Package edu.wpi.first.math.system

Class Discretization

java.lang.Object

edu.wpi.first.math.system.Discretization

public final class Discretization
extends Object

Method Summary

Modifier and Type	Method	Description
static <States extends Num> Matrix<States,States>	discretizeA(Matrix<States,States> contA, double dtSeconds)	Discretizes the given continuous A matrix.
static <States extends Num, Inputs extends Num> Pair<Matrix<States,States>,Matrix<States,Inputs>>	discretizeAB(Matrix<States,States> contA, Matrix<States,Inputs> contB, double dtSeconds)	Discretizes the given continuous A and B matrices.
static <States extends Num> Pair<Matrix<States,States>,Matrix<States,States>>	discretizeAQ(Matrix<States,States> contA, Matrix<States,States> contQ, double dtSeconds)	Discretizes the given continuous A and Q matrices.
static <States extends Num> Pair<Matrix<States,States>,Matrix<States,States>>	discretizeAQTaylor(Matrix<States,States> contA, Matrix<States,States> contQ, double dtSeconds)	Discretizes the given continuous A and Q matrices.
static <O extends Num> Matrix<O,O>	discretizeR(Matrix<O,O> contR, double dtSeconds)	Returns a discretized version of the provided continuous measurement noise covariance matrix.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

discretizeA

public static <States extends Num> Matrix<States,States> discretizeA(Matrix<States,States> contA, double dtSeconds)

Discretizes the given continuous A matrix.

Type Parameters:

States - Num representing the number of states.

Parameters:

contA - Continuous system matrix.

dtSeconds - Discretization timestep.

Returns:

the discrete matrix system.

discretizeAB

public static <States extends Num, Inputs extends Num> Pair<Matrix<States,States>,Matrix<States,Inputs>> discretizeAB(Matrix<States,States> contA, Matrix<States,Inputs> contB, double dtSeconds)

Discretizes the given continuous A and B matrices.

Type Parameters:

States - Nat representing the states of the system.

Inputs - Nat representing the inputs to the system.

Parameters:

contA - Continuous system matrix.

contB - Continuous input matrix.

dtSeconds - Discretization timestep.

Returns:

a Pair representing discA and diskB.

discretizeAQ

public static <States extends Num> Pair<Matrix<States,States>,Matrix<States,States>> discretizeAQ(Matrix<States,States> contA, Matrix<States,States> contQ, double dtSeconds)

Discretizes the given continuous A and Q matrices.

Type Parameters:

States - Nat representing the number of states.

Parameters:

contA - Continuous system matrix.

contQ - Continuous process noise covariance matrix.

dtSeconds - Discretization timestep.

Returns:

a pair representing the discrete system matrix and process noise covariance matrix.

discretizeAQTaylor

public static <States extends Num> Pair<Matrix<States,States>,Matrix<States,States>> discretizeAQTaylor(Matrix<States,States> contA, Matrix<States,States> contQ, double dtSeconds)

Discretizes the given continuous A and Q matrices.

Rather than solving a 2N x 2N matrix exponential like in DiscretizeQ() (which is expensive), we take advantage of the structure of the block matrix of A and Q.

• eᴬᵀ, which is only N x N, is relatively cheap.
• The upper-right quarter of the 2N x 2N matrix, which we can approximate using a taylor series to several terms and still be substantially cheaper than taking the big exponential.

Type Parameters:

States - Nat representing the number of states.

Parameters:

contA - Continuous system matrix.

contQ - Continuous process noise covariance matrix.

dtSeconds - Discretization timestep.

Returns:

a pair representing the discrete system matrix and process noise covariance matrix.

discretizeR

public static <O extends Num> Matrix<O,O> discretizeR(Matrix<O,O> contR, double dtSeconds)

Returns a discretized version of the provided continuous measurement noise covariance matrix. Note that dt=0.0 divides R by zero.

Type Parameters:

O - Nat representing the number of outputs.

Parameters:

contR - Continuous measurement noise covariance matrix.

dtSeconds - Discretization timestep.

Returns:

Discretized version of the provided continuous measurement noise covariance matrix.