the discrete Riccati equation to obtain P and thence Ke, as shown in
Equation 6-7 and Equation 6-8.
(6-7)
where
and the discrete feedback gain Ke is given by
(6-8)
estimator( )[Ke,ev,P] = estimator(Sys,Qxx,Qyy,{Qxy})
The estimator( ) function calculates the optimal gain matrix Ke
for a given dynamic system with specified process, measurement, and
(optionally) cross-weighting noise matrices.
Alternatively, Ke can be obtained through a call to riccati( ):
[P,resid,Ke,ev]=riccati(Sys',Qxx,Qyy,{S=Qxy})
The syntax for riccati( ) is described in the Riccati Equation section.
As shown in the estimator diagram in Figure 6-4, the state equation for the
estimator is:
x
ˆkxkKeykCxk
–()+=
PkMk
1–C'Qyy
1–C+()
1–
=
A'PA A'PC'Qyy CPC'+()
1–CPA–Qxx
+P=
AA'C'Qyy
1–Qxy
–=
Qxx Qxx Qxy'Qyy
1–Qxy
–=
K′eQyy CPC′+()
1–CPA′Qxy
+()=
x
ˆ
·AK
eC–()x
ˆBD–()uGω++=