lqed

Calculates the discrete Kalman estimator configuration based on a continuous cost function.

Syntax

• [L, P, Z, E] = LQED(A, G, C, Q, R, Ts)

Input argument

• A - State matrix: n x n matrix.
• G - Defines a matrix linking the process noise to the states.
• C - The output matrix, with dimensions (q x n), where q is the number of outputs.
• Q - State-cost weighted matrix
• R - Input-cost weighted matrix
• N - Optional cross term matrix: 0 by default.
• Ts - sample time: scalare.

Output argument

• L - Kalman gain matrix.
• P - Solution of the Discrete Algebraic Riccati Equation.
• E - Closed-loop pole locations
• Z - Discrete estimator poles

Description

[L, P, Z, E] = LQED(A, G, C, Q, R, Ts) Calculates the discrete Kalman gain matrix L to minimize the discrete estimation error, equivalent to the estimation error in the continuous system.

Example

A = [10     1.2;  3.3     4];
B = [5     0;   0     6];
C = B;
D = [0,0;0,0];
R = [2,0;0,3];
Q = [5,0;0,4];
G = [6,0;0,7];
Ts = 0.004;

[L, P, Z, E] = lqed(A, G, C, Q, R, Ts)

See also

lqr, lqe.

History

Author

Allan CORNET