Transfer functions and state-space models

Functions
int	c_alloc_polynomial (int order, c_polynomial *p)
	Allocate a polynomial.
void	c_free_polynomial (c_polynomial *p)
	Release a polynomial.
int	c_alloc_transfer_function (int numer_order, int denom_order, c_transfer_function *tf)
	Allocate a transfer function.
void	c_free_transfer_function (c_transfer_function *tf)
	Release a transfer function.
int	c_alloc_state_space_model (int dimension, int n_inputs, int n_outputs, c_state_space_model *mdl)
	Allocate a continuous state-space model.
void	c_free_state_space_model (c_state_space_model *mdl)
	Release a state-space model.
void	c_evaluate_transfer_function (const c_transfer_function *tf, int n, const double complex *s, double complex *z)
	Evaluate a transfer function at complex points.
void	c_transfer_function_poles (const c_transfer_function *tf, int n, double complex *p)
	Compute transfer-function poles.
void	c_transfer_function_zeros (const c_transfer_function *tf, int n, double complex *z)
	Compute transfer-function zeros.
void	c_to_ccf_state_space (const c_transfer_function *tf, c_state_space_model *ss)
	Convert a transfer function to controllable canonical state space.
void	c_to_ocf_state_space (const c_transfer_function *tf, c_state_space_model *ss)
	Convert a transfer function to observable canonical state space.
void	c_create_state_space_model (int n, int n_out, const double *m, int ldm, const double *b, int ldb, const double *k, int ldk, c_state_space_model *mdl)
	Create a state-space model from mass, damping, and stiffness matrices.
void	c_create_pid_state_space_model (double kp, double ki, double kd, double tau, const c_state_space_model *plant, c_state_space_model *mdl)
	Create a PID-controlled plant state-space model.
void	c_transfer_function_multiply (const c_transfer_function *tf1, const c_transfer_function *tf2, c_transfer_function *tf)
	Multiply two transfer functions.
void	c_scale_transfer_function (double x, const c_transfer_function *tf1, c_transfer_function *tf)
	Scale a transfer function.
void	c_lti_solve (const c_state_space_model *mdl, const c_ss_excitation u, int n, const double *t, int ndof, const double *ic, int solver, int nout, double *y, int ldy, void *user_data)
	Integrate a continuous state-space model.
void	c_state_space_poles (const c_state_space_model *mdl, int n, double complex *p)
	Compute state-space poles.
void	c_state_space_zeros (const c_state_space_model *mdl, int n, double complex *z, int *nz)
	Compute state-space zeros.
void	c_state_space_transfer_function (const c_state_space_model *mdl, int nin, int nout, int n, const double complex *s, double complex *z, int ldz)
	Evaluate the state-space transfer matrix.

Detailed Description

Function Documentation

c_alloc_polynomial()

int c_alloc_polynomial	(	int	order,
		c_polynomial *	p
	)

Allocate a polynomial.

Parameters

order	Polynomial order.
p	Polynomial initialized by the routine.

Returns

Zero on success; nonzero on allocation failure.

c_free_polynomial()

void c_free_polynomial

(

c_polynomial *

p

)

Release a polynomial.

Parameters

p	Polynomial to release.

c_alloc_transfer_function()

int c_alloc_transfer_function	(	int	numer_order,
		int	denom_order,
		c_transfer_function *	tf
	)

Allocate a transfer function.

Parameters

numer_order	Numerator order.
denom_order	Denominator order.
tf	Transfer function initialized by the routine.

Returns

Zero on success; nonzero on allocation failure.

c_free_transfer_function()

void c_free_transfer_function

(

c_transfer_function *

tf

)

Release a transfer function.

Parameters

tf	Transfer function to release.

c_alloc_state_space_model()

int c_alloc_state_space_model	(	int	dimension,
		int	n_inputs,
		int	n_outputs,
		c_state_space_model *	mdl
	)

Allocate a continuous state-space model.

Parameters

dimension	State dimension.
n_inputs	Input count.
n_outputs	Output count.
mdl	Model initialized by the routine.

Returns

Zero on success; nonzero on allocation failure.

c_free_state_space_model()

void c_free_state_space_model

(

c_state_space_model *

mdl

)

Release a state-space model.

Parameters

mdl	Model to release.

c_evaluate_transfer_function()

void c_evaluate_transfer_function	(	const c_transfer_function *	tf,
		int	n,
		const double complex *	s,
		double complex *	z
	)

Evaluate a transfer function at complex points.

Parameters

tf	Transfer function.
n	Evaluation count.
s	Complex evaluation points.
z	Output complex values.

c_transfer_function_poles()

void c_transfer_function_poles	(	const c_transfer_function *	tf,
		int	n,
		double complex *	p
	)

Compute transfer-function poles.

Parameters

tf	Transfer function.
n	Pole count.
p	Output poles.

c_transfer_function_zeros()

void c_transfer_function_zeros	(	const c_transfer_function *	tf,
		int	n,
		double complex *	z
	)

Compute transfer-function zeros.

Parameters

tf	Transfer function.
n	Zero count.
z	Output zeros.

c_to_ccf_state_space()

void c_to_ccf_state_space	(	const c_transfer_function *	tf,
		c_state_space_model *	ss
	)

Convert a transfer function to controllable canonical state space.

Parameters

tf	Transfer function.
ss	Output state-space model.

c_to_ocf_state_space()

void c_to_ocf_state_space	(	const c_transfer_function *	tf,
		c_state_space_model *	ss
	)

Convert a transfer function to observable canonical state space.

Parameters

tf	Transfer function.
ss	Output state-space model.

c_create_state_space_model()

void c_create_state_space_model	(	int	n,
		int	n_out,
		const double *	m,
		int	ldm,
		const double *	b,
		int	ldb,
		const double *	k,
		int	ldk,
		c_state_space_model *	mdl
	)

Create a state-space model from mass, damping, and stiffness matrices.

Parameters

n	State dimension.
n_out	Output count.
m	Mass matrix.
ldm	Leading dimension of m.
b	Damping matrix.
ldb	Leading dimension of b.
k	Stiffness matrix.
ldk	Leading dimension of k.
mdl	Output model.

c_create_pid_state_space_model()

void c_create_pid_state_space_model	(	double	kp,
		double	ki,
		double	kd,
		double	tau,
		const c_state_space_model *	plant,
		c_state_space_model *	mdl
	)

Create a PID-controlled plant state-space model.

Parameters

kp	Proportional gain.
ki	Integral gain.
kd	Derivative gain.
tau	Derivative filter time constant.
plant	Plant model.
mdl	Output model.

c_transfer_function_multiply()

void c_transfer_function_multiply	(	const c_transfer_function *	tf1,
		const c_transfer_function *	tf2,
		c_transfer_function *	tf
	)

Multiply two transfer functions.

Parameters

tf1	First transfer function.
tf2	Second transfer function.
tf	Output product.

c_scale_transfer_function()

void c_scale_transfer_function	(	double	x,
		const c_transfer_function *	tf1,
		c_transfer_function *	tf
	)

Scale a transfer function.

Parameters

x	Scale factor.
tf1	Input transfer function.
tf	Output scaled transfer function.

c_lti_solve()

void c_lti_solve	(	const c_state_space_model *	mdl,
		const c_ss_excitation	u,
		int	n,
		const double *	t,
		int	ndof,
		const double *	ic,
		int	solver,
		int	nout,
		double *	y,
		int	ldy,
		void *	user_data
	)

Integrate a continuous state-space model.

Parameters

mdl	State-space model.
u	Input callback.
n	Time-sample count.
t	Time samples.
ndof	Input degrees of freedom.
ic	Initial state.
solver	Integration method.
nout	Output count.
y	Output samples.
ldy	Leading dimension of y.
user_data	Opaque caller data forwarded to u.

c_state_space_poles()

void c_state_space_poles	(	const c_state_space_model *	mdl,
		int	n,
		double complex *	p
	)

Compute state-space poles.

Parameters

mdl	State-space model.
n	Pole count.
p	Output poles.

c_state_space_zeros()

void c_state_space_zeros	(	const c_state_space_model *	mdl,
		int	n,
		double complex *	z,
		int *	nz
	)

Compute state-space zeros.

Parameters

mdl	State-space model.
n	Zero count.
z	Output zeros.
nz	Output number of zeros.

c_state_space_transfer_function()

void c_state_space_transfer_function	(	const c_state_space_model *	mdl,
		int	nin,
		int	nout,
		int	n,
		const double complex *	s,
		double complex *	z,
		int	ldz
	)

Evaluate the state-space transfer matrix.

Parameters

mdl	State-space model.
nin	Input count.
nout	Output count.
n	Evaluation count.
s	Complex evaluation points.
z	Output transfer values.
ldz	Leading dimension of z.