Routines for converting a state space system from continuous- to discrete-time and vice versa. More...

#include <BilinearTransformation.hpp>

Classes
struct	mallocStructC2D

struct	mallocStructD2C

Public Member Functions
template<typename TScalar , int TStateDim, int TInputDim, int TOutputDim>
void	c2d (const ls::systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > ss, double dt, double alpha, ls::systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > out, mallocStructC2D< TScalar, TStateDim, TInputDim, TOutputDim > *memStruct, LS_IS_DYNAMIC(TStateDim, TInputDim, TOutputDim))

template<typename TScalar , int TStateDim, int TInputDim, int TOutputDim>
void	c2d (const ls::systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > ss, double dt, double alpha, ls::systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > out, mallocStructC2D< TScalar, TStateDim, TInputDim, TOutputDim > *memStruct, LS_IS_STATIC(TStateDim, TInputDim, TOutputDim))

template<typename TScalar , int TStateDim, int TInputDim, int TOutputDim>
void	d2c (const ls::systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > ss, double dt, double alpha, ls::systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > out, mallocStructD2C< TScalar, TStateDim, TInputDim, TOutputDim > *memStruct, LS_IS_DYNAMIC(TStateDim, TInputDim, TOutputDim))

template<typename TScalar , int TStateDim, int TInputDim, int TOutputDim>
void	d2c (const ls::systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > ss, double dt, double alpha, ls::systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > out, mallocStructD2C< TScalar, TStateDim, TInputDim, TOutputDim > *memStruct, LS_IS_STATIC(TStateDim, TInputDim, TOutputDim))

Static Public Member Functions
static systems::StateSpace	c2d (const Eigen::MatrixXd &A, const Eigen::MatrixXd &B, const Eigen::MatrixXd &C, const Eigen::MatrixXd &D, double dt, double alpha=1)
	Generates generalized bilinear transform of a continuous-time state space system. More...

static systems::StateSpace	c2d (const Eigen::MatrixXd A, const Eigen::MatrixXd B, const Eigen::MatrixXd C, const Eigen::MatrixXd D, double dt, double alpha)
	Generates generalized bilinear transform of a continuous-time state space system. More...

static systems::StateSpace	c2d (const systems::StateSpace<> &ss, double dt, double alpha=1)
	Generates generalized bilinear transform of a continuous-time state space system. More...

template<typename TScalar , int TStateDim, int TInputDim, int TOutputDim>
static void	c2d (const systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > ss, double dt, double alpha, systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > out, mallocStructC2D< TScalar, TStateDim, TInputDim, TOutputDim > *memStruct, LS_IS_DYNAMIC_DEFAULT(TStateDim, TInputDim, TOutputDim))

template<typename TScalar , int TStateDim, int TInputDim, int TOutputDim>
static void	c2d (const systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > ss, double dt, double alpha, systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > out, mallocStructC2D< TScalar, TStateDim, TInputDim, TOutputDim > *memStruct, LS_IS_STATIC_DEFAULT(TStateDim, TInputDim, TOutputDim))

static systems::StateSpace	d2c (const systems::StateSpace<> &ss, double dt, double alpha=1)
	Generates generalized bilinear transform of a discrete-time state space system. More...

template<typename TScalar , int TStateDim, int TInputDim, int TOutputDim>
static void	d2c (const systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > ss, double dt, double alpha, systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > out, mallocStructD2C< TScalar, TStateDim, TInputDim, TOutputDim > *memStruct, LS_IS_DYNAMIC_DEFAULT(TStateDim, TInputDim, TOutputDim))

template<typename TScalar , int TStateDim, int TInputDim, int TOutputDim>
static void	d2c (const systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > ss, double dt, double alpha, systems::StateSpace< TScalar, TStateDim, TInputDim, TOutputDim > out, mallocStructD2C< TScalar, TStateDim, TInputDim, TOutputDim > *memStruct, LS_IS_STATIC_DEFAULT(TStateDim, TInputDim, TOutputDim))

static systems::StateSpace	d2c (const systems::StateSpace<> &ss, double alpha=1)
	Generates generalized bilinear transform of a discrete-time state space system. More...

static systems::StateSpace	d2c (const Eigen::MatrixXd &A, const Eigen::MatrixXd &B, const Eigen::MatrixXd &C, const Eigen::MatrixXd &D, double dt, double alpha=1)
	Generates generalized bilinear transform of a discrete-time state space system. More...

static systems::StateSpace	d2c (const Eigen::MatrixXd A, const Eigen::MatrixXd B, const Eigen::MatrixXd C, const Eigen::MatrixXd D, double dt, double alpha)
	Generates generalized bilinear transform of a discrete-time state space system. More...

static systems::StateSpace	c2dTustin (const systems::StateSpace<> &ss, double dt)
	Generates Tustin transform of a continuous-time state space system. More...

static systems::StateSpace	d2cTustin (const systems::StateSpace<> &ss, double dt)
	Generates Tustin transform of a discrete-time state space system. More...

static systems::StateSpace	c2dEuler (const systems::StateSpace<> &ss, double dt)
	Generates Euler transform of a continuous-time state space system. More...

static systems::StateSpace	d2cEuler (const systems::StateSpace<> &ss, double dt)
	Generates Euler transform of a discrete-time state space system. More...

static systems::StateSpace	c2dBwdDiff (const systems::StateSpace<> &ss, double dt)
	Generates backward differencing transform of a continuous-time state space system. More...

static systems::StateSpace	d2cBwdDiff (const systems::StateSpace<> &ss, double dt)
	Generates backward differencing transform of a discrete-time state space system. More...

Detailed Description

Routines for converting a state space system from continuous- to discrete-time and vice versa.

Note: Corresponds to SLICOT Routine AB04MD (Discrete-time <-> continuous-time conversion by bilinear transformation).

Member Function Documentation

◆ c2d() [1/3]

ls::systems::StateSpace ls::analysis::BilinearTransformation::c2d	(	const Eigen::MatrixXd &	A,
		const Eigen::MatrixXd &	B,
		const Eigen::MatrixXd &	C,
		const Eigen::MatrixXd &	D,
		double	dt,
		double	alpha = `1`
	)

static

Generates generalized bilinear transform of a continuous-time state space system.

Parameters

A	TState matrix.
B	Input matrix.
C	Output matrix.
D	Feedforward matrix.
dt	Sampling period.
alpha	Generalized bilinear transformation parameter; default parameter corresponds to backward differencing transform.

Returns: Transformed discrete-time state space system.

◆ c2d() [2/3]

ls::systems::StateSpace ls::analysis::BilinearTransformation::c2d	(	const Eigen::MatrixXd *	A,
		const Eigen::MatrixXd *	B,
		const Eigen::MatrixXd *	C,
		const Eigen::MatrixXd *	D,
		double	dt,
		double	alpha
	)

static

Generates generalized bilinear transform of a continuous-time state space system.

Parameters

A	Pointer to state matrix.
B	Pointer to input matrix.
C	Pointer to output matrix.
D	Pointer to feedforward matrix.
dt	Sampling period.
alpha	Generalized bilinear transformation parameter; default parameter corresponds to backward differencing transform.

Returns: Transformed discrete-time state space system.

◆ c2d() [3/3]

ls::systems::StateSpace ls::analysis::BilinearTransformation::c2d	(	const systems::StateSpace<> &	ss,
		double	dt,
		double	alpha = `1`
	)

static

Generates generalized bilinear transform of a continuous-time state space system.

Parameters

ss	TState space system.
dt	Sampling period.
alpha	Generalized bilinear transformation parameter; default parameter corresponds to backward differencing transform.

Returns: Transformed discrete-time state space system.

◆ c2dBwdDiff()

ls::systems::StateSpace ls::analysis::BilinearTransformation::c2dBwdDiff	(	const systems::StateSpace<> &	ss,
		double	dt
	)

static

Generates backward differencing transform of a continuous-time state space system.

Parameters

ss	TState space system.
dt	Sampling period.

Returns: Transformed discrete-time state space system.

◆ c2dEuler()

ls::systems::StateSpace ls::analysis::BilinearTransformation::c2dEuler	(	const systems::StateSpace<> &	ss,
		double	dt
	)

static

Generates Euler transform of a continuous-time state space system.

Parameters

ss	TState space system.
dt	Sampling period.

Returns: Transformed discrete-time state space system.

◆ c2dTustin()

ls::systems::StateSpace ls::analysis::BilinearTransformation::c2dTustin	(	const systems::StateSpace<> &	ss,
		double	dt
	)

static

Generates Tustin transform of a continuous-time state space system.

Parameters

ss	TState space system.
dt	Sampling period.

Returns: Transformed discrete-time state space system.

◆ d2c() [1/4]

ls::systems::StateSpace ls::analysis::BilinearTransformation::d2c	(	const Eigen::MatrixXd &	A,
		const Eigen::MatrixXd &	B,
		const Eigen::MatrixXd &	C,
		const Eigen::MatrixXd &	D,
		double	dt,
		double	alpha = `1`
	)

static

Generates generalized bilinear transform of a discrete-time state space system.

Parameters

A	TState matrix.
B	Input matrix.
C	Output matrix.
D	Feedforward matrix.
dt	Sampling period.
alpha	Generalized bilinear transformation parameter; default parameter corresponds to backward differencing transform.

Returns: Transformed continuous-time state space system.

◆ d2c() [2/4]

ls::systems::StateSpace ls::analysis::BilinearTransformation::d2c	(	const Eigen::MatrixXd *	A,
		const Eigen::MatrixXd *	B,
		const Eigen::MatrixXd *	C,
		const Eigen::MatrixXd *	D,
		double	dt,
		double	alpha
	)

static

Generates generalized bilinear transform of a discrete-time state space system.

Parameters

A	Pointer to state matrix.
B	Pointer to input matrix.
C	Pointer to output matrix.
D	Pointer to feedforward matrix.
dt	Sampling period.
alpha	Generalized bilinear transformation parameter; default parameter corresponds to backward differencing transform.

Returns: Transformed continuous-time state space system.

◆ d2c() [3/4]

ls::systems::StateSpace ls::analysis::BilinearTransformation::d2c	(	const systems::StateSpace<> &	ss,
		double	alpha = `1`
	)

static

Generates generalized bilinear transform of a discrete-time state space system.

This method retrieves the sampling period from the state space object.

Parameters

ss	TState space system.
alpha	Generalized bilinear transformation parameter; default parameter corresponds to backward differencing transform.

Returns: Transformed continuous-time state space system.

◆ d2c() [4/4]

ls::systems::StateSpace ls::analysis::BilinearTransformation::d2c	(	const systems::StateSpace<> &	ss,
		double	dt,
		double	alpha = `1`
	)

static

Generates generalized bilinear transform of a discrete-time state space system.

Parameters

ss	TState space system.
dt	Sampling period.
alpha	Generalized bilinear transformation parameter; default parameter corresponds to backward differencing transform.

Returns: Transformed continuous-time state space system.

◆ d2cBwdDiff()

ls::systems::StateSpace ls::analysis::BilinearTransformation::d2cBwdDiff	(	const systems::StateSpace<> &	ss,
		double	dt
	)

static

Generates backward differencing transform of a discrete-time state space system.

Parameters

ss	TState space system.
dt	Sampling period.

Returns: Transformed continuous-time state space system.

◆ d2cEuler()

ls::systems::StateSpace ls::analysis::BilinearTransformation::d2cEuler	(	const systems::StateSpace<> &	ss,
		double	dt
	)

static

Generates Euler transform of a discrete-time state space system.

Parameters

ss	TState space system.
dt	Sampling period.

Returns: Transformed continuous-time state space system.

◆ d2cTustin()

ls::systems::StateSpace ls::analysis::BilinearTransformation::d2cTustin	(	const systems::StateSpace<> &	ss,
		double	dt
	)

static

Generates Tustin transform of a discrete-time state space system.

Parameters

ss	TState space system.
dt	Sampling period.

Returns: Transformed continuous-time state space system.

The documentation for this class was generated from the following files:

Lodestar/analysis/BilinearTransformation.hpp
Lodestar/analysis/BilinearTransformation.cpp

Lodestar An integrated real-time control package in C++

Classes

Public Member Functions

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ c2d() [1/3]

◆ c2d() [2/3]

◆ c2d() [3/3]

◆ c2dBwdDiff()

◆ c2dEuler()

◆ c2dTustin()

◆ d2c() [1/4]

◆ d2c() [2/4]

◆ d2c() [3/4]

◆ d2c() [4/4]

◆ d2cBwdDiff()

◆ d2cEuler()

◆ d2cTustin()