User`s guide

lqgreg
11-117
11lqgreg
Purpose Form LQG regulator given state-feedback gain and Kalman estimator
Syntax rlqg = lqgreg(kest,k)
rlqg = lqgreg(kest,k,'current') % discrete-time only
rlqg = lqgreg(kest,k,controls)
Description lqgreg formstheLQG regulatorbyconnecting theKalman estimatordesigned
with
kalman and the optimal state-feedback gain designed with lqr, dlqr,or
lqry. The LQG regulator minimizes some quadratic cost function that trades
off regulation performance and control effort. This regulator is dynamic and
reliesonnoisyoutputmeasurementstogeneratetheregulatingcommands(see
“LQG Regulator” on page 7-10 for details).
In continuous time, the LQG regulator generates t he commands
where is the Kalman state estimate. The regulator state-space equations are
where is the vector of plant output measurements (see
kalman for
background and notation). The diagram belowshows this dynamic regulator in
relation to the plant.
uKx
ˆ
–=
x
ˆ
x
ˆ
·
ALC– BLD–()K–
x
ˆ
Ly
v
+=
uKx
ˆ
–=
y
v