transfer_function

type, public :: transfer_function

Defines a transfer function for a continuous system of the form $H(s) = \frac{Y(s)}{X(s)}$ .

Variables

X Y

Type-Bound Procedures

evaluate initialize poles to_ccf_state_space to_ocf_state_space zeros

Components

Type	Visibility	Attributes		Name		Initial
type(polynomial),	public		::	X			The denominator polynomial $X(s)$ in $H(s) = \frac{Y(s)}{X(s)}$ . The polynomial coefficients are stored in acending order such that $x_1 + x_2 s + x_3 s^2 ...$ .
type(polynomial),	public		::	Y			The numerator polynomial $Y(s)$ in $H(s) = \frac{Y(s)}{X(s)}$ . The polynomial coefficients are stored in acending order such that $y_1 + y_2 s + y_3 s^2 ...$ .

Type-Bound Procedures

generic, public :: evaluate => tf_eval_omega, tf_eval_s

private pure elemental function tf_eval_omega(this, omega) result(rst)

Evaluates the transfer function at the specified value of the Laplace variable $s$ .

Arguments

Type	Intent	Optional	Attributes		Name
class(transfer_function),	intent(in)			::	this	The transfer_function object.
real(kind=real64),	intent(in)			::	omega	The frequency, in rad/s, at which to evaluate the transfer function.

Return Value complex(kind=real64)

The value of the transfer function.

private pure elemental function tf_eval_s(this, s) result(rst)

Evaluates the transfer function at the specified value of the Laplace variable $s$ .

Arguments

Type	Intent	Optional	Attributes		Name
class(transfer_function),	intent(in)			::	this	The transfer_function object.
complex(kind=real64),	intent(in)			::	s	The Laplace variable at which to evaluate the transfer function.

Return Value complex(kind=real64)

The value of the transfer function.

generic, public :: initialize => tf_init_poly, tf_init_array

private subroutine tf_init_poly(this, y, x)

Initializes a new transfer function.

Arguments

Type	Intent		Name
class(transfer_function),	intent(inout)	::	this	The transfer_function object.
class(polynomial),	intent(in)	::	y	The numerator polynomial $Y(s)$ in $H(s) = \frac{Y(s)}{X(s)}$ .
class(polynomial),	intent(in)	::	x	The denominator polynomial $X(s)$ in $H(s) = \frac{Y(s)}{X(s)}$ .

private subroutine tf_init_array(this, y, x)

Initializes a new transfer function.

Arguments

Type	Intent	Attributes		Name
class(transfer_function),	intent(inout)		::	this	The transfer_function object.
real(kind=real64),	intent(in),	dimension(:)	::	y	The numerator polynomial $Y(s)$ in $H(s) = \frac{Y(s)}{X(s)}$ . The polynomial coefficients are stored in acending order such that $y_1 + y_2 s + y_3 s^2 ...$ .
real(kind=real64),	intent(in),	dimension(:)	::	x	The denominator polynomial $X(s)$ in $H(s) = \frac{Y(s)}{X(s)}$ . The polynomial coefficients are stored in acending order such that $x_1 + x_2 s + x_3 s^2 ...$ .

procedure, public :: poles => tf_poles

private function tf_poles(this, err) result(rst)

Computes the poles of the transfer function.

Arguments

Type	Intent	Optional	Attributes		Name
class(transfer_function),	intent(in)			::	this	The transfer_function object.
class(errors),	intent(inout),	optional,	target	::	err	An error handling object.

Return Value complex(kind=real64), allocatable, dimension(:)

The poles of the transfer function.

procedure, public :: to_ccf_state_space => tf_to_ccf_statespace

private function tf_to_ccf_statespace(this) result(rst)

Converts a transfer_function type into a controllable canonical form state_space type. See this article for a description of this form.

Arguments

Type	Intent	Optional	Attributes		Name
class(transfer_function),	intent(in)			::	this	The transfer_function to convert.

Return Value type(state_space)

The resulting state-space object.

procedure, public :: to_ocf_state_space => tf_to_ocf_statespace

private function tf_to_ocf_statespace(this) result(rst)

Converts a transfer_function type into an observable canonical form state_space type. See this article for a description of this form.

Arguments

Type	Intent	Optional	Attributes		Name
class(transfer_function),	intent(in)			::	this	The transfer_function to convert.

Return Value type(state_space)

The resulting state-space object.

procedure, public :: zeros => tf_zeros

private function tf_zeros(this, err) result(rst)

Computes the zeros of the transfer function.

Arguments

Type	Intent	Optional	Attributes		Name
class(transfer_function),	intent(in)			::	this	The transfer function object.
class(errors),	intent(inout),	optional,	target	::	err	An error handling object.

Return Value complex(kind=real64), allocatable, dimension(:)

The zeros of the transfer function.

transfer_function Derived Type

Contents

Variables

Type-Bound Procedures

type, public :: transfer_function

Contents

Variables

Type-Bound Procedures

Components

Type-Bound Procedures

generic, public :: evaluate => tf_eval_omega, tf_eval_s

private pure elemental function tf_eval_omega(this, omega) result(rst)

Arguments

Return Value complex(kind=real64)

private pure elemental function tf_eval_s(this, s) result(rst)

Arguments

Return Value complex(kind=real64)

generic, public :: initialize => tf_init_poly, tf_init_array

private subroutine tf_init_poly(this, y, x)

Arguments

private subroutine tf_init_array(this, y, x)

Arguments

procedure, public :: poles => tf_poles

private function tf_poles(this, err) result(rst)

Arguments

Return Value complex(kind=real64), allocatable, dimension(:)

procedure, public :: to_ccf_state_space => tf_to_ccf_statespace

private function tf_to_ccf_statespace(this) result(rst)

Arguments

Return Value type(state_space)

procedure, public :: to_ocf_state_space => tf_to_ocf_statespace

private function tf_to_ocf_statespace(this) result(rst)

Arguments

Return Value type(state_space)

procedure, public :: zeros => tf_zeros

private function tf_zeros(this, err) result(rst)

Arguments

Return Value complex(kind=real64), allocatable, dimension(:)