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GPA.cpp@0:78ca29b4c49e, 2018-04-03 (annotated)

Committer:
altb
Date:
Tue Apr 03 08:47:41 2018 +0000
Revision:
0:78ca29b4c49e
Child:
2:769ce5f06d3e
Cuboid Lab RT2 FS 2018

Who changed what in which revision?

UserRevisionLine numberNew contents of line
altb 0:78ca29b4c49e 1 /*
altb 0:78ca29b4c49e 2 GPA: frequency point wise gain and phase analyser to measure the frequency
altb 0:78ca29b4c49e 3 respone of dynamical system
altb 0:78ca29b4c49e 4
altb 0:78ca29b4c49e 5 hint: the measurements should only be perfomed in closed loop
altb 0:78ca29b4c49e 6 assumption: the system is at the desired steady state of interest when
altb 0:78ca29b4c49e 7 the measurment starts
altb 0:78ca29b4c49e 8
altb 0:78ca29b4c49e 9 exc(2) C: controller
altb 0:78ca29b4c49e 10 | P: plant
altb 0:78ca29b4c49e 11 v
altb 0:78ca29b4c49e 12 exc(1) --> o ->| C |--->o------->| P |----------> out
altb 0:78ca29b4c49e 13 ^ | |
altb 0:78ca29b4c49e 14 | --> inp | exc: excitation signal (E)
altb 0:78ca29b4c49e 15 | | inp: input plant (U)
altb 0:78ca29b4c49e 16 -------------------------------- out: output plant (Y)
altb 0:78ca29b4c49e 17
altb 0:78ca29b4c49e 18 instantiate option 1:
altb 0:78ca29b4c49e 19 GPA(float fMin, float fMax, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1)
altb 0:78ca29b4c49e 20
altb 0:78ca29b4c49e 21 fMin: minimal desired frequency that should be measured in Hz
altb 0:78ca29b4c49e 22 fMax: maximal desired frequency that should be measured in Hz
altb 0:78ca29b4c49e 23 NfexcDes: number of logarithmic equaly spaced frequency points
altb 0:78ca29b4c49e 24 NperMin: minimal number of periods that are used for each frequency point
altb 0:78ca29b4c49e 25 NmeasMin: maximal number of samples that are used for each frequency point
altb 0:78ca29b4c49e 26 Ts: sampling time
altb 0:78ca29b4c49e 27 Aexc0: excitation amplitude at fMin
altb 0:78ca29b4c49e 28 Aexc1: excitation amplitude at fMax
altb 0:78ca29b4c49e 29
altb 0:78ca29b4c49e 30 hints: the amplitude drops with 1/fexc, if you're using
altb 0:78ca29b4c49e 31 Axc1 = Aexc0/fMax the d/dt exc = const., this is recommended
altb 0:78ca29b4c49e 32 if your controller does not have a rolloff.
altb 0:78ca29b4c49e 33 if a desired frequency point is not measured try to increase Nmeas.
altb 0:78ca29b4c49e 34
altb 0:78ca29b4c49e 35 pseudo code for a closed loop measurement with a proportional controller Kp:
altb 0:78ca29b4c49e 36
altb 0:78ca29b4c49e 37 float inp = "measurement of inputsignal";
altb 0:78ca29b4c49e 38 float out = "mesurement of outputsignal";
altb 0:78ca29b4c49e 39 float exc = myGPA(inp, out);
altb 0:78ca29b4c49e 40 float off = "desired steady state off the system";
altb 0:78ca29b4c49e 41
altb 0:78ca29b4c49e 42 excitation input at (1):
altb 0:78ca29b4c49e 43 inp = Kp*(exc + off - out);
altb 0:78ca29b4c49e 44
altb 0:78ca29b4c49e 45 excitation input at (2):
altb 0:78ca29b4c49e 46 inp = Kp*(off - out) + exc;
altb 0:78ca29b4c49e 47
altb 0:78ca29b4c49e 48 usage:
altb 0:78ca29b4c49e 49 exc = myGPA(inp, out) does update the internal states of the gpa at the
altb 0:78ca29b4c49e 50 timestep k and returns the excitation signal for the timestep k+1. the
altb 0:78ca29b4c49e 51 results are plotted to a terminal (putty) over serial cennection and look
altb 0:78ca29b4c49e 52 as follows:
altb 0:78ca29b4c49e 53 -----------------------------------------------------------------------------------------
altb 0:78ca29b4c49e 54 fexc[Hz] |Gyu| ang(Gyu) |Gye| ang(Gye) |E| |U| |Y|
altb 0:78ca29b4c49e 55 -----------------------------------------------------------------------------------------
altb 0:78ca29b4c49e 56 7.01e-01 1.08e+01 -7.45e-02 1.08e+01 -7.38e-02 9.99e-01 9.99e-01 1.08e+01
altb 0:78ca29b4c49e 57
altb 0:78ca29b4c49e 58 in matlab you can use:
altb 0:78ca29b4c49e 59 dataNucleo = [... insert measurement data here ...];
altb 0:78ca29b4c49e 60 g = frd(dataNucleo(:,2).*exp(1i*dataNucleo(:,3)), dataNucleo(:,1), Ts, 'Units', 'Hz');
altb 0:78ca29b4c49e 61 gcl = frd(dataNucleo(:,4).*exp(1i*dataNucleo(:,5)), dataNucleo(:,1), Ts, 'Units', 'Hz');
altb 0:78ca29b4c49e 62
altb 0:78ca29b4c49e 63 if you're evaluating more than one measurement which contain equal frequency points try:
altb 0:78ca29b4c49e 64 dataNucleo = [dataNucleo1; dataNucleo2];
altb 0:78ca29b4c49e 65 [~, ind] = unique(dataNucleo(:,1),'stable');
altb 0:78ca29b4c49e 66 dataNucleo = dataNucleo(ind,:);
altb 0:78ca29b4c49e 67
altb 0:78ca29b4c49e 68 autor: M.E. Peter
altb 0:78ca29b4c49e 69 */
altb 0:78ca29b4c49e 70
altb 0:78ca29b4c49e 71 #include "GPA.h"
altb 0:78ca29b4c49e 72 #include "mbed.h"
altb 0:78ca29b4c49e 73 #include "math.h"
altb 0:78ca29b4c49e 74 #define pi 3.1415927f
altb 0:78ca29b4c49e 75
altb 0:78ca29b4c49e 76 using namespace std;
altb 0:78ca29b4c49e 77
altb 0:78ca29b4c49e 78 GPA::GPA(float fMin, float fMax, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1)
altb 0:78ca29b4c49e 79 {
altb 0:78ca29b4c49e 80 this->NfexcDes = NfexcDes;
altb 0:78ca29b4c49e 81 this->NperMin = NperMin;
altb 0:78ca29b4c49e 82 this->NmeasMin = NmeasMin;
altb 0:78ca29b4c49e 83 this->Ts = Ts;
altb 0:78ca29b4c49e 84
altb 0:78ca29b4c49e 85 // calculate logarithmic spaced frequency points
altb 0:78ca29b4c49e 86 fexcDes = (float*)malloc(NfexcDes*sizeof(float));
altb 0:78ca29b4c49e 87 fexcDesLogspace(fMin, fMax, NfexcDes);
altb 0:78ca29b4c49e 88
altb 0:78ca29b4c49e 89 // calculate coefficients for decreasing amplitude (1/fexc)
altb 0:78ca29b4c49e 90 this->aAexcDes = (Aexc1 - Aexc0)/(1.0f/fexcDes[NfexcDes-1] - 1.0f/fexcDes[0]);
altb 0:78ca29b4c49e 91 this->bAexcDes = Aexc0 - aAexcDes/fexcDes[0];
altb 0:78ca29b4c49e 92
altb 0:78ca29b4c49e 93 fnyq = 1/2.0f/Ts;
altb 0:78ca29b4c49e 94 pi2 = 2.0f*pi;
altb 0:78ca29b4c49e 95 pi2Ts = pi2*Ts;
altb 0:78ca29b4c49e 96 piDiv2 = pi/2.0f;
altb 0:78ca29b4c49e 97
altb 0:78ca29b4c49e 98 sU = (float*)malloc(3*sizeof(float));
altb 0:78ca29b4c49e 99 sY = (float*)malloc(3*sizeof(float));
altb 0:78ca29b4c49e 100 reset();
altb 0:78ca29b4c49e 101 }
altb 0:78ca29b4c49e 102
altb 0:78ca29b4c49e 103 GPA::~GPA() {}
altb 0:78ca29b4c49e 104
altb 0:78ca29b4c49e 105 void GPA::reset()
altb 0:78ca29b4c49e 106 {
altb 0:78ca29b4c49e 107 Nmeas = 0;
altb 0:78ca29b4c49e 108 Nper = 0;
altb 0:78ca29b4c49e 109 fexc = 0.0f;
altb 0:78ca29b4c49e 110 fexcPast = 0.0f;
altb 0:78ca29b4c49e 111 ii = 1; // iterating through desired frequency points
altb 0:78ca29b4c49e 112 jj = 1; // iterating through measurement points w.r.t. reachable frequency
altb 0:78ca29b4c49e 113 scaleG = 0.0f;
altb 0:78ca29b4c49e 114 cr = 0.0f;
altb 0:78ca29b4c49e 115 ci = 0.0f;
altb 0:78ca29b4c49e 116 for(int i = 0; i < 3; i++) {
altb 0:78ca29b4c49e 117 sU[i] = 0.0f;
altb 0:78ca29b4c49e 118 sY[i] = 0.0f;
altb 0:78ca29b4c49e 119 }
altb 0:78ca29b4c49e 120 sinarg = 0.0f;
altb 0:78ca29b4c49e 121 NmeasTotal = 0;
altb 0:78ca29b4c49e 122 Aexc = 0.0f;
altb 0:78ca29b4c49e 123 pi2Tsfexc = 0.0f;
altb 0:78ca29b4c49e 124 }
altb 0:78ca29b4c49e 125
altb 0:78ca29b4c49e 126 float GPA::update(float inp, float out)
altb 0:78ca29b4c49e 127 {
altb 0:78ca29b4c49e 128 // a new frequency point has been reached
altb 0:78ca29b4c49e 129 if(jj == 1) {
altb 0:78ca29b4c49e 130 // get a new unique frequency point
altb 0:78ca29b4c49e 131 while(fexc == fexcPast) {
altb 0:78ca29b4c49e 132 // measurement finished
altb 0:78ca29b4c49e 133 if(ii > NfexcDes) {
altb 0:78ca29b4c49e 134 return 0.0f;
altb 0:78ca29b4c49e 135 }
altb 0:78ca29b4c49e 136 calcGPAmeasPara(fexcDes[ii - 1]);
altb 0:78ca29b4c49e 137 // secure fexc is not higher or equal to nyquist frequency
altb 0:78ca29b4c49e 138 if(fexc >= fnyq) {
altb 0:78ca29b4c49e 139 fexc = fexcPast;
altb 0:78ca29b4c49e 140 }
altb 0:78ca29b4c49e 141 // no frequency found
altb 0:78ca29b4c49e 142 if(fexc == fexcPast) {
altb 0:78ca29b4c49e 143 ii += 1;
altb 0:78ca29b4c49e 144 } else {
altb 0:78ca29b4c49e 145 Aexc = aAexcDes/fexc + bAexcDes;
altb 0:78ca29b4c49e 146 pi2Tsfexc = pi2Ts*fexc;
altb 0:78ca29b4c49e 147 }
altb 0:78ca29b4c49e 148 }
altb 0:78ca29b4c49e 149 fexcPast = fexc;
altb 0:78ca29b4c49e 150 // filter scaling
altb 0:78ca29b4c49e 151 scaleG = 1.0f/sqrt((float)Nmeas);
altb 0:78ca29b4c49e 152 // filter coefficients
altb 0:78ca29b4c49e 153 cr = cos(pi2Tsfexc);
altb 0:78ca29b4c49e 154 ci = sin(pi2Tsfexc);
altb 0:78ca29b4c49e 155 // filter storage
altb 0:78ca29b4c49e 156 for(int i = 0; i < 3; i++) {
altb 0:78ca29b4c49e 157 sU[i] = 0.0f;
altb 0:78ca29b4c49e 158 sY[i] = 0.0f;
altb 0:78ca29b4c49e 159 }
altb 0:78ca29b4c49e 160 }
altb 0:78ca29b4c49e 161 // filter step for signal su
altb 0:78ca29b4c49e 162 sU[0] = scaleG*inp + 2.0f*cr*sU[1] - sU[2];
altb 0:78ca29b4c49e 163 sU[2] = sU[1];
altb 0:78ca29b4c49e 164 sU[1] = sU[0];
altb 0:78ca29b4c49e 165 // filter step for signal sy
altb 0:78ca29b4c49e 166 sY[0] = scaleG*out + 2.0f*cr*sY[1] - sY[2];
altb 0:78ca29b4c49e 167 sY[2] = sY[1];
altb 0:78ca29b4c49e 168 sY[1] = sY[0];
altb 0:78ca29b4c49e 169 // measurement of frequencypoint is finished
altb 0:78ca29b4c49e 170 if(jj == Nmeas) {
altb 0:78ca29b4c49e 171 jj = 1;
altb 0:78ca29b4c49e 172 ii += 1;
altb 0:78ca29b4c49e 173 // calculate the one point dft
altb 0:78ca29b4c49e 174 float Ureal = 2.0f*scaleG*(cr*sU[1] - sU[2]);
altb 0:78ca29b4c49e 175 float Uimag = 2.0f*scaleG*ci*sU[1];
altb 0:78ca29b4c49e 176 float Yreal = 2.0f*scaleG*(cr*sY[1] - sY[2]);
altb 0:78ca29b4c49e 177 float Yimag = 2.0f*scaleG*ci*sY[1];
altb 0:78ca29b4c49e 178 // calculate magnitude and angle
altb 0:78ca29b4c49e 179 float Umag = sqrt(Ureal*Ureal + Uimag*Uimag);
altb 0:78ca29b4c49e 180 float Ymag = sqrt(Yreal*Yreal + Yimag*Yimag);
altb 0:78ca29b4c49e 181 float absGyu = Ymag/Umag;
altb 0:78ca29b4c49e 182 float angGyu = atan2(Yimag, Yreal) - atan2(Uimag, Ureal);
altb 0:78ca29b4c49e 183 float absGye = Ymag/Aexc;
altb 0:78ca29b4c49e 184 float angGye = (atan2(Yimag, Yreal) + piDiv2);
altb 0:78ca29b4c49e 185 // user info
altb 0:78ca29b4c49e 186 if(ii == 1) {
altb 0:78ca29b4c49e 187 printLine();
altb 0:78ca29b4c49e 188 printf(" fexc[Hz] |Gyu| ang(Gyu) |Gye| ang(Gye) |E| |U| |Y|\r\n");
altb 0:78ca29b4c49e 189 printLine();
altb 0:78ca29b4c49e 190 }
altb 0:78ca29b4c49e 191 printf("%11.2e %10.2e %10.2e %10.2e %10.2e %10.2e %10.2e %10.2e\r\n", fexc, absGyu, angGyu, absGye, angGye, Aexc, Umag, Ymag);
altb 0:78ca29b4c49e 192 } else {
altb 0:78ca29b4c49e 193 jj += 1;
altb 0:78ca29b4c49e 194 }
altb 0:78ca29b4c49e 195 sinarg = fmod(sinarg + pi2Tsfexc, pi2);
altb 0:78ca29b4c49e 196 NmeasTotal += 1;
altb 0:78ca29b4c49e 197 return Aexc*sin(sinarg);
altb 0:78ca29b4c49e 198 }
altb 0:78ca29b4c49e 199
altb 0:78ca29b4c49e 200 void GPA::fexcDesLogspace(float fMin, float fMax, int NfexcDes)
altb 0:78ca29b4c49e 201 {
altb 0:78ca29b4c49e 202 // calculate logarithmic spaced frequency points
altb 0:78ca29b4c49e 203 float Gain = log10(fMax/fMin)/((float)NfexcDes - 1.0f);
altb 0:78ca29b4c49e 204 float expon = 0.0f;
altb 0:78ca29b4c49e 205 for(int i = 0; i < NfexcDes; i++) {
altb 0:78ca29b4c49e 206 fexcDes[i] = fMin*pow(10.0f, expon);
altb 0:78ca29b4c49e 207 expon += Gain;
altb 0:78ca29b4c49e 208 }
altb 0:78ca29b4c49e 209 }
altb 0:78ca29b4c49e 210
altb 0:78ca29b4c49e 211 void GPA::calcGPAmeasPara(float fexcDes_i)
altb 0:78ca29b4c49e 212 {
altb 0:78ca29b4c49e 213 // Nmeas has to be an integer
altb 0:78ca29b4c49e 214 Nper = NperMin;
altb 0:78ca29b4c49e 215 Nmeas = (int)floor((float)Nper/fexcDes_i/Ts + 0.5f);
altb 0:78ca29b4c49e 216 // secure that the minimal number of measurements is fullfilled
altb 0:78ca29b4c49e 217 int Ndelta = NmeasMin - Nmeas;
altb 0:78ca29b4c49e 218 if(Ndelta > 0) {
altb 0:78ca29b4c49e 219 Nper = (int)ceil((float)NmeasMin*fexcDes_i*Ts);
altb 0:78ca29b4c49e 220 Nmeas = (int)floor((float)Nper/fexcDes_i/Ts + 0.5f);
altb 0:78ca29b4c49e 221 }
altb 0:78ca29b4c49e 222 // evaluating reachable frequency
altb 0:78ca29b4c49e 223 fexc = (float)Nper/(float)Nmeas/Ts;
altb 0:78ca29b4c49e 224 }
altb 0:78ca29b4c49e 225
altb 0:78ca29b4c49e 226 void GPA::printLine()
altb 0:78ca29b4c49e 227 {
altb 0:78ca29b4c49e 228 printf("-----------------------------------------------------------------------------------------\r\n");
altb 0:78ca29b4c49e 229 }
altb 0:78ca29b4c49e 230
altb 0:78ca29b4c49e 231 void GPA::printGPAfexcDes()
altb 0:78ca29b4c49e 232 {
altb 0:78ca29b4c49e 233 printLine();
altb 0:78ca29b4c49e 234 for(int i = 0; i < NfexcDes; i++) {
altb 0:78ca29b4c49e 235 printf("%9.4f\r\n", fexcDes[i]);
altb 0:78ca29b4c49e 236 }
altb 0:78ca29b4c49e 237 }
altb 0:78ca29b4c49e 238
altb 0:78ca29b4c49e 239 void GPA::printGPAmeasPara()
altb 0:78ca29b4c49e 240 {
altb 0:78ca29b4c49e 241 printLine();
altb 0:78ca29b4c49e 242 printf(" fexcDes[Hz] fexc[Hz] Aexc Nmeas Nper\r\n");
altb 0:78ca29b4c49e 243 printLine();
altb 0:78ca29b4c49e 244 for(int i = 0; i < NfexcDes; i++) {
altb 0:78ca29b4c49e 245 calcGPAmeasPara(fexcDes[i]);
altb 0:78ca29b4c49e 246 if(fexc == fexcPast || fexc >= fnyq) {
altb 0:78ca29b4c49e 247 fexc = 0.0f;
altb 0:78ca29b4c49e 248 Nmeas = 0;
altb 0:78ca29b4c49e 249 Nper = 0;
altb 0:78ca29b4c49e 250 Aexc = 0;
altb 0:78ca29b4c49e 251 } else {
altb 0:78ca29b4c49e 252 Aexc = aAexcDes/fexc + bAexcDes;
altb 0:78ca29b4c49e 253 fexcPast = fexc;
altb 0:78ca29b4c49e 254 }
altb 0:78ca29b4c49e 255 NmeasTotal += Nmeas;
altb 0:78ca29b4c49e 256 printf("%12.2e %9.2e %10.2e %7i %6i \r\n", fexcDes[i], fexc, Aexc, Nmeas, Nper);
altb 0:78ca29b4c49e 257 }
altb 0:78ca29b4c49e 258 printGPAmeasTime();
altb 0:78ca29b4c49e 259 reset();
altb 0:78ca29b4c49e 260 }
altb 0:78ca29b4c49e 261
altb 0:78ca29b4c49e 262 void GPA::printGPAmeasTime()
altb 0:78ca29b4c49e 263 {
altb 0:78ca29b4c49e 264 printLine();
altb 0:78ca29b4c49e 265 printf(" number of data points: %9i\r\n", NmeasTotal);
altb 0:78ca29b4c49e 266 printf(" measurment time in sec: %9.2f\r\n", (float)NmeasTotal*Ts);
altb 0:78ca29b4c49e 267 }