Form linear-quadratic-Gaussian (LQG) regulator
rlqg = lqgreg(kest,k)
rlqg = lqgreg(kest,k,controls)
lqgreg forms the linear-quadratic-Gaussian
(LQG) regulator by connecting the Kalman estimator designed with
the optimal state-feedback gain designed with
lqry. The LQG regulator minimizes some quadratic
cost function that trades off regulation performance and control effort.
This regulator is dynamic and relies on noisy output measurements
to generate the regulating commands.
In continuous time, the LQG regulator generates the commands
where is the Kalman state estimate. The regulator state-space equations are
where y is the vector of plant output measurements
kalman for background and notation). The following
diagram shows this dynamic regulator in relation to the plant.
In discrete time, you can form the LQG regulator using either the delayed state estimate of x[n], based on measurements up to y[n–1], or the current state estimate , based on all available measurements including y[n]. While the regulator
is causal only when I-KMD is
kalman for the notation). In addition,
practical implementations of the current regulator should allow for
the processing time required to compute u[n]
after the measurements y[n]
become available (this amounts to a time delay in the feedback loop).
See the example LQG Regulation.
rlqg = lqgreg(kest,k) returns the LQG regulator
state-space model) given the Kalman estimator
the state-feedback gain matrix
k. The same function
handles both continuous- and discrete-time cases. Use consistent tools
Continuous regulator for continuous plant: use
Discrete regulator for discrete plant: use
Discrete regulator for continuous plant: use
In discrete time,
lqgreg produces the regulator
the "current" Kalman estimator
the "delayed" Kalman estimator
For more information on Kalman estimators, see the
kalman reference page.
rlqg = lqgreg(kest,k,controls) handles
estimators that have access to additional deterministic known plant
inputs ud. The index vector
specifies which estimator inputs are the controls u,
and the resulting LQG regulator
rlqg has ud and y as
inputs (see the next figure).
Note Always use positive feedback to connect the LQG regulator to the plant.