RT2_Cuboid_demo / Mbed 2 deprecated nucf446-test_GPA

Test of pmic GPA with filter

Dependencies:   mbed

Fork of nucf446-cuboid-balance1_strong by RT2_Cuboid_demo

GPA.cpp@23:26a1ccd0a856, 2018-04-09 (annotated)

Committer:
pmic
Date:
Mon Apr 09 15:09:54 2018 +0000
Revision:
23:26a1ccd0a856
Parent:
22:715d351d0be7
Child:
24:33ded7d7bcbd
simulation have shown that gpa should be calculated in double prescision

Who changed what in which revision?

UserRevisionLine numberNew contents of line
pmic 8:d68e177e2571 1 /*
pmic 8:d68e177e2571 2 GPA: frequency point wise gain and phase analyser to measure the frequency
pmic 23:26a1ccd0a856 3 respone of a dynamical system
pmic 16:e6fc0af484c2 4
pmic 8:d68e177e2571 5 hint: the measurements should only be perfomed in closed loop
pmic 8:d68e177e2571 6 assumption: the system is at the desired steady state of interest when
pmic 8:d68e177e2571 7 the measurment starts
pmic 16:e6fc0af484c2 8
pmic 8:d68e177e2571 9 exc(2) C: controller
pmic 8:d68e177e2571 10 | P: plant
pmic 16:e6fc0af484c2 11 v
pmic 8:d68e177e2571 12 exc(1) --> o ->| C |--->o------->| P |----------> out
pmic 8:d68e177e2571 13 ^ | |
pmic 8:d68e177e2571 14 | --> inp | exc: excitation signal (E)
pmic 8:d68e177e2571 15 | | inp: input plant (U)
pmic 8:d68e177e2571 16 -------------------------------- out: output plant (Y)
pmic 16:e6fc0af484c2 17
pmic 8:d68e177e2571 18 instantiate option 1:
pmic 8:d68e177e2571 19 GPA(float fMin, float fMax, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1)
pmic 16:e6fc0af484c2 20
pmic 8:d68e177e2571 21 fMin: minimal desired frequency that should be measured in Hz
pmic 8:d68e177e2571 22 fMax: maximal desired frequency that should be measured in Hz
pmic 8:d68e177e2571 23 NfexcDes: number of logarithmic equaly spaced frequency points
pmic 8:d68e177e2571 24 NperMin: minimal number of periods that are used for each frequency point
pmic 23:26a1ccd0a856 25 NmeasMin: minimal number of samples that are used for each frequency point
pmic 8:d68e177e2571 26 Ts: sampling time
pmic 16:e6fc0af484c2 27 Aexc0: excitation amplitude at fMin
pmic 8:d68e177e2571 28 Aexc1: excitation amplitude at fMax
pmic 16:e6fc0af484c2 29
pmic 8:d68e177e2571 30 hints: the amplitude drops with 1/fexc, if you're using
pmic 23:26a1ccd0a856 31 Axc1 = Aexc0/fMax then d/dt exc = const., this is recommended
pmic 8:d68e177e2571 32 if your controller does not have a rolloff.
pmic 8:d68e177e2571 33 if a desired frequency point is not measured try to increase Nmeas.
pmic 16:e6fc0af484c2 34
pmic 23:26a1ccd0a856 35 pseudo code for a closed loop measurement with a controller C:
pmic 16:e6fc0af484c2 36
pmic 8:d68e177e2571 37 excitation input at (1):
pmic 23:26a1ccd0a856 38
pmic 23:26a1ccd0a856 39 - measuring the plant P and the closed loop tf T = PC/(1 + PC):
pmic 23:26a1ccd0a856 40 desTorque = pi_w(omega_desired - omega + excWobble);
pmic 23:26a1ccd0a856 41 inpWobble = desTorque;
pmic 23:26a1ccd0a856 42 outWobble = omega;
pmic 23:26a1ccd0a856 43 excWobble = Wobble(excWobble, outWobble);
pmic 23:26a1ccd0a856 44
pmic 23:26a1ccd0a856 45 - measuring the controller C and the closed loop tf SC = C/(1 + PC)
pmic 23:26a1ccd0a856 46 desTorque = pi_w(omega_desired - omega + excWobble);
pmic 23:26a1ccd0a856 47 inpWobble = n_soll + excWobble - omega;
pmic 23:26a1ccd0a856 48 outWobble = desTorque;
pmic 23:26a1ccd0a856 49 excWobble = Wobble(inpWobble, outWobble);
pmic 16:e6fc0af484c2 50
pmic 8:d68e177e2571 51 excitation input at (2):
pmic 23:26a1ccd0a856 52
pmic 23:26a1ccd0a856 53 - measuring the plant P and the closed loop tf SP = P/(1 + PC):
pmic 23:26a1ccd0a856 54 desTorque = pi_w(omega_desired - omega) + excWobble;
pmic 23:26a1ccd0a856 55 inpWobble = desTorque;
pmic 23:26a1ccd0a856 56 outWobble = omega;
pmic 23:26a1ccd0a856 57 excWobble = Wobble(excWobble, outWobble);
pmic 16:e6fc0af484c2 58
pmic 8:d68e177e2571 59 usage:
pmic 23:26a1ccd0a856 60 exc(k+1) = myGPA(inp(k), out(k)) does update the internal states of the
pmic 23:26a1ccd0a856 61 gpa at the timestep k and returns the excitation signal for the timestep
pmic 23:26a1ccd0a856 62 k+1. the results are plotted to a terminal (putty) over a serial
pmic 23:26a1ccd0a856 63 connection and look as follows:
pmic 8:d68e177e2571 64 -----------------------------------------------------------------------------------------
pmic 8:d68e177e2571 65 fexc[Hz] |Gyu| ang(Gyu) |Gye| ang(Gye) |E| |U| |Y|
pmic 8:d68e177e2571 66 -----------------------------------------------------------------------------------------
pmic 23:26a1ccd0a856 67 1.000e+00 2.924e+01 -1.572e+00 1.017e+00 -4.983e-02 5.000e+00 1.739e-01 5.084e+00
pmic 16:e6fc0af484c2 68
pmic 8:d68e177e2571 69 in matlab you can use:
pmic 8:d68e177e2571 70 dataNucleo = [... insert measurement data here ...];
pmic 8:d68e177e2571 71 g = frd(dataNucleo(:,2).*exp(1i*dataNucleo(:,3)), dataNucleo(:,1), Ts, 'Units', 'Hz');
pmic 8:d68e177e2571 72 gcl = frd(dataNucleo(:,4).*exp(1i*dataNucleo(:,5)), dataNucleo(:,1), Ts, 'Units', 'Hz');
pmic 16:e6fc0af484c2 73
pmic 8:d68e177e2571 74 if you're evaluating more than one measurement which contain equal frequency points try:
pmic 8:d68e177e2571 75 dataNucleo = [dataNucleo1; dataNucleo2];
pmic 8:d68e177e2571 76 [~, ind] = unique(dataNucleo(:,1),'stable');
pmic 8:d68e177e2571 77 dataNucleo = dataNucleo(ind,:);
pmic 16:e6fc0af484c2 78
pmic 8:d68e177e2571 79 autor: M.E. Peter
pmic 16:e6fc0af484c2 80 */
pmic 8:d68e177e2571 81
pmic 6:da0c9587ecae 82 #include "GPA.h"
pmic 6:da0c9587ecae 83 #include "mbed.h"
pmic 6:da0c9587ecae 84 #include "math.h"
pmic 22:715d351d0be7 85 #define pi 3.141592653589793
pmic 6:da0c9587ecae 86
pmic 6:da0c9587ecae 87 using namespace std;
pmic 6:da0c9587ecae 88
pmic 6:da0c9587ecae 89 GPA::GPA(float fMin, float fMax, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1)
pmic 6:da0c9587ecae 90 {
pmic 6:da0c9587ecae 91 this->NfexcDes = NfexcDes;
pmic 6:da0c9587ecae 92 this->NperMin = NperMin;
pmic 6:da0c9587ecae 93 this->NmeasMin = NmeasMin;
pmic 22:715d351d0be7 94 this->Ts = (double)Ts;
pmic 6:da0c9587ecae 95
pmic 6:da0c9587ecae 96 // calculate logarithmic spaced frequency points
pmic 22:715d351d0be7 97 fexcDes = (double*)malloc(NfexcDes*sizeof(double));
pmic 22:715d351d0be7 98 fexcDesLogspace((double)fMin, (double)fMax, NfexcDes);
pmic 6:da0c9587ecae 99
pmic 6:da0c9587ecae 100 // calculate coefficients for decreasing amplitude (1/fexc)
pmic 22:715d351d0be7 101 this->aAexcDes = ((double)Aexc1 - (double)Aexc0)/(1.0/fexcDes[NfexcDes-1] - 1.0/fexcDes[0]);
pmic 22:715d351d0be7 102 this->bAexcDes = (double)Aexc0 - aAexcDes/fexcDes[0];
pmic 6:da0c9587ecae 103
pmic 22:715d351d0be7 104 fnyq = 1.0/2.0/(double)Ts;
pmic 22:715d351d0be7 105 pi2 = 2.0*pi;
pmic 22:715d351d0be7 106 pi2Ts = pi2*(double)Ts;
pmic 22:715d351d0be7 107 piDiv2 = pi/2.0;
pmic 6:da0c9587ecae 108
pmic 22:715d351d0be7 109 sU = (double*)malloc(3*sizeof(double));
pmic 22:715d351d0be7 110 sY = (double*)malloc(3*sizeof(double));
pmic 6:da0c9587ecae 111 reset();
pmic 6:da0c9587ecae 112 }
pmic 6:da0c9587ecae 113
pmic 6:da0c9587ecae 114 GPA::~GPA() {}
pmic 6:da0c9587ecae 115
pmic 6:da0c9587ecae 116 void GPA::reset()
pmic 6:da0c9587ecae 117 {
pmic 6:da0c9587ecae 118 Nmeas = 0;
pmic 6:da0c9587ecae 119 Nper = 0;
pmic 22:715d351d0be7 120 fexc = 0.0;
pmic 22:715d351d0be7 121 fexcPast = 0.0;
pmic 6:da0c9587ecae 122 ii = 1; // iterating through desired frequency points
pmic 6:da0c9587ecae 123 jj = 1; // iterating through measurement points w.r.t. reachable frequency
pmic 22:715d351d0be7 124 scaleG = 0.0;
pmic 22:715d351d0be7 125 cr = 0.0;
pmic 22:715d351d0be7 126 ci = 0.0;
pmic 6:da0c9587ecae 127 for(int i = 0; i < 3; i++) {
pmic 22:715d351d0be7 128 sU[i] = 0.0;
pmic 22:715d351d0be7 129 sY[i] = 0.0;
pmic 6:da0c9587ecae 130 }
pmic 22:715d351d0be7 131 sinarg = 0.0;
pmic 6:da0c9587ecae 132 NmeasTotal = 0;
pmic 22:715d351d0be7 133 Aexc = 0.0;
pmic 22:715d351d0be7 134 pi2Tsfexc = 0.0;
pmic 6:da0c9587ecae 135 }
pmic 6:da0c9587ecae 136
pmic 22:715d351d0be7 137 float GPA::update(double inp, double out)
pmic 6:da0c9587ecae 138 {
pmic 6:da0c9587ecae 139 // a new frequency point has been reached
pmic 6:da0c9587ecae 140 if(jj == 1) {
pmic 6:da0c9587ecae 141 // get a new unique frequency point
pmic 6:da0c9587ecae 142 while(fexc == fexcPast) {
pmic 6:da0c9587ecae 143 // measurement finished
pmic 6:da0c9587ecae 144 if(ii > NfexcDes) {
pmic 6:da0c9587ecae 145 return 0.0f;
pmic 6:da0c9587ecae 146 }
pmic 6:da0c9587ecae 147 calcGPAmeasPara(fexcDes[ii - 1]);
pmic 6:da0c9587ecae 148 // secure fexc is not higher or equal to nyquist frequency
pmic 6:da0c9587ecae 149 if(fexc >= fnyq) {
pmic 6:da0c9587ecae 150 fexc = fexcPast;
pmic 6:da0c9587ecae 151 }
pmic 6:da0c9587ecae 152 // no frequency found
pmic 6:da0c9587ecae 153 if(fexc == fexcPast) {
pmic 6:da0c9587ecae 154 ii += 1;
pmic 6:da0c9587ecae 155 } else {
pmic 6:da0c9587ecae 156 Aexc = aAexcDes/fexc + bAexcDes;
pmic 6:da0c9587ecae 157 pi2Tsfexc = pi2Ts*fexc;
pmic 6:da0c9587ecae 158 }
pmic 6:da0c9587ecae 159 }
pmic 16:e6fc0af484c2 160 // secure sinarg starts at 0 (numerically maybe not given)
pmic 22:715d351d0be7 161 sinarg = 0.0;
pmic 6:da0c9587ecae 162 // filter scaling
pmic 22:715d351d0be7 163 scaleG = 1.0/sqrt((double)Nmeas);
pmic 6:da0c9587ecae 164 // filter coefficients
pmic 6:da0c9587ecae 165 cr = cos(pi2Tsfexc);
pmic 6:da0c9587ecae 166 ci = sin(pi2Tsfexc);
pmic 6:da0c9587ecae 167 // filter storage
pmic 6:da0c9587ecae 168 for(int i = 0; i < 3; i++) {
pmic 22:715d351d0be7 169 sU[i] = 0.0;
pmic 22:715d351d0be7 170 sY[i] = 0.0;
pmic 6:da0c9587ecae 171 }
pmic 6:da0c9587ecae 172 }
pmic 6:da0c9587ecae 173 // filter step for signal su
pmic 22:715d351d0be7 174 sU[0] = scaleG*inp + 2.0*cr*sU[1] - sU[2];
pmic 6:da0c9587ecae 175 sU[2] = sU[1];
pmic 6:da0c9587ecae 176 sU[1] = sU[0];
pmic 6:da0c9587ecae 177 // filter step for signal sy
pmic 22:715d351d0be7 178 sY[0] = scaleG*out + 2.0*cr*sY[1] - sY[2];
pmic 6:da0c9587ecae 179 sY[2] = sY[1];
pmic 6:da0c9587ecae 180 sY[1] = sY[0];
pmic 6:da0c9587ecae 181 // measurement of frequencypoint is finished
pmic 6:da0c9587ecae 182 if(jj == Nmeas) {
pmic 6:da0c9587ecae 183 jj = 1;
pmic 7:87b823282bf0 184 ii += 1;
pmic 16:e6fc0af484c2 185 fexcPast = fexc;
pmic 6:da0c9587ecae 186 // calculate the one point dft
pmic 22:715d351d0be7 187 double Ureal = 2.0*scaleG*(cr*sU[1] - sU[2]);
pmic 22:715d351d0be7 188 double Uimag = 2.0*scaleG*ci*sU[1];
pmic 22:715d351d0be7 189 double Yreal = 2.0*scaleG*(cr*sY[1] - sY[2]);
pmic 22:715d351d0be7 190 double Yimag = 2.0*scaleG*ci*sY[1];
pmic 6:da0c9587ecae 191 // calculate magnitude and angle
pmic 22:715d351d0be7 192 float Umag = (float)(sqrt(Ureal*Ureal + Uimag*Uimag));
pmic 22:715d351d0be7 193 float Ymag = (float)(sqrt(Yreal*Yreal + Yimag*Yimag));
pmic 22:715d351d0be7 194 float absGyu = (float)(Ymag/Umag);
pmic 22:715d351d0be7 195 float angGyu = (float)(atan2(Yimag, Yreal) - atan2(Uimag, Ureal));
pmic 22:715d351d0be7 196 float absGye = (float)(Ymag/Aexc);
pmic 22:715d351d0be7 197 float angGye = (float)(atan2(Yimag, Yreal) + piDiv2);
pmic 6:da0c9587ecae 198 // user info
pmic 16:e6fc0af484c2 199 if(ii == 2) {
pmic 6:da0c9587ecae 200 printLine();
pmic 6:da0c9587ecae 201 printf(" fexc[Hz] |Gyu| ang(Gyu) |Gye| ang(Gye) |E| |U| |Y|\r\n");
pmic 6:da0c9587ecae 202 printLine();
pmic 6:da0c9587ecae 203 }
pmic 23:26a1ccd0a856 204 printf("%11.3e %10.3e %10.3e %10.3e %10.3e %10.3e %10.3e %10.3e\r\n", (float)fexc, absGyu, angGyu, absGye, angGye, (float)Aexc, Umag, Ymag);
pmic 6:da0c9587ecae 205 } else {
pmic 6:da0c9587ecae 206 jj += 1;
pmic 6:da0c9587ecae 207 }
pmic 6:da0c9587ecae 208 sinarg = fmod(sinarg + pi2Tsfexc, pi2);
pmic 6:da0c9587ecae 209 NmeasTotal += 1;
pmic 22:715d351d0be7 210 return (float)(Aexc*sin(sinarg));
pmic 6:da0c9587ecae 211 }
pmic 6:da0c9587ecae 212
pmic 22:715d351d0be7 213 void GPA::fexcDesLogspace(double fMin, double fMax, int NfexcDes)
pmic 6:da0c9587ecae 214 {
pmic 6:da0c9587ecae 215 // calculate logarithmic spaced frequency points
pmic 22:715d351d0be7 216 double Gain = log10(fMax/fMin)/((double)NfexcDes - 1.0);
pmic 22:715d351d0be7 217 double expon = 0.0;
pmic 6:da0c9587ecae 218 for(int i = 0; i < NfexcDes; i++) {
pmic 22:715d351d0be7 219 fexcDes[i] = fMin*pow(10.0, expon);
pmic 6:da0c9587ecae 220 expon += Gain;
pmic 6:da0c9587ecae 221 }
pmic 6:da0c9587ecae 222 }
pmic 6:da0c9587ecae 223
pmic 22:715d351d0be7 224 void GPA::calcGPAmeasPara(double fexcDes_i)
pmic 6:da0c9587ecae 225 {
pmic 6:da0c9587ecae 226 // Nmeas has to be an integer
pmic 6:da0c9587ecae 227 Nper = NperMin;
pmic 22:715d351d0be7 228 Nmeas = (int)floor((double)Nper/fexcDes_i/Ts + 0.5);
pmic 6:da0c9587ecae 229 // secure that the minimal number of measurements is fullfilled
pmic 6:da0c9587ecae 230 int Ndelta = NmeasMin - Nmeas;
pmic 6:da0c9587ecae 231 if(Ndelta > 0) {
pmic 22:715d351d0be7 232 Nper = (int)ceil((double)NmeasMin*fexcDes_i*Ts);
pmic 22:715d351d0be7 233 Nmeas = (int)floor((double)Nper/fexcDes_i/Ts + 0.5);
pmic 6:da0c9587ecae 234 }
pmic 6:da0c9587ecae 235 // evaluating reachable frequency
pmic 22:715d351d0be7 236 fexc = (double)Nper/(double)Nmeas/Ts;
pmic 6:da0c9587ecae 237 }
pmic 6:da0c9587ecae 238
pmic 6:da0c9587ecae 239 void GPA::printLine()
pmic 6:da0c9587ecae 240 {
pmic 6:da0c9587ecae 241 printf("-----------------------------------------------------------------------------------------\r\n");
pmic 6:da0c9587ecae 242 }
pmic 6:da0c9587ecae 243
pmic 6:da0c9587ecae 244 void GPA::printGPAfexcDes()
pmic 6:da0c9587ecae 245 {
pmic 6:da0c9587ecae 246 printLine();
pmic 6:da0c9587ecae 247 for(int i = 0; i < NfexcDes; i++) {
pmic 22:715d351d0be7 248 printf("%9.4f\r\n", (float)fexcDes[i]);
pmic 6:da0c9587ecae 249 }
pmic 6:da0c9587ecae 250 }
pmic 6:da0c9587ecae 251
pmic 6:da0c9587ecae 252 void GPA::printGPAmeasPara()
pmic 6:da0c9587ecae 253 {
pmic 6:da0c9587ecae 254 printLine();
pmic 6:da0c9587ecae 255 printf(" fexcDes[Hz] fexc[Hz] Aexc Nmeas Nper\r\n");
pmic 6:da0c9587ecae 256 printLine();
pmic 6:da0c9587ecae 257 for(int i = 0; i < NfexcDes; i++) {
pmic 6:da0c9587ecae 258 calcGPAmeasPara(fexcDes[i]);
pmic 6:da0c9587ecae 259 if(fexc == fexcPast || fexc >= fnyq) {
pmic 22:715d351d0be7 260 fexc = 0.0;
pmic 6:da0c9587ecae 261 Nmeas = 0;
pmic 6:da0c9587ecae 262 Nper = 0;
pmic 22:715d351d0be7 263 Aexc = 0.0;
pmic 6:da0c9587ecae 264 } else {
pmic 6:da0c9587ecae 265 Aexc = aAexcDes/fexc + bAexcDes;
pmic 6:da0c9587ecae 266 fexcPast = fexc;
pmic 6:da0c9587ecae 267 }
pmic 6:da0c9587ecae 268 NmeasTotal += Nmeas;
pmic 22:715d351d0be7 269 printf("%12.2e %9.2e %10.2e %7i %6i \r\n", (float)fexcDes[i], (float)fexc, (float)Aexc, Nmeas, Nper);
pmic 6:da0c9587ecae 270 }
pmic 6:da0c9587ecae 271 printGPAmeasTime();
pmic 6:da0c9587ecae 272 reset();
pmic 6:da0c9587ecae 273 }
pmic 6:da0c9587ecae 274
pmic 6:da0c9587ecae 275 void GPA::printGPAmeasTime()
pmic 6:da0c9587ecae 276 {
pmic 6:da0c9587ecae 277 printLine();
pmic 6:da0c9587ecae 278 printf(" number of data points: %9i\r\n", NmeasTotal);
pmic 22:715d351d0be7 279 printf(" measurment time in sec: %9.2f\r\n", (float)((double)NmeasTotal*Ts));
pmic 6:da0c9587ecae 280 }