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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. lqgtrack assumes that r and y have the same length.
Note 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
estimator kest and the state-feedback gain k,
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 k determines 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
Note The syntax C = lqgtrack(kest,k,'2dof') is equivalent to 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 kest has access to additional known (deterministic) commands Ud of the plant. In the index vector CONTROLS, specify 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.
You can use lqgtrack for both continuous- and discrete-time systems.
In discrete-time systems, integrators are based on forward Euler
(see lqi for details). The
state estimate
is either x[n|n]
or x[n|n-1],
depending on the type of estimator (see kalman for
details).
See the example Example — Designing an LQG Servo Controller.
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