kalmd (Control Design and Simulation Module, MathScript Function)

LabView Control Design MathScript Functions

kalmd (Control Design and Simulation Module, MathScript Function)

Member of the ssdesign class.

Syntax

[SysKalDisc, L, P, M, Z] = kalmd(SysInSSCont, Q, R, Ts)

[SysKalDisc, L, P, M, Z] = kalmd(SysInSSCont, Q, R, N, Ts)

Description

Calculates the optimal steady-state Kalman gain L that minimizes the covariance of the state estimation error. The input system and noise covariance are based on a continuous system. All outputs are based on a discretized system SysKalDisc, which is based on the sample rate Ts.

Examples

Inputs

Name Description
SysInSSCont Specifies a continuous linear time-invariant (LTI) model in state-space form.
Q Specifies the auto-covariance matrix of the continuous process noise. Q is a real matrix that is symmetric and positive semi-definite.
R Specifies the auto-covariance matrix of the continuous measurement noise. R is a real matrix that is symmetric and positive definite.
Ts Specifies the sampling time this VI uses to discretize the SysInSSCont model. Ts is a real scalar.
N Specifies the cross-covariance matrix between the process noise and measurement noise. The default is an appropriately-sized matrix of zeros, which specifies the process noise and measurement noise are uncorrelated. N must be valid such that (Q-N*inv(R)*N') is positive semi-definite. N is a real matrix.

Outputs

Name Description
SysKalDisc Returns the definition of the discrete Kalman filter with the gain matrix L applied. SysKalDisc is a discrete LTI model in state-space form.
L Returns the gain matrix that minimizes the covariance of the state estimation error. L is a real matrix.
P Returns the steady-state covariance of the estimation error. P is a real matrix.
M Returns the steady-state innovation gain matrix. This gain matrix weights the difference between the observed and estimated outputs in the state update equation for discrete estimators. M is a real matrix.
Z Returns the steady-state error covariance of the error between the actual states and the updated state estimates in the discrete estimation process. Z is a real matrix.

Examples

SysInSSCont = ss(-1, 1, 1, 0)[SysKalDisc, L, P] = kalmd(SysInSSCont, 1, 2, 1)

Related Topics

acker
estim
kalman
place