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incubator-nuttx/libs/libdsp/lib_observer.c

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/****************************************************************************
* libs/libdsp/lib_observer.c
*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership. The
* ASF licenses this file to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance with the
* License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations
* under the License.
*
****************************************************************************/
/****************************************************************************
* Included Files
****************************************************************************/
#include <dsp.h>
#include <string.h>
/****************************************************************************
* Pre-processor Definitions
****************************************************************************/
/* nan check for floats */
#define IS_NAN(x) ((x) != (x))
#define NAN_ZERO(x) (x = IS_NAN(x) ? 0.0 : x)
/* Squared */
#define SQ(x) ((x) * (x))
/****************************************************************************
* Public Functions
****************************************************************************/
/****************************************************************************
* Name: motor_sobserver_init
*
* Description:
* Initialize motor speed observer
*
* Input Parameters:
* observer - pointer to the speed observer data
* so - pointer to the speed specific observer data
* per - observer execution period
*
* Returned Value:
* None
*
****************************************************************************/
void motor_sobserver_init(FAR struct motor_sobserver_f32_s *observer,
FAR void *so, float per)
{
LIBDSP_DEBUGASSERT(observer != NULL);
LIBDSP_DEBUGASSERT(so != NULL);
LIBDSP_DEBUGASSERT(per > 0.0f);
/* Reset observer data */
memset(observer, 0, sizeof(struct motor_sobserver_f32_s));
/* Set observer period */
observer->per = per;
/* Connect speed estimation observer data */
observer->so = so;
}
/****************************************************************************
* Name: motor_aobserver_init
*
* Description:
* Initialize motor angle observer
*
* Input Parameters:
* observer - pointer to the angle observer data
* ao - pointer to the angle specific observer data
* per - observer execution period
*
* Returned Value:
* None
*
****************************************************************************/
void motor_aobserver_init(FAR struct motor_aobserver_f32_s *observer,
FAR void *ao, float per)
{
LIBDSP_DEBUGASSERT(observer != NULL);
LIBDSP_DEBUGASSERT(ao != NULL);
LIBDSP_DEBUGASSERT(per > 0.0f);
/* Reset observer data */
memset(observer, 0, sizeof(struct motor_aobserver_f32_s));
/* Set observer period */
observer->per = per;
/* Connect angle estimation observer data */
observer->ao = ao;
}
/****************************************************************************
* Name: motor_aobserver_smo_init
*
* Description:
* Initialize motor sliding mode observer.
*
* Input Parameters:
* smo - pointer to the sliding mode observer private data
* kslide - SMO gain
* err_max - linear region upper limit
*
* Returned Value:
* None
*
****************************************************************************/
void motor_aobserver_smo_init(FAR struct motor_aobserver_smo_f32_s *smo,
float kslide, float err_max)
{
LIBDSP_DEBUGASSERT(smo != NULL);
LIBDSP_DEBUGASSERT(kslide > 0.0f);
LIBDSP_DEBUGASSERT(err_max > 0.0f);
/* Reset structure */
memset(smo, 0, sizeof(struct motor_aobserver_smo_f32_s));
/* Initialize structure */
smo->k_slide = kslide;
smo->err_max = err_max;
/* Store inverted err_max to avoid division */
smo->one_by_err_max = (1.0f / err_max);
}
/****************************************************************************
* Name: motor_aobserver_smo
*
* Description:
* One step of the SMO observer.
* REFERENCE: http://ww1.microchip.com/downloads/en/AppNotes/01078B.pdf
*
* Below some theoretical backgrounds about SMO.
*
* The digitalized motor model can be represent as:
*
* d(i_s.)/dt = (-R/L)*i_s. + (1/L)*(v_s - e_s. - z)
*
* We compare estimated current (i_s.) with measured current (i_s):
*
* err = i_s. - i_s
*
* and get correction factor (z):
*
* sign = sign(err)
* z = sign*K_SLIDE
*
* Once the digitalized model is compensated, we estimate BEMF (e_s.) by
* filtering z:
*
* e_s. = low_pass(z)
*
* The estimated BEMF is filtered once again and used to approximate the
* motor angle:
*
* e_filtered_s. = low_pass(e_s.)
* theta = arctan(-e_alpha/e_beta)
*
* The estimated theta is phase-shifted due to low pass filtration, so we
* need some phase compensation. More details below.
*
* where:
* v_s - phase input voltage vector
* i_s. - estimated phase current vector
* i_s - phase current vector
* e_s. - estimated phase BEMF vector
* R - motor winding resistance
* L - motor winding inductance
* z - output correction factor voltage
*
* Input Parameters:
* o - (in/out) pointer to the angle observer data
* i_ab - (in) inverter alpha-beta current
* v_ab - (in) inverter alpha-beta voltage
* phy - (in) pointer to the motor physical parameters
* dir - (in) rotation direction (1.0 for CCW, -1.0 for CW)
* NOTE: (mechanical dir) = -(electrical dir)
* speed - (in) electrical speed
* TODO: pass rotation direction with speed sign
*
* Returned Value:
* None
*
****************************************************************************/
void motor_aobserver_smo(FAR struct motor_aobserver_f32_s *o,
FAR ab_frame_f32_t *i_ab, FAR ab_frame_f32_t *v_ab,
FAR struct motor_phy_params_f32_s *phy, float dir,
float speed)
{
LIBDSP_DEBUGASSERT(o != NULL);
LIBDSP_DEBUGASSERT(i_ab != NULL);
LIBDSP_DEBUGASSERT(v_ab != NULL);
LIBDSP_DEBUGASSERT(phy != NULL);
FAR struct motor_aobserver_smo_f32_s *smo =
(FAR struct motor_aobserver_smo_f32_s *)o->ao;
FAR ab_frame_f32_t *emf = &smo->emf;
FAR ab_frame_f32_t *emf_f = &smo->emf_f;
FAR ab_frame_f32_t *z = &smo->z;
FAR ab_frame_f32_t *i_est = &smo->i_est;
FAR ab_frame_f32_t *v_err = &smo->v_err;
FAR ab_frame_f32_t *i_err = &smo->i_err;
FAR ab_frame_f32_t *sign = &smo->sign;
float i_err_a_abs = 0.0f;
float i_err_b_abs = 0.0f;
float angle = 0.0f;
float filter = 0.0f;
LIBDSP_DEBUGASSERT(smo != NULL);
/* REVISIT: observer works only when IQ current is high enough
* Lower IQ current -> lower K_SLIDE
*/
/* Calculate observer gains */
smo->F = (1.0f - o->per * phy->res * phy->one_by_ind);
smo->G = o->per * phy->one_by_ind;
/* Saturate F gain */
if (smo->F < 0.0f)
{
smo->F = 0.0f;
}
/* Saturate G gain */
if (smo->G > 0.999f)
{
smo->G = 0.999f;
}
/* Configure low pass filters
*
* We tune low-pass filters to achieve cutoff frequency equal to
* input signal frequency. This gives us constant phase shift between
* input and output signals equals to:
*
* phi = -arctan(f_in/f_c) = -arctan(1) = -45deg = -PI/4
*
* Input signal frequency is equal to the frequency of the motor currents,
* which give us:
*
* f_c = omega_e/(2*PI)
* omega_m = omega_e/pole_pairs
* f_c = omega_m*pole_pairs/(2*PI)
*
* filter = T * (2*PI) * f_c
* filter = T * omega_m * pole_pairs
*
* T - [s] period at which the digital filter is being
* calculated
* f_in - [Hz] input frequency of the filter
* f_c - [Hz] cutoff frequency of the filter
* omega_m - [rad/s] mechanical angular velocity
* omega_e - [rad/s] electrical angular velocity
* pole_pairs - pole pairs
*
*/
filter = o->per * speed * phy->p;
/* Limit SMO filters
* REVISIT: lowest filter limit should depend on minimum speed:
* filter = T * (2*PI) * f_c = T * omega0
*
*/
if (filter >= 1.0f)
{
filter = 0.99f;
}
else if (filter < 0.005f)
{
filter = 0.005f;
}
smo->emf_lp_filter1 = filter;
smo->emf_lp_filter2 = smo->emf_lp_filter1;
/* Get voltage error: v_err = v_ab - emf */
v_err->a = v_ab->a - emf->a;
v_err->b = v_ab->b - emf->b;
/* Estimate stator current */
i_est->a = smo->F * i_est->a + smo->G * (v_err->a - z->a);
i_est->b = smo->F * i_est->b + smo->G * (v_err->b - z->b);
/* Get motor current error */
i_err->a = i_ab->a - i_est->a;
i_err->b = i_ab->b - i_est->b;
/* Slide-mode controller */
sign->a = (i_err->a > 0.0f ? 1.0f : -1.0f);
sign->b = (i_err->b > 0.0f ? 1.0f : -1.0f);
/* Get current error absolute value - just multiply value with its sign */
i_err_a_abs = i_err->a * sign->a;
i_err_b_abs = i_err->b * sign->b;
/* Calculate new output correction factor voltage */
if (i_err_a_abs < smo->err_max)
{
/* Enter linear region if error is small enough */
z->a = i_err->a * smo->k_slide * smo->one_by_err_max;
}
else
{
/* Non-linear region */
z->a = sign->a * smo->k_slide;
}
if (i_err_b_abs < smo->err_max)
{
/* Enter linear region if error is small enough */
z->b = i_err->b * smo->k_slide * smo->one_by_err_max;
}
else
{
/* Non-linear region */
z->b = sign->b * smo->k_slide;
}
/* Filter z to obtain estimated emf */
LP_FILTER(emf->a, z->a, smo->emf_lp_filter1);
LP_FILTER(emf->b, z->b, smo->emf_lp_filter1);
/* Filter emf one more time before angle stimation */
LP_FILTER(emf_f->a, emf->a, smo->emf_lp_filter2);
LP_FILTER(emf_f->b, emf->b, smo->emf_lp_filter2);
/* Estimate phase angle according to:
* emf_a = -|emf| * sin(th)
* emf_b = |emf| * cos(th)
* th = atan2(-emf_a, emf->b)
*
* NOTE: bottleneck but we can't do much more to optimise this
*/
angle = fast_atan2(-emf->a, emf->b);
/* Angle compensation.
* Due to low pass filtering we have some delay in estimated phase angle.
*
* Adaptive filters introduced above cause -PI/4 phase shift for each
* filter. We use 2 times filtering which give us constant -PI/2 (-90deg)
* phase shift.
*/
angle = angle + dir * M_PI_2_F;
/* Normalize angle to range <0, 2PI> */
angle_norm_2pi(&angle, 0.0f, 2.0f*M_PI_F);
/* Store estimated angle in observer data */
o->angle = angle;
}
/****************************************************************************
* Name: motor_sobserver_div_init
*
* Description:
* Initialize DIV speed observer
*
* Input Parameters:
* so - (in/out) pointer to the DIV speed observer data
* sample - (in) number of angle samples
* filter - (in) low-pass filter for final omega
* per - (in) speed observer execution period
*
* Returned Value:
* None
*
****************************************************************************/
void motor_sobserver_div_init(FAR struct motor_sobserver_div_f32_s *so,
uint8_t samples, float filter, float per)
{
LIBDSP_DEBUGASSERT(so != NULL);
LIBDSP_DEBUGASSERT(samples > 0);
LIBDSP_DEBUGASSERT(filter > 0.0f);
/* Reset observer data */
memset(so, 0, sizeof(struct motor_sobserver_div_f32_s));
/* Store number of samples for DIV observer */
so->samples = samples;
/* Store low-pass filter for DIV observer speed */
so->filter = filter;
/* Store inverted sampling period */
so->one_by_dt = 1.0f / (so->samples * per);
}
/****************************************************************************
* Name: motor_sobserver_div
*
* Description:
* Estimate motor speed based on motor angle difference (electrical
* or mechanical)
*
* Input Parameters:
* o - (in/out) pointer to the speed observer data
* angle - (in) angle normalized to <0.0, 2PI>
* dir - (in) rotation direction. Valid values:
* DIR_CW (1.0f) or DIR_CCW(-1.0f)
*
****************************************************************************/
void motor_sobserver_div(FAR struct motor_sobserver_f32_s *o, float angle)
{
LIBDSP_DEBUGASSERT(o != NULL);
LIBDSP_DEBUGASSERT(angle >= 0.0f && angle <= 2*M_PI_F);
FAR struct motor_sobserver_div_f32_s *so =
(FAR struct motor_sobserver_div_f32_s *)o->so;
volatile float omega = 0.0f;
LIBDSP_DEBUGASSERT(so != NULL);
/* Normalize angle to range <-PI, PI> */
angle_norm_2pi(&angle, -M_PI_F, M_PI_F);
/* Get angle diff */
so->angle_diff = angle - so->angle_prev;
/* Normalize angle to range <-PI, PI> */
angle_norm_2pi(&so->angle_diff, -M_PI_F, M_PI_F);
/* Accumulate angle only if sample is valid */
so->angle_acc += so->angle_diff;
/* Increase counter */
so->cntr += 1;
/* Accumulate angle until we get configured number of samples */
if (so->cntr >= so->samples)
{
/* Estimate omega using accumulated angle samples.
* In this case use simple estimation:
*
* omega = delta_theta/delta_time
* speed_now = low_pass(omega)
*
*/
omega = so->angle_acc*so->one_by_dt;
/* Store filtered omega.
*
* REVISIT: cut-off frequency for this filter should be
* (probably) set according to minimum supported omega:
*
* filter = T * (2*PI) * f_c = T * omega0
*
* where:
* omega0 - minimum angular speed
* T - speed estimation period (samples*per)
*/
LP_FILTER(o->speed, omega, so->filter);
/* Reset samples counter and accumulated angle */
so->cntr = 0;
so->angle_acc = 0.0f;
}
/* Store current angle as previous angle */
so->angle_prev = angle;
}
/****************************************************************************
* Name: motor_aobserver_nfo_init
*
* Description:
* Initialize motor nolinear fluxlink observer.
*
* Input Parameters:
* nfo - pointer to the nolinear fluxlink observer private data
*
* Returned Value:
* None
*
****************************************************************************/
void motor_aobserver_nfo_init(FAR struct motor_aobserver_nfo_f32_s *nfo)
{
LIBDSP_DEBUGASSERT(nfo != NULL);
/* Reset structure */
memset(nfo, 0, sizeof(struct motor_aobserver_nfo_f32_s));
}
/****************************************************************************
* Name: motor_aobserver_nfo
*
* Description:
* nolinear fluxlink observer.
* REFERENCE: http://cas.ensmp.fr/~praly/Telechargement/Journaux/
* 2010-IEEE_TPEL-Lee-Hong-Nam-Ortega-Praly-Astolfi.pdf
*
* Input Parameters:
* o - (in/out) pointer to the angle observer data
* i_ab - (in) inverter alpha-beta current
* v_ab - (in) inverter alpha-beta voltage
* phy - (in) pointer to the motor physical parameters
* gain - (in) dynamic observer gain
*
* Returned Value:
* None
*
****************************************************************************/
void motor_aobserver_nfo(FAR struct motor_aobserver_f32_s *o,
FAR ab_frame_f32_t *i_ab, FAR ab_frame_f32_t *v_ab,
FAR struct motor_phy_params_f32_s *phy, float gain)
{
FAR struct motor_aobserver_nfo_f32_s *nfo =
(FAR struct motor_aobserver_nfo_f32_s *)o->ao;
float angle;
float err;
float x1_dot;
float x2_dot;
float l_ia = (3.0f / 2.0f) * phy->ind * i_ab->a;
float l_ib = (3.0f / 2.0f) * phy->ind * i_ab->b;
float r_ia = (3.0f / 2.0f) * phy->res * i_ab->a;
float r_ib = (3.0f / 2.0f) * phy->res * i_ab->b;
LIBDSP_DEBUGASSERT(nfo != NULL);
err = SQ(phy->flux_link) - (SQ(nfo->x1 - l_ia) + SQ(nfo->x2 - l_ib));
/* Forcing this term to stay negative helps convergence according to
* http://cas.ensmp.fr/Publications/Publications/Papers/
* ObserverPermanentMagnet.pdf and
* https://arxiv.org/pdf/1905.00833.pdf
*/
if (err > 0.0f)
{
err = 0.0f;
}
x1_dot = -r_ia + v_ab->a + gain * (nfo->x1 - l_ia) * err;
x2_dot = -r_ib + v_ab->b + gain * (nfo->x2 - l_ib) * err;
nfo->x1 += x1_dot * o->per;
nfo->x2 += x2_dot * o->per;
NAN_ZERO(nfo->x1);
NAN_ZERO(nfo->x2);
/* Prevent the magnitude from getting too low
* as that makes the angle very unstable.
*/
if (vector2d_mag(nfo->x1, nfo->x2) < (phy->flux_link * 0.5f))
{
nfo->x1 *= 1.1f;
nfo->x2 *= 1.1f;
}
angle = fast_atan2(nfo->x2 - l_ib, nfo->x1 - l_ia);
/* Normalize angle to range <0, 2PI> */
angle_norm_2pi(&angle, 0.0f, 2.0f * M_PI_F);
/* Store estimated angle in observer data */
o->angle = angle;
}
/****************************************************************************
* Name: motor_sobserver_pll_init
*
* Description:
* Initialize PLL speed observer
*
* Input Parameters:
* so - (in/out) pointer to the PLL speed observer data
* pll_kp - (in) pll proportional gain
* pll_ki - (in) pll integral gain
*
* Returned Value:
* None
*
****************************************************************************/
void motor_sobserver_pll_init(FAR struct motor_sobserver_pll_f32_s *so,
float pll_kp, float pll_ki)
{
LIBDSP_DEBUGASSERT(so != NULL);
LIBDSP_DEBUGASSERT(pll_kp > 0.0f);
LIBDSP_DEBUGASSERT(pll_ki > 0.0f);
/* Reset observer data */
memset(so, 0, sizeof(struct motor_sobserver_pll_f32_s));
/* Store kp for PLL observer */
so->pll_kp = pll_kp;
/* Store ki for PLL observer speed */
so->pll_ki = pll_ki;
}
/****************************************************************************
* Name: motor_sobserver_pll
*
* Description:
* Estimate motor electrical speed based on motor electrical angle
* difference.
*
* Input Parameters:
* o - (in/out) pointer to the speed observer data
* angle - (in) electrical angle normalized to <0.0, 2PI>
*
****************************************************************************/
void motor_sobserver_pll(FAR struct motor_sobserver_f32_s *o, float angle)
{
FAR struct motor_sobserver_pll_f32_s *so =
(FAR struct motor_sobserver_pll_f32_s *)o->so;
float delta_theta = 0.0f;
LIBDSP_DEBUGASSERT(so != NULL);
NAN_ZERO(so->pll_phase);
/* Normalize angle to range <-PI, PI> */
angle_norm_2pi(&angle, -M_PI_F, -M_PI_F);
delta_theta = angle - so->pll_phase;
/* Normalize angle to range <-PI, PI> */
angle_norm_2pi(&delta_theta, -M_PI_F, -M_PI_F);
NAN_ZERO(o->speed);
so->pll_phase += (o->speed + so->pll_kp * delta_theta) * o->per;
/* Normalize angle to range <-PI, PI> */
angle_norm_2pi(&so->pll_phase, -M_PI_F, -M_PI_F);
o->speed += so->pll_ki * delta_theta * o->per;
}
/****************************************************************************
* Name: motor_sobserver_speed_get
*
* Description:
* Get the estmiated motor speed from the observer
*
* Input Parameters:
* o - (in/out) pointer to the speed observer data
*
* Returned Value:
* Return estimated motor speed from observer
*
****************************************************************************/
float motor_sobserver_speed_get(FAR struct motor_sobserver_f32_s *o)
{
LIBDSP_DEBUGASSERT(o != NULL);
return o->speed;
}
/****************************************************************************
* Name: motor_aobserver_angle_get
*
* Description:
* Get the estmiated motor electrical angle from the observer
*
* Input Parameters:
* o - (in/out) pointer to the angle observer data
*
* Returned Value:
* Return estimated motor electrical angle from observer
*
****************************************************************************/
float motor_aobserver_angle_get(FAR struct motor_aobserver_f32_s *o)
{
LIBDSP_DEBUGASSERT(o != NULL);
return o->angle;
}
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