Modular Multilevel Converter with arm dynamics and control loops. More...

#include <MMC.h>

Inheritance diagram for MMC:

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Collaboration diagram for MMC:

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Public Member Functions
	MMC (const std::string &symbol, const std::string &location, double omega, double activePower, double reactivePower, double angle, double acVoltage, double Pdc, double dcVoltage, double armInductance, double armResistance, double armCapacitance, int numSubmodules, double reactorInductance, double reactorResistance, double timeDelay)
	Construct an MMC from individual scalar parameters.

	MMC (const std::string &symbol, const std::string &location, const std::vector< double > &converter_params)
	Construct an MMC from a converter parameter vector.

	MMC (const std::string &symbol, const std::string &location, const std::vector< double > &converter_params, const std::vector< double > &controller_params)
	Construct an MMC with converter and controller parameters.

	MMC (const std::string &symbol, const std::string &location, const std::vector< double > &converter_params, const std::vector< double > &controller_params, const std::vector< double > &filter_params)
	Construct an MMC with converter, controller, and filter parameters.

void	init_Controller (const std::vector< double > &converter_params)
	Initialize the controller(s) in MMC using provided parameters.

void	init_Filter (const std::vector< double > &converter_params)
	Initialize the filter(s) in MMC using provided parameters.

void	update_MMC (double Vm, double theta, double Pac, double Qac, double Vdc, double Pdc)
	Update MMC operating point and controller references.

	~MMC () override=default

virtual void	solveEquilibrium () override
	Solve for the steady-state operating point x using Newton-Raphson.

virtual Eigen::MatrixXd	computeStateDerivatives (const Eigen::VectorXd &x, const Eigen::VectorXd &u) override
	Compute the state derivatives for the MMC system.

virtual void	computeABCD () override
	Numerically compute the Jacobian matrices A and B using finite differences.

Eigen::MatrixXd	computePlantJacobian (double w, double mDd, double mDq, double mDZd, double mDZq, double mSd, double mSq, double mSz) const
	Exact 12×12 plant Jacobian (modulation treated as fixed parameters)

void	computeABCD_analytical ()
	computeABCD variant: exact plant block + numerical controller block

std::vector< std::vector< complex< double > > >	compute_y_parameters (double frequency) override
	Compute the numerical admittance (Y) parameters for the MMC.

virtual void	printElementValues () override
	Print MMC element and controller parameter values.

void	computePowerFlow (std::map< std::string, double > &data, std::map< std::string, double > &globalParams) const override
	Compute branch power-flow quantities (override in derived classes).

void	writeMNAmatrix (SymEngine::DenseMatrix &, std::unordered_map< Bus , int > &, int, std::map< Element , std::vector< RCP< const Basic > > > &) override
	Stamp this element into the symbolic MNA matrix (override in derived classes).

std::vector< RCP< const Basic > >	getVirtualInputSymbols () const override
	Return symbolic names for virtual inputs used in stamping.

std::vector< MatrixXcd >	simulateInputStep (const std::vector< MatrixXcd > &states, int nKeep) const override
	Simulate a step response given input states (override in dynamic elements).

int	getNumberOfInternalStates () const override
	Number of internal state variables for dynamic elements.

int	getNumberOfPlantStates () const override
	Number of plant states exposed for simulation (may differ from internal states).

void	stepControllers (double dt, const std::vector< Eigen::MatrixXcd > &states, const Eigen::Vector2d &Vg_dq)

map_basic_basic	getParameterSubstitutions () const override
	Return parameter substitutions for symbolic evaluation.

Public Member Functions inherited from Converter
	Converter (const std::string &symbol, const std::string &location)
	Construct a three-phase, two-terminal converter element.

virtual	~Converter ()

Eigen::MatrixXd	getA () const

Eigen::MatrixXd	getB () const

Eigen::MatrixXd	getC () const

Eigen::MatrixXd	getD () const

Eigen::MatrixXd	getAd () const

Eigen::MatrixXd	getBd () const

Eigen::MatrixXd	getCd () const

Eigen::MatrixXd	getDd () const

Eigen::VectorXd	getEquilibriumState () const

VectorXcd	getEigenvalues ()

VectorXcd	getEigenvectors ()

string	getACarea () const

string	getDCarea () const

virtual void	discretize (double Ts)

void	computeEigenvalues ()

Eigen::MatrixXd	computeParticipationFactors (const Eigen::MatrixXd &A_matrix)

virtual vector< MatrixXcd >	simulateTimeStep (const vector< MatrixXcd > &input, double Ts, int nKeep1, int nKeep2)

void	checkStability () const
	Check system stability by evaluating eigenvalues of the A matrix.

void	printEigenvalues () const
	Print eigenvalues of the A matrix.

virtual void	plotEigenvalues () override
	Plot eigenvalues in the complex plane.

virtual void	plotParticipationFactors () override
	Plot participation factors (override in state-space elements).

Public Member Functions inherited from Element
	Element (const std::string &symbol, const std::string &location, int inputPins, int outputPins)
	Construct an element with symbol, location, and pin counts.

virtual	~Element ()
	Virtual destructor for derived-class cleanup.

int	getInputPins () const
	Get the number of input pins/phases.

int	getOutputPins () const
	Get the number of output pins/phases.

void	setInputPins (int pins)
	Set the number of input pins/phases.

void	setOutputPins (int pins)
	Set the number of output pins/phases.

void	setTransformation (bool flag)
	Enable or disable coordinate transformation for this element.

std::string	getElementSymbol () const
	Get the element type symbol.

std::vector< Bus * >	getBuses ()
	Collect all buses connected to this element.

int	getBusIndex (Bus *bus)
	Find the terminal index associated with a given bus.

Bus *	getOtherBus (Bus *)
	Get the bus connected at the opposite terminal from a given bus.

const std::map< Bus *, int > &	getConnections () const
	Const access to the bus-to-terminal connection map.

std::map< Bus *, int >	getConnections ()
	Copy of the bus-to-terminal connection map.

string	getElementLocation () const
	Get the element's grid or partition location label.

void	attachBus (Bus *, int)
	Attach a bus to a specific element terminal.

void	printElementInfo () const
	Print basic element metadata (symbol, input/output pin counts).

void	writeFile (double start_frequency, double end_frequency, int number_of_points)
	Write Y-parameter matrix samples over a frequency sweep to a file.

void	plotYParameters (double start_frequency, double end_frequency, int number_of_points)
	Plot Y-parameter matrix entries versus frequency.

virtual DenseMatrix	get_y_parameters ()
	Get the symbolic or stored Y-parameter matrix.

virtual std::vector< std::vector< complex< double > > >	apply_transformation (std::vector< std::vector< complex< double > > > &Y1, std::vector< std::vector< complex< double > > > &Y2)
	Apply a coordinate or coupling transformation to Y-parameter blocks.

std::map< std::string, double >	getOPFInfo () const
	Get stored OPF-related metadata for this element.

void	setOPFInfo (std::map< std::string, double > &info)
	Store OPF-related metadata for this element.

Public Attributes
Eigen::VectorXd	x_ctrl_dqsym_

Eigen::MatrixXcd	mD_dqsym_

Eigen::MatrixXcd	mS_dqsym_

bool	dqsym_initialized_ = false

double	last_vMDelta_d_ref_ = 0.0

double	last_vMDelta_q_ref_ = 0.0

double	last_vMSigma_d_ref_ = 0.0

double	last_vMSigma_q_ref_ = 0.0

double	last_vMSigma_z_ref_ = 0.0

Additional Inherited Members
Protected Attributes inherited from Converter
double	omega_0

double	P

double	Q

double	P_dc

double	P_min

double	P_max

double	Q_min

double	Q_max

double	theta

double	V_m

double	V_dc

double	L_reactor

double	R_reactor

double	t_delay

MatrixXd	A_matrix

MatrixXd	B_matrix

MatrixXd	C_matrix

MatrixXd	D_matrix

MatrixXd	Adelay

MatrixXd	Bdelay

MatrixXd	Cdelay

MatrixXd	Ddelay

MatrixXd	Ad_matrix

MatrixXd	Bd_matrix

MatrixXd	Cd_matrix

MatrixXd	Dd_matrix

int	pade_order = 2

VectorXd	equilibrium_state

VectorXcd	eigenvalues

VectorXcd	eigenvectors

VectorXcd	initial_state

std::map< std::string, Controller * >	controls

std::map< std::string, Filter * >	filters

const std::vector< std::string >	controller_list

const std::vector< std::string >	filter_list

Protected Attributes inherited from Element
bool	transformation = false

std::string	element_symbol

std::string	element_location

int	input_pins

int	output_pins

std::map< Bus *, int >	connections

std::map< std::string, double >	element_OPF_info = {}

DenseMatrix	Y_matrix

Detailed Description

Modular Multilevel Converter with arm dynamics and control loops.

Constructor & Destructor Documentation

◆ MMC() [1/4]

MMC::MMC	(	const std::string &	symbol,
		const std::string &	location,
		double	omega,
		double	activePower,
		double	reactivePower,
		double	angle,
		double	acVoltage,
		double	Pdc,
		double	dcVoltage,
		double	armInductance,
		double	armResistance,
		double	armCapacitance,
		int	numSubmodules,
		double	reactorInductance,
		double	reactorResistance,
		double	timeDelay
	)

Construct an MMC from individual scalar parameters.

MMC constructor with explicit parameters.

Parameters

symbol	Element identifier.
location	Network area string encoding AC and DC areas.
omega	Nominal angular frequency (rad/s).
activePower	Active power setpoint (W).
reactivePower	Reactive power setpoint (VAR).
angle	AC voltage angle (rad).
acVoltage	AC voltage amplitude (V).
Pdc	DC power (W).
dcVoltage	DC bus voltage (V).
armInductance	Arm inductance (H).
armResistance	Arm resistance (Ω).
armCapacitance	Submodule capacitance (F).
numSubmodules	Number of submodules per arm.
reactorInductance	Phase reactor inductance (H).
reactorResistance	Phase reactor resistance (Ω).
timeDelay	Control time delay (s).
symbol	Element symbol/name.
omega	Nominal angular frequency (rad/s).
activePower	Active power (W).
reactivePower	Reactive power (VAR).
angle	Initial phase angle (rad).
acVoltage	AC voltage amplitude (V).
dcVoltage	DC voltage (V).
armInductance	Arm inductance (H).
armResistance	Arm resistance (Ohm).
armCapacitance	Arm capacitance (F).
numSubmodules	Number of submodules.
reactorInductance	Reactor inductance (H).
reactorResistance	Reactor resistance (Ohm).
timeDelay	Modulation time delay (s).

References Converter::A_matrix, Converter::Adelay, Converter::B_matrix, Converter::Bdelay, Converter::C_matrix, Converter::Cdelay, Converter::D_matrix, Converter::Ddelay, Converter::L_reactor, omega, Converter::omega_0, Converter::P, Converter::P_dc, Converter::P_max, Converter::P_min, Converter::pade_order, padeDelaySystemMulti2(), padeDelaySystemMulti3(), Converter::Q, Converter::Q_max, Converter::Q_min, Converter::R_reactor, Converter::t_delay, Converter::theta, Converter::V_dc, Converter::V_m, and Element::Y_matrix.

◆ MMC() [2/4]

MMC::MMC	(	const std::string &	symbol,
		const std::string &	location,
		const std::vector< double > &	converter_params
	)

Construct an MMC from a converter parameter vector.

MMC constructor with converter parameter vector.

Parameters

symbol	Element identifier.
location	Network area string encoding AC and DC areas.
converter_params	Packed converter parameters from init_MMC.
symbol	Element symbol/name.
converter_params	Vector of converter parameters.

References Converter::A_matrix, Converter::Adelay, Converter::B_matrix, Converter::Bdelay, Converter::C_matrix, Converter::Cdelay, Converter::D_matrix, Converter::Ddelay, Converter::equilibrium_state, Converter::L_reactor, Converter::omega_0, Converter::P, Converter::P_dc, Converter::P_max, Converter::P_min, Converter::pade_order, padeDelaySystemMulti2(), padeDelaySystemMulti3(), Converter::Q, Converter::Q_max, Converter::Q_min, Converter::R_reactor, Converter::t_delay, Converter::theta, Converter::V_dc, Converter::V_m, and Element::Y_matrix.

◆ MMC() [3/4]

MMC::MMC	(	const std::string &	symbol,
		const std::string &	location,
		const std::vector< double > &	converter_params,
		const std::vector< double > &	controller_params
	)

Construct an MMC with converter and controller parameters.

MMC constructor with converter and controller parameter vectors.

Parameters

symbol	Element identifier.
location	Network area string encoding AC and DC areas.
converter_params	Packed converter parameters.
controller_params	Controller gain and setpoint parameters.
symbol	Element symbol/name.
converter_params	Vector of converter parameters.
controller_params	Vector of controller parameters.

References init_Controller().

◆ MMC() [4/4]

MMC::MMC	(	const std::string &	symbol,
		const std::string &	location,
		const std::vector< double > &	converter_params,
		const std::vector< double > &	controller_params,
		const std::vector< double > &	filter_params
	)

Construct an MMC with converter, controller, and filter parameters.

MMC constructor with converter, controller, and filter parameter vectors.

Parameters

symbol	Element identifier.
location	Network area string encoding AC and DC areas.
converter_params	Packed converter parameters.
controller_params	Controller gain and setpoint parameters.
filter_params	Filter time-constant and gain parameters.
symbol	Element symbol/name.
converter_params	Vector of converter parameters.
controller_params	Vector of controller parameters.
filter_params	Vector of filter parameters.

References init_Controller(), and init_Filter().

◆ ~MMC()

MMC::~MMC ( )

overridedefault

Member Function Documentation

◆ compute_y_parameters()

std::vector< std::vector< complex< double > > > MMC::compute_y_parameters ( double frequency )

overridevirtual

Compute the numerical admittance (Y) parameters for the MMC.

Parameters

omega Angular frequency (rad/s).

Returns: Eigen::MatrixXcd Admittance matrix.

Reimplemented from Element.

References Converter::A_matrix, Converter::B_matrix, Converter::C_matrix, Converter::controls, Converter::D_matrix, j, and Element::Y_matrix.

Referenced by example_MMC(), and example_stability_check().

◆ computeABCD()

void MMC::computeABCD ( )

overridevirtual

Numerically compute the Jacobian matrices A and B using finite differences.

Parameters

x0	Operating point state vector.
u0	Operating point input vector.

Reimplemented from Converter.

References Converter::A_matrix, Converter::B_matrix, Converter::C_matrix, computeJacobians(), computeStateDerivatives(), Converter::controls, Converter::D_matrix, Converter::equilibrium_state, makeOperatingInput(), Converter::P_dc, Converter::theta, Converter::V_dc, and Converter::V_m.

Referenced by example_MMC().

◆ computeABCD_analytical()

void MMC::computeABCD_analytical ( )

computeABCD variant: exact plant block + numerical controller block

References Converter::A_matrix, Converter::B_matrix, Converter::C_matrix, computeJacobians(), computePlantJacobian(), computeStateDerivatives(), Converter::controls, Converter::D_matrix, Converter::equilibrium_state, makeOperatingInput(), Converter::omega_0, Converter::P_dc, Converter::theta, Converter::V_dc, and Converter::V_m.

Referenced by example_MMC().

◆ computePlantJacobian()

Eigen::MatrixXd MMC::computePlantJacobian	(	double	w,
		double	mDd,
		double	mDq,
		double	mDZd,
		double	mDZq,
		double	mSd,
		double	mSq,
		double	mSz
	)		const

Exact 12×12 plant Jacobian (modulation treated as fixed parameters)

References Converter::L_reactor, and Converter::R_reactor.

Referenced by computeABCD_analytical().

◆ computePowerFlow()

void MMC::computePowerFlow	(	std::map< std::string, double > &	branchData,
		std::map< std::string, double > &	globalParams
	)		const

inlineoverridevirtual

Compute branch power-flow quantities (override in derived classes).

Parameters

branchData	Output map of branch OPF results.
globalParams	Shared global OPF parameters.

Reimplemented from Element.

References Converter::controls, Element::element_location, Element::element_OPF_info, Converter::L_reactor, Converter::P, Converter::Q, Converter::R_reactor, and Converter::V_dc.

◆ computeStateDerivatives()

MatrixXd MMC::computeStateDerivatives	(	const Eigen::VectorXd &	x,
		const Eigen::VectorXd &	u
	)

overridevirtual

Compute the state derivatives for the MMC system.

Parameters

x	State vector.
u	Input vector.

Returns: MatrixXd State derivatives vector.

The state vector ordering is described at the top of this file. Controller, filter, PLL, and delay states are prepended to the main MMC states.

Reimplemented from Converter.

References Converter::Adelay, Converter::Bdelay, Converter::Cdelay, Converter::controls, Converter::Ddelay, Converter::filters, j, Converter::L_reactor, last_vMDelta_d_ref_, last_vMDelta_q_ref_, last_vMSigma_d_ref_, last_vMSigma_q_ref_, last_vMSigma_z_ref_, Converter::omega_0, Converter::pade_order, Converter::R_reactor, Converter::t_delay, Converter::theta, and Converter::V_dc.

Referenced by computeABCD(), computeABCD_analytical(), solveEquilibrium(), and stepControllers().

◆ getNumberOfInternalStates()

int MMC::getNumberOfInternalStates ( ) const

inlineoverridevirtual

Number of internal state variables for dynamic elements.

Returns: State count; zero for static linear elements.

Reimplemented from Element.

◆ getNumberOfPlantStates()

int MMC::getNumberOfPlantStates ( ) const

inlineoverridevirtual

Number of plant states exposed for simulation (may differ from internal states).

Returns: Plant state count; defaults to getNumberOfInternalStates().

Reimplemented from Element.

◆ getParameterSubstitutions()

map_basic_basic MMC::getParameterSubstitutions ( ) const

overridevirtual

Return parameter substitutions for symbolic evaluation.

Returns: Map from symbols to replacement expressions.

Reimplemented from Element.

References Element::element_symbol.

◆ getVirtualInputSymbols()

std::vector< RCP< const Basic > > MMC::getVirtualInputSymbols ( ) const

overridevirtual

Return symbolic names for virtual inputs used in stamping.

Returns: List of SymEngine symbol RCPs; empty if none.

Reimplemented from Element.

References Element::element_symbol.

Referenced by writeMNAmatrix().

◆ init_Controller()

void MMC::init_Controller ( const std::vector< double > & controller_params )

Initialize the controller(s) in MMC using provided parameters.

Parameters

controller_params Vector of controller parameters.

References Converter::controller_list, Converter::controls, Converter::pade_order, and Converter::t_delay.

Referenced by MMC(), and MMC().

◆ init_Filter()

void MMC::init_Filter ( const std::vector< double > & filter_params )

Initialize the filter(s) in MMC using provided parameters.

Parameters

filter_params	Vector of filter parameters, conaining filter names and their parameters.
filter_list	List of filter name to initialize.
filter_size	Size of the filter (default is 1). Only used for AC voltage dq filter.
filter_order	Order of the filter (default is 2). Only used for AC voltage dq filter.

filter_params should contain the following structure: 0 if the filer is not used, 1 if the filter is used, followed by the filter parameters (3 double values for each filter, representing Kp, Ki, and T). For the first order fiter, only T is used, and Kp and Ki are set to 0 in the main.cpp.

References Converter::filter_list, and Converter::filters.

Referenced by MMC().

◆ printElementValues()

void MMC::printElementValues ( )

overridevirtual

Print MMC element and controller parameter values.

Reimplemented from Element.

References Converter::controls, Converter::L_reactor, Converter::omega_0, Converter::P, Converter::P_dc, Element::printElementInfo(), Controller::printValues(), Converter::Q, Converter::R_reactor, Converter::t_delay, Converter::V_dc, and Converter::V_m.

◆ simulateInputStep()

std::vector< MatrixXcd > MMC::simulateInputStep	(	const std::vector< MatrixXcd > &	states,
		int	nKeep
	)		const

overridevirtual

Simulate a step response given input states (override in dynamic elements).

Parameters

states	Input state trajectories per channel.
nKeep	Number of states to retain in the output.

Returns: Simulated state matrices; empty for static elements.

Reimplemented from Element.

References dq_multiply(), dqsym_initialized_, mD_dqsym_, mS_dqsym_, and truncateHarmonics().

◆ solveEquilibrium()

void MMC::solveEquilibrium ( )

overridevirtual

Solve for the steady-state operating point x using Newton-Raphson.

Reimplemented from Converter.

References computeStateDerivatives(), Converter::controls, Converter::equilibrium_state, findEquilibriumRobust(), makeOperatingInput(), Converter::P, Converter::P_dc, Converter::Q, Converter::theta, Converter::V_dc, and Converter::V_m.

Referenced by example_MMC().

◆ stepControllers()

void MMC::stepControllers	(	double	dt,
		const std::vector< Eigen::MatrixXcd > &	states,
		const Eigen::Vector2d &	Vg_dq
	)

References computeStateDerivatives(), Converter::controls, dqsym_initialized_, last_vMDelta_d_ref_, last_vMDelta_q_ref_, last_vMSigma_z_ref_, mD_dqsym_, mS_dqsym_, Converter::V_dc, and x_ctrl_dqsym_.

Referenced by DQsym::run().

◆ update_MMC()

void MMC::update_MMC	(	double	Vm,
		double	theta,
		double	Pac,
		double	Qac,
		double	Vdc,
		double	Pdc
	)

Update MMC operating point and controller references.

Parameters

Vm	AC voltage magnitude.
theta	AC voltage phase angle.
Pac	Active power.
Qac	Reactive power.
Vdc	DC voltage.
Pdc	DC power.

References Converter::controls, Converter::P, Converter::P_dc, Converter::Q, Converter::theta, Converter::V_dc, and Converter::V_m.

◆ writeMNAmatrix()

void MMC::writeMNAmatrix	(	SymEngine::DenseMatrix &	,
		std::unordered_map< Bus *, int > &	,
		int	,
		std::map< Element *, std::vector< RCP< const Basic > > > &
	)

overridevirtual

Stamp this element into the symbolic MNA matrix (override in derived classes).

Parameters

mna	Global MNA matrix being assembled.
busIndexMap	Maps buses to global node indices.
offset	Current matrix offset for stamping.
elementSymbols	Per-element symbolic substitution table.

Reimplemented from Element.

References addSym(), Element::connections, Element::element_symbol, and getVirtualInputSymbols().

Member Data Documentation

◆ dqsym_initialized_

bool MMC::dqsym_initialized_ = false

Referenced by simulateInputStep(), and stepControllers().

◆ last_vMDelta_d_ref_

double MMC::last_vMDelta_d_ref_ = 0.0

mutable

Referenced by computeStateDerivatives(), and stepControllers().

◆ last_vMDelta_q_ref_

double MMC::last_vMDelta_q_ref_ = 0.0

mutable

Referenced by computeStateDerivatives(), and stepControllers().

◆ last_vMSigma_d_ref_

double MMC::last_vMSigma_d_ref_ = 0.0

mutable

Referenced by computeStateDerivatives().

◆ last_vMSigma_q_ref_

double MMC::last_vMSigma_q_ref_ = 0.0

mutable

Referenced by computeStateDerivatives().

◆ last_vMSigma_z_ref_

double MMC::last_vMSigma_z_ref_ = 0.0

mutable

Referenced by computeStateDerivatives(), and stepControllers().

◆ mD_dqsym_

Eigen::MatrixXcd MMC::mD_dqsym_

Referenced by simulateInputStep(), and stepControllers().

◆ mS_dqsym_

Eigen::MatrixXcd MMC::mS_dqsym_

Referenced by simulateInputStep(), and stepControllers().

◆ x_ctrl_dqsym_

Eigen::VectorXd MMC::x_ctrl_dqsym_

Referenced by stepControllers().

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

harmony/src/Elements/Converter/MMC.h
harmony/src/Elements/Converter/MMC.cpp

Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MMC() [1/4]

◆ MMC() [2/4]

◆ MMC() [3/4]

◆ MMC() [4/4]

◆ ~MMC()

Member Function Documentation

◆ compute_y_parameters()

◆ computeABCD()

◆ computeABCD_analytical()

◆ computePlantJacobian()

◆ computePowerFlow()

◆ computeStateDerivatives()

◆ getNumberOfInternalStates()

◆ getNumberOfPlantStates()

◆ getParameterSubstitutions()

◆ getVirtualInputSymbols()

◆ init_Controller()

◆ init_Filter()

◆ printElementValues()

◆ simulateInputStep()

◆ solveEquilibrium()

◆ stepControllers()

◆ update_MMC()

◆ writeMNAmatrix()

Member Data Documentation

◆ dqsym_initialized_

◆ last_vMDelta_d_ref_

◆ last_vMDelta_q_ref_

◆ last_vMSigma_d_ref_

◆ last_vMSigma_q_ref_

◆ last_vMSigma_z_ref_

◆ mD_dqsym_

◆ mS_dqsym_

◆ x_ctrl_dqsym_