First Version of ACS Controller #329
126
mission/controller/acs/Igrf13Model.cpp
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mission/controller/acs/Igrf13Model.cpp
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/*
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* Igrf13Model.cpp
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*
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* Created on: 10 Mar 2022
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* Author: Robin Marquardt
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*/
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#include "Igrf13Model.h"
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#include <cmath>
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#include <stdint.h>
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#include <string.h>
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#include <time.h>
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#include <fsfw/src/fsfw/globalfunctions/constants.h>
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#include <fsfw/src/fsfw/globalfunctions/math/MatrixOperations.h>
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#include <fsfw/src/fsfw/globalfunctions/math/QuaternionOperations.h>
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#include <fsfw/src/fsfw/globalfunctions/math/VectorOperations.h>
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#include <acs/math/MathOperations.h>
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using namespace Math;
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Igrf13Model::Igrf13Model(){
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}
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Igrf13Model::~Igrf13Model(){
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}
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void Igrf13Model::magFieldComp(const double longitude, const double gcLatitude,
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const double altitude, timeval timeOfMagMeasurement, double* magFieldModelInertial) {
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double phi = longitude, theta = gcLatitude; //geocentric
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/* Here is the co-latitude needed*/
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theta -= 90*PI/180;
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theta *= (-1);
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double rE = 6371200.0; // radius earth [m]
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/* Predefine recursive associated Legendre polynomials */
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double P11 = 1;
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double P10 = P11; //P10 = P(n-1,m-0)
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double dP11 = 0; //derivative
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double dP10 = dP11; //derivative
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double P2 = 0, dP2 = 0, P20 = 0, dP20 = 0, K = 0;
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for (int m = 0; m <= igrfOrder; m++) {
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for (int n = 1; n <= igrfOrder; n++) {
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if (m <= n) {
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/* Calculation of Legendre Polynoms (normalised) */
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if (n == m) {
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P2 = sin(theta) * P11;
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dP2 = sin(theta) * dP11 - cos(theta) * P11;
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P11 = P2;
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P10 = P11;
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P20 = 0;
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dP11 = dP2;
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dP10 = dP11;
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dP20 = 0;
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} else if (n == 1) {
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P2 = cos(theta) * P10;
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dP2 = cos(theta) * dP10 - sin(theta) * P10;
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P20 = P10;
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P10 = P2;
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dP20 = dP10;
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dP10 = dP2;
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} else {
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K = (pow((n - 1), 2) - pow(m, 2))
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/ ((2 * n - 1) * (2 * n - 3));
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P2 = cos(theta) * P10 - K * P20;
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dP2 = cos(theta) * dP10 - sin(theta) * P10 - K * dP20;
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P20 = P10;
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P10 = P2;
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dP20 = dP10;
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dP10 = dP2;
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}
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/* gradient of scalar potential towards radius */
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magFieldModel[0]+=pow(rE/(altitude+rE),(n+2))*(n+1)*
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((updatedG[m][n-1]*cos(m*phi) + updatedH[m][n-1]*sin(m*phi))*P2);
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/* gradient of scalar potential towards phi */
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magFieldModel[1]+=pow(rE/(altitude+rE),(n+2))*
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((updatedG[m][n-1]*cos(m*phi) + updatedH[m][n-1]*sin(m*phi))*dP2);
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/* gradient of scalar potential towards theta */
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magFieldModel[2]+=pow(rE/(altitude+rE),(n+2))*
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((-updatedG[m][n-1]*sin(m*phi) + updatedH[m][n-1]*cos(m*phi))*P2*m);
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}
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}
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}
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magFieldModel[1] *= -1;
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magFieldModel[2] *= (-1 / sin(theta));
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/* Next step: transform into inertial KOS (IJK)*/
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//Julean Centuries
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double JD2000Floor = 0;
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double JD2000 = MathOperations<double>::convertUnixToJD2000(timeOfMagMeasurement);
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JD2000Floor = floor(JD2000);
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double JC2000 = JD2000Floor / 36525;
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double gst = 100.4606184 + 36000.77005361 * JC2000 + 0.00038793 * pow(JC2000,2)
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- 0.000000026 * pow(JC2000,3); //greenwich sidereal time
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gst *= PI/180; //convert to radians
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double sec = (JD2000 - JD2000Floor) * 86400; // Seconds on this day (Universal time) // FROM GPS ?
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double omega0 = 0.00007292115; // mean angular velocity earth [rad/s]
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gst +=omega0 * sec;
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double lst = gst + longitude; //local sidereal time [rad]
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magFieldModelInertial[0] = magFieldModel[0] * cos(theta) + magFieldModel[1] * sin(theta)*cos(lst) - magFieldModel[1] * sin(lst);
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magFieldModelInertial[1] = magFieldModel[0] * cos(theta) + magFieldModel[1] * sin(theta)*sin(lst) + magFieldModel[1] * cos(lst);
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magFieldModelInertial[2] = magFieldModel[0] * sin(theta) + magFieldModel[1] * cos(lst);
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double normVecMagFieldInert[3] = {0,0,0};
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VectorOperations<double>::normalize(magFieldModelInertial, normVecMagFieldInert, 3);
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}
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void Igrf13Model::updateCoeffGH(timeval timeOfMagMeasurement){
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double JD2000Igrf = (2458850.0-2451545); //Begin of IGRF-13 (2020-01-01,00:00:00) in JD2000
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double JD2000 = MathOperations<double>::convertUnixToJD2000(timeOfMagMeasurement);
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double days = ceil(JD2000-JD2000Igrf);
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for(int i = 0;i <= igrfOrder; i++){
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for(int j = 0;j <= (igrfOrder-1); j++){
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updatedG[i][j] = coeffG[i][j] + svG[i][j] * (days/365);
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updatedH[i][j] = coeffH[i][j] + svH[i][j] * (days/365);
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}
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}
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}
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117
mission/controller/acs/Igrf13Model.h
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mission/controller/acs/Igrf13Model.h
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/*
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* Igrf13Model.h
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*
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* Created on: 10 Mar 2022
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* Author: Robin Marquardt
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* Description: Calculates the magnetic field vector of earth with the IGRF Model.
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* Sources: https://www.ngdc.noaa.gov/IAGA/vmod/igrf.html
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* https://doi.org/10.1186/s40623-020-01288-x
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* J. Davis, Mathematical Modeling of Earth's Magnetic Field, TN, 2004
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*
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* [Conversion of ENU (geocentric) to IJK: Skript Bahnmechanik für Raumfahrzeuge,
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* Prof. Dr.-Ing. Stefanos Fasoulas / Dr.-Ing. Frank Zimmermann]
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*
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*/
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#ifndef IGRF13MODEL_H_
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#define IGRF13MODEL_H_
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#include <cmath>
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#include <stdint.h>
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#include <string.h>
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#include <time.h>
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// Output should be transformed to [T] instead of [nT]
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// Updating Coefficients has to be implemented yet. Question, updating everyday ?
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class Igrf13Model {
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public:
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Igrf13Model();
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virtual ~Igrf13Model();
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// Main Function
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void magFieldComp(const double longitude, const double gcLatitude, const double altitude, timeval timeOfMagMeasurement,double* magFieldModelInertial);
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// Right now the radius for igrf is simply with r0 + altitude calculated. In reality the radius is oriented from the satellite to earth COM
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// Difference up to 25 km, which is 5 % of the total flight altitude
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/* Inputs:
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* - longitude: geocentric longitude [rad]
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* - latitude: geocentric latitude [rad]
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* - altitude: [m]
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* - timeOfMagMeasurement: time of actual measurement [s]
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*
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* Outputs:
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* - magFieldModelInertial: Magnetic Field Vector in IJK KOS [nT]*/
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// Coefficient wary over year, could be updated sometimes.
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void updateCoeffGH(timeval timeOfMagMeasurement); //Secular variation (SV)
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double magFieldModel[3];
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private:
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const double coeffG[14][13] = {{-29404.8, -2499.6, 1363.2, 903.0, -234.3, 66.0, 80.6, 23.7, 5.0, -1.9, 3.0, -2.0, 0.1},
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{-1450.9, 2982.0, -2381.2, 809.5, 363.2, 65.5, -76.7, 9.7, 8.4, -6.2, -1.4, -0.1, -0.9},
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{0, 1677.0, 1236.2, 86.3, 187.8, 72.9, -8.2, -17.6, 2.9, -0.1, -2.5, 0.5, 0.5},
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{0, 0, 525.7, -309.4, -140.7, -121.5, 56.5, -0.5, -1.5, 1.7, 2.3, 1.3 ,0.7},
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{0 ,0 ,0, 48.0, -151.2, -36.2, 15.8, -21.1, -1.1, -0.9, -0.9, -1.2, -0.3},
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{0, 0, 0, 0, 13.5, 13.5, 6.4, 15.3, -13.2, 0.7, 0.3, 0.7, 0.8},
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{0, 0, 0, 0, 0,-64.7, -7.2, 13.7, 1.1, -0.9, -0.7, 0.3, 0.0},
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{0, 0, 0, 0, 0, 0, 9.8, -16.5, 8.8, 1.9, -0.1, 0.5, 0.8},
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{0, 0, 0, 0, 0, 0, 0, -0.3, -9.3, 1.4, 1.4, -0.3, 0.0},
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{0, 0, 0, 0, 0, 0, 0, 0, -11.9, -2.4, -0.6, -0.5, 0.4},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, -3.8, 0.2, 0.1, 0.1},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.1, -1.1, 0.5},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.3, -0.5},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.4}}; // [m][n] in nT
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const double coeffH[14][13] = {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{4652.5, -2991.6, -82.1, 281.9, 47.7, -19.1, -51.5, 8.4, -23.4, 3.4, 0.0, -1.2, -0.9},
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{0, -734.6, 241.9, -158.4, 208.3, 25.1, -16.9, -15.3, 11.0, -0.2, 2.5, 0.5, 0.6},
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{0, 0, -543.4, 199.7, -121.2, 52.8, 2.2, 12.8, 9.8, 3.6, -0.6, 1.4, 1.4},
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{0, 0, 0, -349.7, 32.3, -64.5, 23.5, -11.7, -5.1, 4.8, -0.4, -1.8, -0.4},
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{0, 0, 0, 0, 98.9, 8.9, -2.2, 14.9, -6.3, -8.6, 0.6, 0.1, -1.3},
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{0, 0, 0, 0, 0, 68.1, -27.2, 3.6, 7.8, -0.1, -0.2, 0.8, -0.1},
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{0, 0, 0, 0, 0, 0, -1.8, -6.9, 0.4, -4.3, -1.7, -0.2, 0.3},
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{0, 0, 0, 0, 0, 0, 0, 2.8, -1.4, -3.4, -1.6, 0.6, -0.1},
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{0, 0, 0, 0, 0, 0, 0, 0, 9.6, -0.1, -3.0, 0.2, 0.5},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, -8.8, -2.0, -0.9, 0.5},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2.6, 0.0, -0.4},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, -0.4},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.6}}; // [m][n] in nT
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const double svG[14][13] = {{5.7, -11, 2.2, -1.2, -0.3, -0.5, -0.1, 0, 0, 0, 0, 0 ,0},
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{7.4, -7, -5.9, -1.6, 0.5, -0.3, -0.2, 0.1, 0, 0, 0, 0,0},
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{0, -2.1, 3.1, -5.9, -0.6, 0.4, 0, -0.1, 0, 0, 0, 0, 0},
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{0, 0, -12, 5.2, 0.2, 1.3, 0.7, 0.4, 0, 0, 0, 0, 0},
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{0 ,0 ,0, -5.1, 1.3, -1.4, 0.1, -0.1, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0.9, 0, -0.5, 0.4, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0.9, -0.8, 0.3, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0.8, -0.1, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0.4, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}; // [m][n] in nT
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const double svH[14][13] = {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{-25.9, -30.2, 6, -0.1, 0, 0, 0.6, -0.2, 0, 0, 0, 0,0},
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{0, -22.4, -1.1, 6.5, 2.5, -1.6, 0.6, 0.6, 0, 0, 0, 0, 0},
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{0, 0, 0.5, 3.6, -0.6, -1.3, -0.8, -0.2, 0, 0, 0, 0, 0},
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{0 ,0 ,0, -5, 3, 0.8, -0.2, 0.5, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0.3, 0, -1.1, -0.3, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 1, 0.1, -0.4, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0.3, 0.5, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}; // [m][n] in nT
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double updatedG[14][13];
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double updatedH[14][13];
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static const int igrfOrder = 13; // degree of truncation
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};
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#endif /* IGRF13MODEL_H_ */
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