Form Linear-Quadratic-Gaussian (LQG) servo controller
C = lqgtrack(kest,k)
C = lqgtrack(kest,k,'2dof')
C = lqgtrack(kest,k,'1dof')
C = lqgtrack(kest,k,...CONTROLS)
lqgtrack forms a Linear-Quadratic-Gaussian
(LQG) servo controller with integral action for the loop shown in
the following figure. This compensator ensures that the output y tracks
the reference command r and rejects process disturbances w and
measurement noise v.
that r and y have the same length.
Always use positive feedback to connect the LQG servo controller C to the plant output y.
C = lqgtrack(kest,k) forms a two-degree-of-freedom
LQG servo controller
C by connecting the Kalman
kest and the state-feedback gain
as shown in the following figure.
C has inputs and generates
the command , where is the Kalman
estimate of the plant state, and xi is
the integrator output.
The size of the gain matrix
the length of xi. xi, y,
and r all have the same length.
The two-degree-of-freedom LQG servo controller state-space equations are
C = lqgtrack(kest,k,'2dof') is
C = lqgtrack(kest,k).
C = lqgtrack(kest,k,'1dof') forms a one-degree-of-freedom
LQG servo controller
C that takes the tracking
error e = r – y as
input instead of [r ; y], as
shown in the following figure.
The one-degree-of-freedom LQG servo controller state-space equations are
C = lqgtrack(kest,k,...CONTROLS) forms
an LQG servo controller
C when the Kalman estimator
access to additional known (deterministic) commands Ud of
the plant. In the index vector
which inputs of
kest are the control channels u.
The resulting compensator C has inputs
[Ud ; r ; y] in the two-degree-of-freedom case
[Ud ; e] in the one-degree-of-freedom case
The corresponding compensator structure for the two-degree-of-freedom cases appears in the following figure.
See the example Design an LQG Servo Controller.
You can use
lqgtrack for both continuous-
and discrete-time systems.
For a discrete-time plant with equations:
connecting the "current" Kalman estimator to the LQR gain is optimal only when and y[n] does not depend on
w[n] (H = 0). If these conditions are not satisfied, compute the optimal LQG