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Diff: GPA.cpp
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diff -r 000000000000 -r 78ca29b4c49e GPA.cpp --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/GPA.cpp Tue Apr 03 08:47:41 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); +} \ No newline at end of file