Contains the controller coefficients and logic for a linear-quadratic regulator (LQR). More...

#include <frc/controller/LinearQuadraticRegulator.h>

Public Types
using	StateVector = Vectord< States >

using	InputVector = Vectord< Inputs >

using	StateArray = wpi::array< double, States >

using	InputArray = wpi::array< double, Inputs >

Public Member Functions
template<int Outputs>
	LinearQuadraticRegulator (const LinearSystem< States, Inputs, Outputs > &plant, const StateArray &Qelems, const InputArray &Relems, units::second_t dt)
	Constructs a controller with the given coefficients and plant. More...

	LinearQuadraticRegulator (const Matrixd< States, States > &A, const Matrixd< States, Inputs > &B, const StateArray &Qelems, const InputArray &Relems, units::second_t dt)
	Constructs a controller with the given coefficients and plant. More...

	LinearQuadraticRegulator (const Matrixd< States, States > &A, const Matrixd< States, Inputs > &B, const Matrixd< States, States > &Q, const Matrixd< Inputs, Inputs > &R, units::second_t dt)
	Constructs a controller with the given coefficients and plant. More...

	LinearQuadraticRegulator (const Matrixd< States, States > &A, const Matrixd< States, Inputs > &B, const Matrixd< States, States > &Q, const Matrixd< Inputs, Inputs > &R, const Matrixd< States, Inputs > &N, units::second_t dt)
	Constructs a controller with the given coefficients and plant. More...

	LinearQuadraticRegulator (LinearQuadraticRegulator &&)=default

LinearQuadraticRegulator &	operator= (LinearQuadraticRegulator &&)=default

const Matrixd< Inputs, States > &	K () const
	Returns the controller matrix K. More...

double	K (int i, int j) const
	Returns an element of the controller matrix K. More...

const StateVector &	R () const
	Returns the reference vector r. More...

double	R (int i) const
	Returns an element of the reference vector r. More...

const InputVector &	U () const
	Returns the control input vector u. More...

double	U (int i) const
	Returns an element of the control input vector u. More...

void	Reset ()
	Resets the controller. More...

InputVector	Calculate (const StateVector &x)
	Returns the next output of the controller. More...

InputVector	Calculate (const StateVector &x, const StateVector &nextR)
	Returns the next output of the controller. More...

template<int Outputs>
void	LatencyCompensate (const LinearSystem< States, Inputs, Outputs > &plant, units::second_t dt, units::second_t inputDelay)
	Adjusts LQR controller gain to compensate for a pure time delay in the input. More...

Detailed Description

template<int States, int Inputs>
class frc::LinearQuadraticRegulator< States, Inputs >

Contains the controller coefficients and logic for a linear-quadratic regulator (LQR).

LQRs use the control law u = K(r - x).

For more on the underlying math, read https://file.tavsys.net/control/controls-engineering-in-frc.pdf.

Template Parameters

States	Number of states.
Inputs	Number of inputs.

Member Typedef Documentation

◆ InputArray

template<int States, int Inputs>

using frc::LinearQuadraticRegulator< States, Inputs >::InputArray = wpi::array<double, Inputs>

◆ InputVector

template<int States, int Inputs>

using frc::LinearQuadraticRegulator< States, Inputs >::InputVector = Vectord<Inputs>

◆ StateArray

template<int States, int Inputs>

using frc::LinearQuadraticRegulator< States, Inputs >::StateArray = wpi::array<double, States>

◆ StateVector

template<int States, int Inputs>

using frc::LinearQuadraticRegulator< States, Inputs >::StateVector = Vectord<States>

Constructor & Destructor Documentation

◆ LinearQuadraticRegulator() [1/5]

template<int States, int Inputs>

template<int Outputs>

frc::LinearQuadraticRegulator< States, Inputs >::LinearQuadraticRegulator	(	const LinearSystem< States, Inputs, Outputs > &	plant,
		const StateArray &	Qelems,
		const InputArray &	Relems,
		units::second_t	dt
	)

Constructs a controller with the given coefficients and plant.

See https://docs.wpilib.org/en/stable/docs/software/advanced-controls/state-space/state-space-intro.html#lqr-tuning for how to select the tolerances.

Template Parameters

Outputs Number of outputs.

Parameters

plant	The plant being controlled.
Qelems	The maximum desired error tolerance for each state.
Relems	The maximum desired control effort for each input.
dt	Discretization timestep.

Exceptions

std::invalid_argument If the system is uncontrollable.

◆ LinearQuadraticRegulator() [2/5]

template<int States, int Inputs>

frc::LinearQuadraticRegulator< States, Inputs >::LinearQuadraticRegulator	(	const Matrixd< States, States > &	A,
		const Matrixd< States, Inputs > &	B,
		const StateArray &	Qelems,
		const InputArray &	Relems,
		units::second_t	dt
	)

Constructs a controller with the given coefficients and plant.

See https://docs.wpilib.org/en/stable/docs/software/advanced-controls/state-space/state-space-intro.html#lqr-tuning for how to select the tolerances.

Parameters

A	Continuous system matrix of the plant being controlled.
B	Continuous input matrix of the plant being controlled.
Qelems	The maximum desired error tolerance for each state.
Relems	The maximum desired control effort for each input.
dt	Discretization timestep.

Exceptions

std::invalid_argument If the system is uncontrollable.

◆ LinearQuadraticRegulator() [3/5]

template<int States, int Inputs>

frc::LinearQuadraticRegulator< States, Inputs >::LinearQuadraticRegulator	(	const Matrixd< States, States > &	A,
		const Matrixd< States, Inputs > &	B,
		const Matrixd< States, States > &	Q,
		const Matrixd< Inputs, Inputs > &	R,
		units::second_t	dt
	)

Constructs a controller with the given coefficients and plant.

Parameters

A	Continuous system matrix of the plant being controlled.
B	Continuous input matrix of the plant being controlled.
Q	The state cost matrix.
R	The input cost matrix.
dt	Discretization timestep.

Exceptions

std::invalid_argument If the system is uncontrollable.

◆ LinearQuadraticRegulator() [4/5]

template<int States, int Inputs>

frc::LinearQuadraticRegulator< States, Inputs >::LinearQuadraticRegulator	(	const Matrixd< States, States > &	A,
		const Matrixd< States, Inputs > &	B,
		const Matrixd< States, States > &	Q,
		const Matrixd< Inputs, Inputs > &	R,
		const Matrixd< States, Inputs > &	N,
		units::second_t	dt
	)

Constructs a controller with the given coefficients and plant.

Parameters

A	Continuous system matrix of the plant being controlled.
B	Continuous input matrix of the plant being controlled.
Q	The state cost matrix.
R	The input cost matrix.
N	The state-input cross-term cost matrix.
dt	Discretization timestep.

Exceptions

std::invalid_argument If the system is uncontrollable.

◆ LinearQuadraticRegulator() [5/5]

template<int States, int Inputs>

frc::LinearQuadraticRegulator< States, Inputs >::LinearQuadraticRegulator ( LinearQuadraticRegulator< States, Inputs > && )

default

Member Function Documentation

◆ Calculate() [1/2]

template<int States, int Inputs>

LinearQuadraticRegulator< States, Inputs >::InputVector frc::LinearQuadraticRegulator< States, Inputs >::Calculate ( const StateVector & x )

Returns the next output of the controller.

Parameters

x	The current state x.

◆ Calculate() [2/2]

template<int States, int Inputs>

LinearQuadraticRegulator< States, Inputs >::InputVector frc::LinearQuadraticRegulator< States, Inputs >::Calculate	(	const StateVector &	x,
		const StateVector &	nextR
	)

Returns the next output of the controller.

Parameters

x	The current state x.
nextR	The next reference vector r.

◆ K() [1/2]

template<int States, int Inputs>

const Matrixd< Inputs, States > & frc::LinearQuadraticRegulator< States, Inputs >::K ( ) const

inline

Returns the controller matrix K.

◆ K() [2/2]

template<int States, int Inputs>

double frc::LinearQuadraticRegulator< States, Inputs >::K	(	int	i,
		int	j
	)		const

inline

Returns an element of the controller matrix K.

Parameters

i	Row of K.
j	Column of K.

◆ LatencyCompensate()

template<int States, int Inputs>

template<int Outputs>

void frc::LinearQuadraticRegulator< States, Inputs >::LatencyCompensate	(	const LinearSystem< States, Inputs, Outputs > &	plant,
		units::second_t	dt,
		units::second_t	inputDelay
	)

Adjusts LQR controller gain to compensate for a pure time delay in the input.

Linear-Quadratic regulator controller gains tend to be aggressive. If sensor measurements are time-delayed too long, the LQR may be unstable. However, if we know the amount of delay, we can compute the control based on where the system will be after the time delay.

See https://file.tavsys.net/control/controls-engineering-in-frc.pdf appendix C.4 for a derivation.

Parameters

plant	The plant being controlled.
dt	Discretization timestep.
inputDelay	Input time delay.

◆ operator=()

template<int States, int Inputs>

LinearQuadraticRegulator & frc::LinearQuadraticRegulator< States, Inputs >::operator= ( LinearQuadraticRegulator< States, Inputs > && )

default

◆ R() [1/2]

template<int States, int Inputs>

const StateVector & frc::LinearQuadraticRegulator< States, Inputs >::R ( ) const

inline

Returns the reference vector r.

Returns: The reference vector.

◆ R() [2/2]

template<int States, int Inputs>

double frc::LinearQuadraticRegulator< States, Inputs >::R ( int i ) const

inline

Returns an element of the reference vector r.

Parameters

i Row of r.

Returns: The row of the reference vector.

◆ Reset()

template<int States, int Inputs>

void frc::LinearQuadraticRegulator< States, Inputs >::Reset ( )

inline

Resets the controller.

◆ U() [1/2]

template<int States, int Inputs>

const InputVector & frc::LinearQuadraticRegulator< States, Inputs >::U ( ) const

inline

Returns the control input vector u.

Returns: The control input.

◆ U() [2/2]

template<int States, int Inputs>

double frc::LinearQuadraticRegulator< States, Inputs >::U ( int i ) const

inline

Returns an element of the control input vector u.

Parameters

i Row of u.

Returns: The row of the control input vector.

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

frc/controller/LinearQuadraticRegulator.h
frc/controller/LinearQuadraticRegulator.inc

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ InputArray

◆ InputVector

◆ StateArray

◆ StateVector

Constructor & Destructor Documentation

◆ LinearQuadraticRegulator() [1/5]

◆ LinearQuadraticRegulator() [2/5]

◆ LinearQuadraticRegulator() [3/5]

◆ LinearQuadraticRegulator() [4/5]

◆ LinearQuadraticRegulator() [5/5]

Member Function Documentation

◆ Calculate() [1/2]

◆ Calculate() [2/2]

◆ K() [1/2]

◆ K() [2/2]

◆ LatencyCompensate()

◆ operator=()

◆ R() [1/2]

◆ R() [2/2]

◆ Reset()

◆ U() [1/2]

◆ U() [2/2]