altb_pmic
Control Library by altb
Dependents: My_Libraries IndNav_QK3_T265
Diff: GPA.cpp
- Revision:
- 0:d49418189c5c
- Child:
- 4:74a4318390ea
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/GPA.cpp Mon Mar 04 11:03:08 2019 +0000
@@ -0,0 +1,550 @@
+/*
+ GPA: Frequency point wise gain and phase analyser to measure the frequency respone function (FRF) of a dynamical system, based on the one point DFT
+
+ Hint: If the plant has a pole at zero, is unstable or weakly damped the measurement has to be perfomed
+ in closed loop (this is NOT tfestimate, the algorithm is based on the one point DFT).
+ Assumption: The system is and remains at the desired steady state of interest when the measurment starts
+
+ Instantiate option 0: ("Not a Jedi yet" users, for logarithmic equaly spaced frequency points)
+
+ GPA(float fMin, float fMax, int NfexcDes, float Aexc0, float Aexc1, float Ts)
+
+ fMin: Minimal desired frequency that should be measured in Hz
+ fMax: Maximal desired frequency that should be measured in Hz
+ NfexcDes: Number of logarithmic equaly spaced frequency points between fMin and fMax
+ Aexc0: Excitation amplitude at fMin
+ Aexc1: Excitation amplitude at fMax
+ Ts: Sampling time in sec
+
+ Default values are as follows:
+ int NperMin = 3;
+ int NmeasMin = (int)ceil(1.0f/Ts);
+ int NstartMin = (int)ceil(3.0f/Ts);
+ int NsweepMin = 0;
+
+ Instantiate option 1: ("Jedi or Sith Lord", for logarithmic equaly spaced frequency points)
+
+ GPA(float fMin, float fMax, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1, int NstartMin, int NsweepMin)
+
+ fMin: Minimal desired frequency that should be measured in Hz
+ fMax: Maximal desired frequency that should be measured in Hz
+ NfexcDes: Number of logarithmic equaly spaced frequency points
+ NperMin: Minimal number of periods that are used for each frequency point
+ NmeasMin: Minimal number of samples that are used for each frequency point
+ Ts: Sampling time in sec
+ Aexc0: Excitation amplitude at fMin
+ Aexc1: Excitation amplitude at fMax
+ NstartMin: Minimal number of samples to sweep to the first frequency point (can be equal 0)
+ NsweepMin: Minimal number of samples to sweep from freq. point to freq. point (can be equal 0)
+
+
+ Instantiate option 2: (for a second, refined frequency grid measurement)
+
+ GPA(float f0, float f1, float *fexcDes, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1, int NstartMin, int NsweepMin)
+
+ f0: Frequency point for the calculation of Aexc0 in Hz (should be chosen like in the first measurement)
+ f1: Frequency point for the calculation of Aexc1 in Hz (should be chosen like in the first measurement)
+ *fexcDes: Sorted frequency point array in Hz
+ NfexcDes: Length of fexcDes
+
+ For the other parameters see above.
+
+ Instantiate option 3: (for an arbitary but sorted frequency grid measurement)
+
+ GPA(float *fexcDes, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1, int NstartMin, int NsweepMin)
+
+ *fexcDes: Sorted frequency point array in Hz
+ Aexc0: Excitation amplitude at fexcDes[0]
+ Aexc1: Excitation amplitude at fexcDes[NfexcDes-1]
+ NfexcDes: Length of fexcDes
+
+ For the other parameters see above.
+
+ Note: The amplitude drops with 1/fexc, if you're using Axc1 = Aexc0/fMax then d/dt exc = const.,
+ this is recommended if your controller does not have a rolloff. If a desired frequency point
+ is not measured (could not be reached) try to increase Nmeas.
+
+
+ Block diagram:
+
+ w (const.) exc(2) C: controller
+ | | P: plant
+ v e v
+ exc(1) --> o ->| C |--->o------->| P |----------> out (y)
+ ^ - | |
+ | --> inp (u) | exc (R): excitation signal
+ | | inp (U): input plant
+ -------------------------------- out (Y): output plant
+
+
+ Pseudo code for an open loop measurement:
+
+ - Measuring the plant P = Gyu = Gyr:
+
+ u = w + exc;
+ ... write output u here! it follows exc(k+1) ...
+ exc = Wobble(exc, y);
+
+ Closed loop FRF calculus with a stabilizing controller C:
+ S = 1/(1 + C*P); % ( exc1 -> e , 1/(1 + C*P) ) contr. error rejection, robustness (1/max|S|)
+ T = 1 - S; % ( w -> y , C*P/(1 + C*P) ) tracking
+ CS = C*S; % ( exc1 -> u , C/(1 + C*P) ) disturbance plant output
+ PS = P*S; % ( exc2 -> y , P/(1 + C*P) ) disturbance plant input
+
+
+ Pseudo code for a closed loop measurement with stabilizing controller C:
+
+ Excitation at excitation input (1):
+
+ - Measuring the plant P = Gyu and the closed loop tf T = PC/(1 + PC) = Gyr:
+
+ u = C(w - y + exc);
+ ... write output u here! it follows exc(k+1) ...
+ exc = Wobble(u, y);
+
+ Closed loop FRF calculus:
+ S = 1 - T;
+ PS = P*S;
+ CS = T/P;
+ C = C/S;
+
+ Excitation at excitation input (2):
+
+ - Measuring the plant P = Gyu and the closed loop tf PS = P/(1 + PC) = Gyr:
+
+ u = C(w - y) + exc;
+ ... write output u here! it follows exc(k+1) ...
+ exc = Wobble(u, y);
+
+ Closed loop FRF calculus:
+ S = PS/P;
+ T = 1 - S;
+ CS = T/P;
+ C = C/S;
+
+
+ Usage:
+ exc(k+1) = myGPA(inp(k), out(k)) does update the internal states of the
+ gpa at the timestep k and returns the excitation signal for the timestep
+ k+1. The FRF data are plotted to a terminal (Putty) over a serial
+ connection and look as follows:
+
+--------------------------------------------------------------------------------
+ fexc[Hz] |Gyu| deg(Gyu) |Gyr| deg(Gyr) |U| |Y| |R|
+--------------------------------------------------------------------------------
+ 5.0000e-02 1.001e+00 -0.309 1.001e+00 -0.309 4.000e-01 4.000e-01 4.005e-01
+ . . . . . . . .
+ . . . . . . . .
+ . . . . . . . .
+
+ In Matlab you can use the editor as follows:
+ data = [... insert measurement data here ...];
+ gyu = frd(data(:,2).*exp(1i*data(:,3)*pi/180), data(:,1), Ts, 'Units', 'Hz');
+ gyr = frd(data(:,4).*exp(1i*data(:,5)*pi/180), data(:,1), Ts, 'Units', 'Hz');
+
+ If you're evaluating more than one measurement which contain equal frequency points use:
+ data = [data1; data2];
+ [~, ind] = unique(data(:,1), 'stable');
+ data = data(ind,:);
+
+
+ Autor and Copyrigth: 2018 / 2019 / M.E. Peter
+
+*/
+
+#include "GPA.h"
+#include "mbed.h"
+#include "math.h"
+#define pi 3.141592653589793
+
+using namespace std;
+
+// -----------------------------------------------------------------------------
+// instantiate
+// -----------------------------------------------------------------------------
+
+GPA::GPA(float fMin, float fMax, int NfexcDes, float Aexc0, float Aexc1, float Ts)
+{
+ int NperMin = 3;
+ int NmeasMin = (int)ceil(1.0f/Ts);
+ int NstartMin = (int)ceil(3.0f/Ts);
+ int NsweepMin = 0;
+
+ assignParameters(NfexcDes, NperMin, NmeasMin, (double)Ts, NstartMin, NsweepMin);
+
+ // calculate logarithmic spaced frequency points
+ fexcDes = (double*)malloc(NfexcDes*sizeof(double));
+ fexcDesLogspace((double)fMin, (double)fMax, NfexcDes);
+
+ calculateDecreasingAmplitudeCoefficients((double)Aexc0, (double)Aexc1);
+ initializeConstants((double)Ts);
+ assignFilterStorage();
+ reset();
+}
+
+GPA::GPA(float fMin, float fMax, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1, int NstartMin, int NsweepMin)
+{
+ assignParameters(NfexcDes, NperMin, NmeasMin, (double)Ts, NstartMin, NsweepMin);
+
+ // calculate logarithmic spaced frequency points
+ fexcDes = (double*)malloc(NfexcDes*sizeof(double));
+ fexcDesLogspace((double)fMin, (double)fMax, NfexcDes);
+
+ calculateDecreasingAmplitudeCoefficients((double)Aexc0, (double)Aexc1);
+ initializeConstants((double)Ts);
+ assignFilterStorage();
+ reset();
+}
+
+GPA::GPA(float f0, float f1, float *fexcDes, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1, int NstartMin, int NsweepMin)
+{
+ assignParameters(NfexcDes, NperMin, NmeasMin, (double)Ts, NstartMin, NsweepMin);
+
+ // convert fexcDes from float to double, it is assumed that it is sorted
+ this->fexcDes = (double*)malloc(NfexcDes*sizeof(double));
+ for(int i = 0; i < NfexcDes; i++) {
+ this->fexcDes[i] = (double)fexcDes[i];
+ }
+
+ calculateDecreasingAmplitudeCoefficients((double)Aexc0, (double)Aexc1);
+ initializeConstants((double)Ts);
+ assignFilterStorage();
+ reset();
+}
+
+GPA::GPA(float *fexcDes, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1, int NstartMin, int NsweepMin)
+{
+ assignParameters(NfexcDes, NperMin, NmeasMin, (double)Ts, NstartMin, NsweepMin);
+
+ // convert fexcDes from float to double, it is assumed that it is sorted
+ this->fexcDes = (double*)malloc(NfexcDes*sizeof(double));
+ for(int i = 0; i < NfexcDes; i++) {
+ this->fexcDes[i] = (double)fexcDes[i];
+ }
+
+ calculateDecreasingAmplitudeCoefficients((double)Aexc0, (double)Aexc1);
+ initializeConstants((double)Ts);
+ assignFilterStorage();
+ reset();
+}
+
+// -----------------------------------------------------------------------------
+// virtual and reset
+// -----------------------------------------------------------------------------
+
+GPA::~GPA() {}
+
+void GPA::reset()
+{
+ Nmeas = 0;
+ Nper = 0;
+ dfexc = 0.0;
+ fexc = 0.0;
+ fexcPast = 0.0;
+ i = 1; // iterating through desired frequency points
+ j = 1; // iterating through measurement points w.r.t. reachable frequency
+ scaleG = 0.0;
+ cr = 0.0;
+ ci = 0.0;
+ for(int i = 0; i < 3; i++) {
+ sU[i] = 0.0;
+ sY[i] = 0.0;
+ }
+ sinarg = 0.0;
+ NmeasTotal = 0;
+ Aexc = 0.0;
+ pi2Tsfexc = 0.0;
+ Nsweep = NstartMin;
+ bfexc = 0.0;
+ afexc = 0.0;
+ aAexc = 0.0;
+ bAexc = 0.0;
+ AexcOut = 0.0;
+}
+
+// -----------------------------------------------------------------------------
+// update (operator)
+// -----------------------------------------------------------------------------
+
+float GPA::update(double inp, double out)
+{
+ // a new frequency point has been reached
+ if(j == 1) {
+ // user info
+ if(i == 1) {
+ printLine();
+ printf(" fexc[Hz] |Gyu| deg(Gyu) |Gyr| deg(Gyr) |U| |Y| |R|\r\n");
+ printLine();
+ }
+ // get a new unique frequency point
+ while(fexc == fexcPast) {
+ // measurement finished
+ if(i > NfexcDes) {
+ return 0.0f;
+ }
+ calcGPAmeasPara(fexcDes[i - 1]);
+ // secure fexc is not higher or equal to nyquist frequency
+ if(fexc >= fnyq) {
+ fexc = fexcPast;
+ }
+ // no frequency found
+ if(fexc == fexcPast) {
+ i += 1;
+ } else {
+ Aexc = aAexcDes/fexc + bAexcDes;
+ pi2Tsfexc = pi2Ts*fexc;
+ }
+ }
+ // filter scaling
+ scaleG = 1.0/sqrt((double)Nmeas);
+ // filter coefficients
+ cr = cos(pi2Tsfexc);
+ ci = sin(pi2Tsfexc);
+ // set filter storage zero
+ for(int i = 0; i < 3; i++) {
+ sU[i] = 0.0;
+ sY[i] = 0.0;
+ }
+ // calculate the parameters for the frequency sweep from fexcPast to fexc
+ if(Nsweep > 0) calcGPAsweepPara();
+ }
+ // perfomre the sweep or measure
+ if(j <= Nsweep) {
+ dfexc = afexc*(double)j + bfexc;
+ AexcOut = aAexc*(double)j + bAexc;
+ } else {
+ dfexc = fexc;
+ AexcOut = Aexc;
+ // one point DFT filter step for signal su
+ sU[0] = scaleG*inp + 2.0*cr*sU[1] - sU[2];
+ sU[2] = sU[1];
+ sU[1] = sU[0];
+ // one point DFT filter step for signal sy
+ sY[0] = scaleG*out + 2.0*cr*sY[1] - sY[2];
+ sY[2] = sY[1];
+ sY[1] = sY[0];
+ }
+ // secure sinarg starts at 0 (numerically maybe not given)
+ if(j == 1 || j == Nsweep + 1) sinarg = 0.0;
+ // measurement of frequencypoint is finished
+ if(j == Nmeas + Nsweep) {
+ fexcPast = fexc;
+ AexcPast = Aexc;
+ Nsweep = NsweepMin;
+ // calculate the one point dft
+ double Ureal = 2.0*scaleG*(cr*sU[1] - sU[2]);
+ double Uimag = 2.0*scaleG*ci*sU[1];
+ double Yreal = 2.0*scaleG*(cr*sY[1] - sY[2]);
+ double Yimag = 2.0*scaleG*ci*sY[1];
+ // calculate magnitude and angle
+ float Umag = (float)(sqrt(Ureal*Ureal + Uimag*Uimag));
+ float Ymag = (float)(sqrt(Yreal*Yreal + Yimag*Yimag));
+ float absGyu = (float)(Ymag/Umag);
+ float angGyu = (float)wrapAngle(atan2(Yimag, Yreal) - atan2(Uimag, Ureal));
+ float absGyr = (float)(Ymag/Aexc);
+ float angGyr = (float)wrapAngle(atan2(Yimag, Yreal) + piDiv2);
+ // user info
+ printf("%11.4e %9.3e %8.3f %9.3e %8.3f %9.3e %9.3e %9.3e\r\n", (float)fexc, absGyu, angGyu*rad2deg, absGyr, angGyr*rad2deg, Umag, Ymag, (float)Aexc);
+ i += 1;
+ j = 1;
+ } else {
+ j += 1;
+ }
+ // calculate the excitation
+ sinarg = fmod(sinarg + pi2Ts*dfexc, pi2);
+ NmeasTotal += 1;
+ return (float)(AexcOut*sin(sinarg));
+}
+
+// -----------------------------------------------------------------------------
+// private functions
+// -----------------------------------------------------------------------------
+
+void GPA::assignParameters(int NfexcDes, int NperMin, int NmeasMin, double Ts, int NstartMin, int NsweepMin)
+{
+ this->NfexcDes = NfexcDes;
+ this->NperMin = NperMin;
+ this->NmeasMin = NmeasMin;
+ this->Ts = Ts;
+ this->NstartMin = NstartMin;
+ this->NsweepMin = NsweepMin;
+}
+
+void GPA::calculateDecreasingAmplitudeCoefficients(double Aexc0, double Aexc1)
+{
+ // calculate coefficients for decreasing amplitude (1/fexc)
+ this->aAexcDes = (Aexc1 - Aexc0)/(1.0/fexcDes[NfexcDes-1] - 1.0/fexcDes[0]);
+ this->bAexcDes = Aexc0 - aAexcDes/fexcDes[0];
+}
+
+void GPA::initializeConstants(double Ts)
+{
+ fnyq = 1.0/2.0/Ts;
+ pi2 = 2.0*pi;
+ pi2Ts = pi2*Ts;
+ piDiv2 = pi/2.0;
+ rad2deg = 180.0f/(float)pi;
+}
+
+void GPA::assignFilterStorage()
+{
+ sU = (double*)malloc(3*sizeof(double));
+ sY = (double*)malloc(3*sizeof(double));
+}
+
+void GPA::fexcDesLogspace(double fMin, double fMax, int NfexcDes)
+{
+ // calculate logarithmic spaced frequency points
+ double Gain = log10(fMax/fMin)/((double)NfexcDes - 1.0);
+ double expon = 0.0;
+ for(int i = 0; i < NfexcDes; i++) {
+ fexcDes[i] = fMin*pow(10.0, expon);
+ expon += Gain;
+ }
+}
+
+void GPA::calcGPAmeasPara(double fexcDes_i)
+{
+ // Nmeas has to be an integer
+ Nper = NperMin;
+ Nmeas = (int)floor((double)Nper/fexcDes_i/Ts + 0.5);
+ // secure that the minimal number of measurements is fullfilled
+ int Ndelta = NmeasMin - Nmeas;
+ if(Ndelta > 0) {
+ Nper = (int)ceil((double)NmeasMin*fexcDes_i*Ts);
+ Nmeas = (int)floor((double)Nper/fexcDes_i/Ts + 0.5);
+ }
+ // evaluating reachable frequency
+ fexc = (double)Nper/(double)Nmeas/Ts;
+}
+
+void GPA::calcGPAsweepPara()
+{
+ // calculate linear frequency sweep parameters
+ double ksta = ceil(Ts*(double)Nsweep/2.0*(fexc + fexcPast));
+ Nsweep = (int)floor(2.0*ksta/Ts/(fexc + fexcPast) + 0.5);
+ bfexc = 2.0*ksta/Ts/(double)Nsweep - fexc;
+ afexc = (fexc - bfexc)/((double)Nsweep + 1.0);
+ aAexc = (Aexc - AexcPast)/((double)Nsweep + 1.0);
+ bAexc = AexcPast;
+}
+
+double GPA::wrapAngle(double angle)
+{
+ // wrap angle from (-2pi,2pi) into (-pi,pi)
+ if(abs(angle) > pi) angle -= copysign(-pi2, angle); // -1*sign(angle)*2*pi + angle;
+ return angle;
+}
+
+void GPA::printLine()
+{
+ printf("--------------------------------------------------------------------------------\r\n");
+}
+
+void GPA::printLongLine()
+{
+ printf("-------------------------------------------------------------------------------------------------------\r\n");
+}
+
+// -----------------------------------------------------------------------------
+// public functions
+// -----------------------------------------------------------------------------
+
+void GPA::printGPAfexcDes()
+{
+ printLine();
+ for(int i = 0; i < NfexcDes; i++) {
+ printf("%9.4f\r\n", (float)fexcDes[i]);
+ }
+}
+
+void GPA::printGPAmeasPara()
+{
+ printLine();
+ printf(" fexcDes[Hz] fexc[Hz] Aexc Nmeas Nper Nsweep\r\n");
+ printLine();
+ for(int i = 0; i < NfexcDes; i++) {
+ calcGPAmeasPara(fexcDes[i]);
+ if(fexc == fexcPast || fexc >= fnyq) {
+ fexc = 0.0;
+ Aexc = 0.0;
+ Nmeas = 0;
+ Nper = 0;
+ Nsweep = 0;
+ afexc = 0.0;
+ bfexc = 0.0;
+ aAexc = 0.0;
+ bAexc = 0.0;
+
+ } else {
+ Aexc = aAexcDes/fexc + bAexcDes;
+ if(Nsweep > 0) calcGPAsweepPara();
+ else{
+ afexc = 0.0;
+ bfexc = 0.0;
+ aAexc = 0.0;
+ bAexc = 0.0;
+ }
+ fexcPast = fexc;
+ AexcPast = Aexc;
+ }
+ NmeasTotal += Nmeas;
+ NmeasTotal += Nsweep;
+ printf("%11.4e %12.4e %10.3e %7i %6i %7i\r\n", (float)fexcDes[i], (float)fexc, (float)Aexc, Nmeas, Nper, Nsweep);
+ Nsweep = NsweepMin;
+ }
+ printGPAmeasTime();
+ reset();
+}
+
+void GPA::printFullGPAmeasPara()
+{
+ printLongLine();
+ printf(" fexcDes[Hz] fexc[Hz] Aexc Nmeas Nper Nsweep afexc bfexc aAexc bAexc\r\n");
+ printLongLine();
+ for(int i = 0; i < NfexcDes; i++) {
+ calcGPAmeasPara(fexcDes[i]);
+ if(fexc == fexcPast || fexc >= fnyq) {
+ fexc = 0.0;
+ Aexc = 0.0;
+ Nmeas = 0;
+ Nper = 0;
+ Nsweep = 0;
+ afexc = 0.0;
+ bfexc = 0.0;
+ aAexc = 0.0;
+ bAexc = 0.0;
+
+ } else {
+ Aexc = aAexcDes/fexc + bAexcDes;
+ if(Nsweep > 0) calcGPAsweepPara();
+ else{
+ afexc = 0.0;
+ bfexc = 0.0;
+ aAexc = 0.0;
+ bAexc = 0.0;
+ }
+ fexcPast = fexc;
+ AexcPast = Aexc;
+ }
+ NmeasTotal += Nmeas;
+ NmeasTotal += Nsweep;
+ printf("%11.4e %12.4e %10.3e %7i %6i %7i %10.3e %10.3e %10.3e %10.3e\r\n", (float)fexcDes[i], (float)fexc, (float)Aexc, Nmeas, Nper, Nsweep, (float)afexc, (float)bfexc, (float)aAexc, (float)bAexc);
+ Nsweep = NsweepMin;
+ }
+ printGPAmeasTime();
+ reset();
+}
+
+void GPA::printGPAmeasTime()
+{
+ printLine();
+ printf(" Number of data points : %11i\r\n", NmeasTotal);
+ printf(" Measurment time in sec: %12.2f\r\n", (float)((double)NmeasTotal*Ts));
+}
+
+void GPA::printNfexcDes()
+{
+ printLine();
+ printf(" Number of frequancy points: %3i\r\n", NfexcDes);
+}