Bode Utilities

Utilities to work with Bode data. More...

Functions
template<class T >
Bode< T >	controlpp::prewarp_tustin (const Bode< T > &bode, const T &Ts)
	Prewarps the frequency axis of a bode plot for tustin discretisation.
template<class T >
Bode< T >	controlpp::unwarp_tustin (const Bode< T > &bode, const T &Ts)
	Unwarps the frequency axis of a bode plot for tustin discretisation.
template<class T >
const Eigen::Vector< T, Eigen::Dynamic > &	controlpp::frequencies (const Bode< T > &bode)
	Converts and returns the frequency vector in rad.
template<class T >
Eigen::Vector< T, Eigen::Dynamic >	controlpp::frequencies_hz (const Bode< T > &bode)
	Converts and returns the frequency vector in Hz.
template<class T >
Eigen::Vector< T, Eigen::Dynamic >	controlpp::real (const Bode< T > &bode)
	Converts and returns the frequency vector in rad/s.
template<class T >
Eigen::Vector< T, Eigen::Dynamic >	controlpp::imag (const Bode< T > &bode)
	Converts and returns the frequency vector in rad/s.
template<class T >
const Eigen::Vector< T, Eigen::Dynamic > &	controlpp::values (const Bode< T > &bode)
	Returns the complex values of the bode data.
template<class T >
Eigen::Vector< T, Eigen::Dynamic >	controlpp::magnitudes (const Bode< T > &bode)
	Creates a vector containing the absolute magnitudes.
template<class T >
Eigen::Vector< T, Eigen::Dynamic >	controlpp::magnitudes_dB (const Bode< T > &bode)
	Creates a vector of magnitudes in dB.
template<class T >
Eigen::Vector< T, Eigen::Dynamic >	controlpp::phases (const Bode< T > &bode)
	Creates a vector of phases in rad.
template<class T >
Eigen::Vector< T, Eigen::Dynamic >	controlpp::phases_deg (const Bode< T > &bode)
	Creates a vector of phases in degree.
template<class T >
TimeSeries< T >	controlpp::impulse (const Bode< T > &bode, const T &time_step, const T &simulation_time)
	Calculates the impulse-response of frequency data.
template<class T >
TimeSeries< T >	controlpp::impulse (const Bode< T > &bode)
	Calculates the time-series of a frequency response.
template<class T >
void	controlpp::integrate (TimeSeries< T > &out, const TimeSeries< T > &in, const T &v0=T(0))
	Integrates the time series and writes it to out.
template<class T >
TimeSeries< T >	controlpp::step (const Bode< T > &bode)
	Calculates the step response time-value pairs from frequency-value data.
template<class T >
TimeSeries< T >	controlpp::step (const Bode< T > &bode, const T &time_step, const T &simulation_time)
	Calculates the step response time-value pairs from frequency-value data.
template<class T >
Bode< T >	controlpp::operator+ (const Bode< T > &l, const Bode< T > &r)
	Adds two bode plots together.
template<class T , std::convertible_to< T > T2>
Bode< T >	controlpp::operator+ (const Bode< T > &l, const T2 &r)
	Adds a bode plot and a scalar value together.
template<class T , std::convertible_to< T > T2>
Bode< T >	controlpp::operator+ (const T2 &l, const Bode< T > &r)
	Adds a scalar value and a bode plot together.
template<class T >
Bode< T >	controlpp::operator+ (const Bode< T > &b)
	Negates the bode plot values.

Detailed Description

Utilities to work with Bode data.

Function Documentation

frequencies()

template<class T >

const Eigen::Vector< T, Eigen::Dynamic > & controlpp::frequencies

(

const Bode< T > &

bode

)

Converts and returns the frequency vector in rad.

Note that this will use a const reference from the bode data and will not allocate a new vector.

Parameters

bode	The bode data to get the frequencies from

Returns

const-reference to an eigen vector

See also

frequencies_hz(const Bode<T>& bode)

frequencies_hz()

template<class T >

Eigen::Vector< T, Eigen::Dynamic > controlpp::frequencies_hz

(

const Bode< T > &

bode

)

Converts and returns the frequency vector in Hz.

Note that this will allocate a new vector.

Parameters

bode	The bode data to get the frequencies from

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Returns

const-reference to an eigen vector

imag()

template<class T >

Eigen::Vector< T, Eigen::Dynamic > controlpp::imag

(

const Bode< T > &

bode

)

Converts and returns the frequency vector in rad/s.

Note that this will allocate a new vector.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

bode	The bode data

Returns

A vector containing the imaginary parts of the complex magnitudes

impulse() [1/2]

template<class T >

TimeSeries< T > controlpp::impulse

(

const Bode< T > &

bode

)

Calculates the time-series of a frequency response.

Allows for arbitrary number, spacing and density-changes of samples.

Automatically estimates time-steps and the simulation time from the bode data.

Tip: For step responses do not do:

stp = impulse(bode * 1/s);

instead use the step function

stp = step(bode * 1/s);

Parameters

bode	A frequency response or bode plot/measurement

Returns

a time series

See also

template<class T> TimeSeries<T> step(const Bode<T>& bode)

impulse() [2/2]

template<class T >

TimeSeries< T > controlpp::impulse	(	const Bode< T > &	bode,
		const T &	time_step,
		const T &	simulation_time
	)

Calculates the impulse-response of frequency data.

Assumes the frequency-response is only the one sided analytical form containing only positive frequencies. Thus it extends the frequency response to negative frequencies by mirroring it around the y axis in its conjugate complex form.

Uses linear piecewise first order integration in between data points

If the bode does not include a DC frequency sample (at 0 Hz) one will be added with the value of the smallest frequency in the data

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

bode	The frequency response data (assumed to only contain the one sided positive frequencies)
time_step	The timestep for the integration
simulation_time	The simulation time over which to simulate. This is the minimal simulation time and may be overstepped by one timestep.

Returns

A timeseries containing the impulse frequency response of the bode data

integrate()

template<class T >

void controlpp::integrate	(	TimeSeries< T > &	out,
		const TimeSeries< T > &	in,
		const T &	v0 = T(0)
	)

Integrates the time series and writes it to out.

Resizes out accordingly

out and in may be the same time-series object

Template Parameters

T	The value type

Parameters

out	The output time-series where the result will be written to
in	The input time-series that will be integrated over
v0	The start of the integration. Integration constant C in other nomiclatures.

magnitudes()

template<class T >

Eigen::Vector< T, Eigen::Dynamic > controlpp::magnitudes

(

const Bode< T > &

bode

)

Creates a vector containing the absolute magnitudes.

Calculates the absolute magnitudes from the complex magnitudes.

Will allocate a new vector and return it.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

bode	The bode data

Returns

A vector containing the absolute magnitudes

magnitudes_dB()

template<class T >

Eigen::Vector< T, Eigen::Dynamic > controlpp::magnitudes_dB

(

const Bode< T > &

bode

)

Creates a vector of magnitudes in dB.

Calculates the magnitudes from the complex magnitudes.

Will allocate a new vector and return it.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

bode	The bode data

Returns

A vector containing the magnitudes in dB

operator+() [1/4]

template<class T >

Bode< T > controlpp::operator+

(

const Bode< T > &

b

)

Negates the bode plot values.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

b	Bode data to negate

Returns

Bode data containing the negated values of the bode plot

operator+() [2/4]

template<class T >

Bode< T > controlpp::operator+	(	const Bode< T > &	l,
		const Bode< T > &	r
	)

Adds two bode plots together.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

l	Bode data on the left side of the addition operator
r	Bode data on the right side of the addition operator

Returns

Bode data containing the sum of the two bode plots

operator+() [3/4]

template<class T , std::convertible_to< T > T2>

Bode< T > controlpp::operator+	(	const Bode< T > &	l,
		const T2 &	r
	)

Adds a bode plot and a scalar value together.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type
T2	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

l	Bode data on the left side of the addition operator
r	A scalar value on the right side of the addition operator

Returns

Bode data containing the sum of the bode plot and the scalar value

operator+() [4/4]

template<class T , std::convertible_to< T > T2>

Bode< T > controlpp::operator+	(	const T2 &	l,
		const Bode< T > &	r
	)

Adds a scalar value and a bode plot together.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type
T2	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

l	A scalar value on the left side of the addition operator
r	Bode data on the right side of the addition operator

Returns

Bode data containing the sum of the scalar value and the bode plot

phases()

template<class T >

Eigen::Vector< T, Eigen::Dynamic > controlpp::phases

(

const Bode< T > &

bode

)

Creates a vector of phases in rad.

Calculates the phases from the complex magnitudes

Will allocate a new vector.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

bode	The bode data

Returns

A vector containing the phases in rad

phases_deg()

template<class T >

Eigen::Vector< T, Eigen::Dynamic > controlpp::phases_deg

(

const Bode< T > &

bode

)

Creates a vector of phases in degree.

Calculates the phases from the complex magnitudes

Will allocate a new vector.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

bode	The bode data

Returns

A vector containing the phases in degree

prewarp_tustin()

template<class T >

Bode< T > controlpp::prewarp_tustin	(	const Bode< T > &	bode,
		const T &	Ts
	)

Prewarps the frequency axis of a bode plot for tustin discretisation.

Note that this will allocate a new Bode object.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

bode	The bode data to prewarp
Ts	The sample time that also the tustin discretisation is using.

Returns

A bode plot with prewarped frequencies

See also

unwarp_tustin(const Bode<T>& bode, const T& Ts)

real()

template<class T >

Eigen::Vector< T, Eigen::Dynamic > controlpp::real

(

const Bode< T > &

bode

)

Converts and returns the frequency vector in rad/s.

Note that this will allocate a new vector.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

bode	The bode data

Returns

A vector containing the real parts of the complex magnitudes

step() [1/2]

template<class T >

TimeSeries< T > controlpp::step

(

const Bode< T > &

bode

)

Calculates the step response time-value pairs from frequency-value data.

Internally this will calculate the impulse response first and then integrates in the time domain. This way is numerically more stable than integrating in the frequency domain by 1/s multiplication and transforming that.

Automatically estimates the time-step and simulation time from the bode/frequency-response data.

Template Parameters

T	The data type. Typically float or double.

Parameters

bode	The step response of the system

Returns

A TimeSeries containing time-value pairs

step() [2/2]

template<class T >

TimeSeries< T > controlpp::step	(	const Bode< T > &	bode,
		const T &	time_step,
		const T &	simulation_time
	)

Calculates the step response time-value pairs from frequency-value data.

Template Parameters

T	The data type. Typically float or double.

Parameters

bode	The step response of the system
time_step	The time step used for the time series data
simulation_time	The time until the step response will be calculated (+1 for rounding).

Returns

The TimeSeries step response of the bode data

unwarp_tustin()

template<class T >

Bode< T > controlpp::unwarp_tustin	(	const Bode< T > &	bode,
		const T &	Ts
	)

Unwarps the frequency axis of a bode plot for tustin discretisation.

Note that this will allocate a new Bode object.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

bode	The bode data to unwarp
Ts	The sample time that also the tustin discretisation is using.

Returns

A bode plot with unwarped frequencies

See also

prewarp_tustin(const Bode<T>& bode, const T& Ts)

values()

template<class T >

const Eigen::Vector< T, Eigen::Dynamic > & controlpp::values

(

const Bode< T > &

bode

)

Returns the complex values of the bode data.

Will allocate a new vector and return it.

Template Parameters

T	The value type used to represent numbers. Usually float, double or a custom fixpoint type

Parameters

bode	The bode data

Returns

A vector containing the complex magnitudes