2nd Library
Diff: GPA.cpp
- Revision:
- 0:a201a6cd4c0c
- Child:
- 1:b54eb3e24d2d
- Child:
- 2:35e1cf78ea6f
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/GPA.cpp Thu Mar 07 07:03:56 2019 +0000 @@ -0,0 +1,551 @@ +/* + 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); +} +