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. lqgtrack assumes that r and y have the same length.
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
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.
See the example Design an LQG Servo Controller.