BA
sfbsg
Dependencies: mbed
Diff: GPA.cpp
- Revision:
- 0:8ab621116ccd
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/GPA.cpp Tue Apr 03 15:17:11 2018 +0000
@@ -0,0 +1,267 @@
+/*
+ GPA: frequency point wise gain and phase analyser to measure the frequency
+ respone of dynamical system
+
+ hint: the measurements should only be perfomed in closed loop
+ assumption: the system is at the desired steady state of interest when
+ the measurment starts
+
+ exc(2) C: controller
+ | P: plant
+ v
+ exc(1) --> o ->| C |--->o------->| P |----------> out
+ ^ | |
+ | --> inp | exc: excitation signal (E)
+ | | inp: input plant (U)
+ -------------------------------- out: output plant (Y)
+
+ instantiate option 1:
+ GPA(float fMin, float fMax, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1)
+
+ 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: maximal number of samples that are used for each frequency point
+ Ts: sampling time
+ Aexc0: excitation amplitude at fMin
+ Aexc1: excitation amplitude at fMax
+
+ hints: the amplitude drops with 1/fexc, if you're using
+ Axc1 = Aexc0/fMax the d/dt exc = const., this is recommended
+ if your controller does not have a rolloff.
+ if a desired frequency point is not measured try to increase Nmeas.
+
+ pseudo code for a closed loop measurement with a proportional controller Kp:
+
+ float inp = "measurement of inputsignal";
+ float out = "mesurement of outputsignal";
+ float exc = myGPA(inp, out);
+ float off = "desired steady state off the system";
+
+ excitation input at (1):
+ inp = Kp*(exc + off - out);
+
+ excitation input at (2):
+ inp = Kp*(off - out) + exc;
+
+ usage:
+ exc = myGPA(inp, out) does update the internal states of the gpa at the
+ timestep k and returns the excitation signal for the timestep k+1. the
+ results are plotted to a terminal (putty) over serial cennection and look
+ as follows:
+ -----------------------------------------------------------------------------------------
+ fexc[Hz] |Gyu| ang(Gyu) |Gye| ang(Gye) |E| |U| |Y|
+ -----------------------------------------------------------------------------------------
+ 7.01e-01 1.08e+01 -7.45e-02 1.08e+01 -7.38e-02 9.99e-01 9.99e-01 1.08e+01
+
+ in matlab you can use:
+ dataNucleo = [... insert measurement data here ...];
+ g = frd(dataNucleo(:,2).*exp(1i*dataNucleo(:,3)), dataNucleo(:,1), Ts, 'Units', 'Hz');
+ gcl = frd(dataNucleo(:,4).*exp(1i*dataNucleo(:,5)), dataNucleo(:,1), Ts, 'Units', 'Hz');
+
+ if you're evaluating more than one measurement which contain equal frequency points try:
+ dataNucleo = [dataNucleo1; dataNucleo2];
+ [~, ind] = unique(dataNucleo(:,1),'stable');
+ dataNucleo = dataNucleo(ind,:);
+
+ autor: M.E. Peter
+*/
+
+#include "GPA.h"
+#include "mbed.h"
+#include "math.h"
+#define pi 3.1415927f
+
+using namespace std;
+
+GPA::GPA(float fMin, float fMax, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1)
+{
+ this->NfexcDes = NfexcDes;
+ this->NperMin = NperMin;
+ this->NmeasMin = NmeasMin;
+ this->Ts = Ts;
+
+ // calculate logarithmic spaced frequency points
+ fexcDes = (float*)malloc(NfexcDes*sizeof(float));
+ fexcDesLogspace(fMin, fMax, NfexcDes);
+
+ // calculate coefficients for decreasing amplitude (1/fexc)
+ this->aAexcDes = (Aexc1 - Aexc0)/(1.0f/fexcDes[NfexcDes-1] - 1.0f/fexcDes[0]);
+ this->bAexcDes = Aexc0 - aAexcDes/fexcDes[0];
+
+ fnyq = 1/2.0f/Ts;
+ pi2 = 2.0f*pi;
+ pi2Ts = pi2*Ts;
+ piDiv2 = pi/2.0f;
+
+ sU = (float*)malloc(3*sizeof(float));
+ sY = (float*)malloc(3*sizeof(float));
+ reset();
+}
+
+GPA::~GPA() {}
+
+void GPA::reset()
+{
+ Nmeas = 0;
+ Nper = 0;
+ fexc = 0.0f;
+ fexcPast = 0.0f;
+ ii = 1; // iterating through desired frequency points
+ jj = 1; // iterating through measurement points w.r.t. reachable frequency
+ scaleG = 0.0f;
+ cr = 0.0f;
+ ci = 0.0f;
+ for(int i = 0; i < 3; i++) {
+ sU[i] = 0.0f;
+ sY[i] = 0.0f;
+ }
+ sinarg = 0.0f;
+ NmeasTotal = 0;
+ Aexc = 0.0f;
+ pi2Tsfexc = 0.0f;
+}
+
+float GPA::update(float inp, float out)
+{
+ // a new frequency point has been reached
+ if(jj == 1) {
+ // get a new unique frequency point
+ while(fexc == fexcPast) {
+ // measurement finished
+ if(ii > NfexcDes) {
+ return 0.0f;
+ }
+ calcGPAmeasPara(fexcDes[ii - 1]);
+ // secure fexc is not higher or equal to nyquist frequency
+ if(fexc >= fnyq) {
+ fexc = fexcPast;
+ }
+ // no frequency found
+ if(fexc == fexcPast) {
+ ii += 1;
+ } else {
+ Aexc = aAexcDes/fexc + bAexcDes;
+ pi2Tsfexc = pi2Ts*fexc;
+ }
+ }
+ fexcPast = fexc;
+ // filter scaling
+ scaleG = 1.0f/sqrt((float)Nmeas);
+ // filter coefficients
+ cr = cos(pi2Tsfexc);
+ ci = sin(pi2Tsfexc);
+ // filter storage
+ for(int i = 0; i < 3; i++) {
+ sU[i] = 0.0f;
+ sY[i] = 0.0f;
+ }
+ }
+ // filter step for signal su
+ sU[0] = scaleG*inp + 2.0f*cr*sU[1] - sU[2];
+ sU[2] = sU[1];
+ sU[1] = sU[0];
+ // filter step for signal sy
+ sY[0] = scaleG*out + 2.0f*cr*sY[1] - sY[2];
+ sY[2] = sY[1];
+ sY[1] = sY[0];
+ // measurement of frequencypoint is finished
+ if(jj == Nmeas) {
+ jj = 1;
+ ii += 1;
+ // calculate the one point dft
+ float Ureal = 2.0f*scaleG*(cr*sU[1] - sU[2]);
+ float Uimag = 2.0f*scaleG*ci*sU[1];
+ float Yreal = 2.0f*scaleG*(cr*sY[1] - sY[2]);
+ float Yimag = 2.0f*scaleG*ci*sY[1];
+ // calculate magnitude and angle
+ float Umag = sqrt(Ureal*Ureal + Uimag*Uimag);
+ float Ymag = sqrt(Yreal*Yreal + Yimag*Yimag);
+ float absGyu = Ymag/Umag;
+ float angGyu = atan2(Yimag, Yreal) - atan2(Uimag, Ureal);
+ float absGye = Ymag/Aexc;
+ float angGye = (atan2(Yimag, Yreal) + piDiv2);
+ // user info
+ if(ii == 1) {
+ printLine();
+ printf(" fexc[Hz] |Gyu| ang(Gyu) |Gye| ang(Gye) |E| |U| |Y|\r\n");
+ printLine();
+ }
+ 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);
+ } else {
+ jj += 1;
+ }
+ sinarg = fmod(sinarg + pi2Tsfexc, pi2);
+ NmeasTotal += 1;
+ return Aexc*sin(sinarg);
+}
+
+void GPA::fexcDesLogspace(float fMin, float fMax, int NfexcDes)
+{
+ // calculate logarithmic spaced frequency points
+ float Gain = log10(fMax/fMin)/((float)NfexcDes - 1.0f);
+ float expon = 0.0f;
+ for(int i = 0; i < NfexcDes; i++) {
+ fexcDes[i] = fMin*pow(10.0f, expon);
+ expon += Gain;
+ }
+}
+
+void GPA::calcGPAmeasPara(float fexcDes_i)
+{
+ // Nmeas has to be an integer
+ Nper = NperMin;
+ Nmeas = (int)floor((float)Nper/fexcDes_i/Ts + 0.5f);
+ // secure that the minimal number of measurements is fullfilled
+ int Ndelta = NmeasMin - Nmeas;
+ if(Ndelta > 0) {
+ Nper = (int)ceil((float)NmeasMin*fexcDes_i*Ts);
+ Nmeas = (int)floor((float)Nper/fexcDes_i/Ts + 0.5f);
+ }
+ // evaluating reachable frequency
+ fexc = (float)Nper/(float)Nmeas/Ts;
+}
+
+void GPA::printLine()
+{
+ printf("-----------------------------------------------------------------------------------------\r\n");
+}
+
+void GPA::printGPAfexcDes()
+{
+ printLine();
+ for(int i = 0; i < NfexcDes; i++) {
+ printf("%9.4f\r\n", fexcDes[i]);
+ }
+}
+
+void GPA::printGPAmeasPara()
+{
+ printLine();
+ printf(" fexcDes[Hz] fexc[Hz] Aexc Nmeas Nper\r\n");
+ printLine();
+ for(int i = 0; i < NfexcDes; i++) {
+ calcGPAmeasPara(fexcDes[i]);
+ if(fexc == fexcPast || fexc >= fnyq) {
+ fexc = 0.0f;
+ Nmeas = 0;
+ Nper = 0;
+ Aexc = 0;
+ } else {
+ Aexc = aAexcDes/fexc + bAexcDes;
+ fexcPast = fexc;
+ }
+ NmeasTotal += Nmeas;
+ printf("%12.2e %9.2e %10.2e %7i %6i \r\n", fexcDes[i], fexc, Aexc, Nmeas, Nper);
+ }
+ printGPAmeasTime();
+ reset();
+}
+
+void GPA::printGPAmeasTime()
+{
+ printLine();
+ printf(" number of data points: %9i\r\n", NmeasTotal);
+ printf(" measurment time in sec: %9.2f\r\n", (float)NmeasTotal*Ts);
+}
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