mirror of
https://gitlab.com/lander-team/lander-cpp.git
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437 lines
13 KiB
C++
437 lines
13 KiB
C++
#include "sVars.h"
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void burnStartTimeCalc(struct sVars &, double g);
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void thrustSelection(struct sVars &, int t);
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void lqrCalc(struct sVars &);
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void TVC(struct sVars &, double g);
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void vehicleDynamics(struct sVars &, int t);
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void write2CSV(struct sVars &, std::fstream &outfile, int t);
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double derivative(double x2, double x1, double dt);
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double integral(double x2, double x1, double dt);
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void sim(struct sVars &Vars) {
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double g = -9.81;
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// defining a few random values here cause I'm lazy
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Vars.burnElapsed = 2000;
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Vars.m = Vars.m0;
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Vars.thrust_prev = 0;
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burnStartTimeCalc(Vars, g);
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// Deleting any previous output file
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if (remove("simOut.csv") != 0)
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perror("Error deleting file");
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else
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puts("File successfully deleted");
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// Define and open output file "simOut.csv"
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std::fstream outfile;
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outfile.open("simOut.csv", std::ios::app);
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// Output file header. These are the variables that we output - useful for
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// debugging
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outfile
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<< "t, x, y, z, vx, vy, vz, ax, ay, az, yaw, pitch, roll, yawdot, "
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"pitchdot, rolldot, yawddot, pitchddot, rollddot, I11, I22, I33, "
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"I11dot, I22dot, I33dot, Servo1, Servo2, m, thrust, burnElapsed, Fz, "
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"LQRx, LQRy"
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<< std::endl;
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// Start Sim
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for (int t = 0; t < Vars.simTime; t++) {
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thrustSelection(Vars, t);
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lqrCalc(Vars);
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TVC(Vars, g);
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vehicleDynamics(Vars, t);
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write2CSV(Vars, outfile, t);
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}
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outfile.close();
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}
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void burnStartTimeCalc(struct sVars &Vars, double g) {
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double v = Vars.vz;
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double h = 0;
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double dt = 0.001;
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double a, j, m, thrust;
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for (double i = 0.148; i < 3.450; i = i + dt) {
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m = Vars.m0 - i * Vars.mdot;
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if ((i > 0.147) & (i < 0.420))
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thrust = 65.165 * i - 2.3921;
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else if ((i > 0.419) & (i < 3.383))
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thrust = 0.8932 * pow(i, 6) - 11.609 * pow(i, 5) + 60.739 * pow(i, 4) -
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162.99 * pow(i, 3) + 235.6 * pow(i, 2) - 174.43 * i + 67.17;
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else if ((i > 3.382) & (i < 3.46))
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thrust = -195.78 * i + 675.11;
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v = (((thrust / m) + g) * dt) + v;
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h = v * dt + h;
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}
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Vars.z = h + (pow(v, 2) / (2 * -g)); // starting height
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Vars.vb = v; // terminal velocity
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double burnStartTime = Vars.vb / -g;
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Vars.simTime = (Vars.tb + burnStartTime) * 1000;
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}
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void thrustSelection(struct sVars &Vars, int t) {
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double tol = 0.001; // 0.001 seems to be a nice tolerance
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// Check to see if current velocity is close to the F15's total velocity
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bool b_burnStart = (Vars.vb < (1 + tol) * Vars.vz * -1) &
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(Vars.vb > (1 - tol) * Vars.vz * -1);
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if (Vars.burnElapsed != 2000) {
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// determine where in the thrust curve we're at based on elapsed burn time
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// as well as current mass
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Vars.burnElapsed = (t - Vars.burnStart) / 1000;
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Vars.m = Vars.m0 - (Vars.mdot * Vars.burnElapsed);
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}
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else if (b_burnStart) {
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// Start burn
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Vars.burnStart = t;
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Vars.burnElapsed = 0;
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}
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else
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Vars.burnElapsed = 2000; // arbitrary number to ensure we don't burn
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if ((Vars.burnElapsed > 0.147) & (Vars.burnElapsed < 0.420))
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Vars.thrust = 65.165 * Vars.burnElapsed - 2.3921;
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else if ((Vars.burnElapsed > 0.419) & (Vars.burnElapsed < 3.383))
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Vars.thrust =
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0.8932 * pow(Vars.burnElapsed, 6) - 11.609 * pow(Vars.burnElapsed, 5) +
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60.739 * pow(Vars.burnElapsed, 4) - 162.99 * pow(Vars.burnElapsed, 3) +
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235.6 * pow(Vars.burnElapsed, 2) - 174.43 * Vars.burnElapsed + 67.17;
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else if ((Vars.burnElapsed > 3.382) & (Vars.burnElapsed < 3.46))
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Vars.thrust = -195.78 * Vars.burnElapsed + 675.11;
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}
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void lqrCalc(struct sVars &Vars) {
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Vars.I11 = Vars.m * ((1 / 12) * pow(Vars.vehicleHeight, 2) +
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pow(Vars.vehicleRadius, 2) / 4);
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Vars.I22 = Vars.m * ((1 / 12) * pow(Vars.vehicleHeight, 2) +
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pow(Vars.vehicleRadius, 2) / 4);
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Vars.I33 = Vars.m * 0.5 * pow(Vars.vehicleRadius, 2);
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/*
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double n = sqrt(398600 / pow(6678, 3));
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double k1 = (Vars.I22 - Vars.I33) / Vars.I11;
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double k2 = (Vars.I11 - Vars.I33) / Vars.I22;
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double k3 = (Vars.I22 - Vars.I11) / Vars.I33;
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double R11 = pow(10, 2);
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double R22 = pow(10, 2);
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double R33 = pow(10, 2);
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double F11 = -2 * pow(n, 2) * 4 * k1;
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double F22 = -2 * pow(n, 2) * 3 * k2;
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double F33 = -2 * pow(n, 2) * k3;
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double G31 = n * (1 - k1);
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double G13 = n * (k3 - 1);
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double d = 0.5;
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/*
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The following calculations are based on output of LQR.m to avoid working
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with matrices in C++ Please see .m file for details on calculation.
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Algorithm taken from LQR wikipedia page:
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https://en.wikipedia.org/wiki/Algebraic_Riccati_equation#Solution
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*/
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/*
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double gain = 0.25;
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double K11 =
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-1 * gain *
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(Vars.I33 * pow(abs(F33), 2) * pow(abs(Vars.I33), 4) * pow(abs(R33), 2) +
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R33 * pow(abs(G31), 2) * pow(abs(Vars.I33), 2) + Vars.I33) /
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(R11 * d * Vars.I11 *
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(pow(abs(F33), 2) * pow(abs(Vars.I33), 4) * pow(abs(R33), 2) + 1));
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double K22 = -1 * gain * Vars.I33 / (R22 * d * Vars.I22);
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double K33 =
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-1 * gain *
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(Vars.I33 *
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(Vars.I33 * pow(abs(F11), 2) * pow(abs(Vars.I11), 4) * pow(abs(R11), 2) +
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R11 * pow(abs(G13), 2) * pow(abs(Vars.I11), 2) + Vars.I33)) /
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(R33 * d * pow(abs(Vars.I33), 2) *
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(pow(abs(F11), 2) * pow(abs(Vars.I11), 4) * pow(abs(R11), 2) + 1));
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double K34 =
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gain * (R11 * pow(abs(Vars.I11), 2) * G13) /
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(R33 * Vars.I33 *
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(pow(abs(F11), 2) * pow(abs(Vars.I11), 4) * pow(abs(R11), 2) + 1));
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double K16 =
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gain * (R33 * pow(abs(Vars.I33), 2) * G31) /
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(R11 * Vars.I11 *
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(pow(abs(F33), 2) * pow(abs(Vars.I33), 4) * pow(abs(R33), 2) + 1));
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// Matrix Multiply K with [YPR/2; w123] column vector and divide by moment arm
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Vars.LQRx = (K11 * Vars.yaw / 2 + K16 * Vars.rolldot) / Vars.momentArm;
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Vars.LQRy = (K22 * Vars.pitch / 2) / Vars.momentArm;
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*/
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// Paste in Values from gainCalc.m
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double K11 = 39.54316;
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double K12 = 0.00000;
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double K13 = -0.00000;
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double K14 = 39.55769;
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double K15 = 0.00000;
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double K16 = 0.00000;
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double K21 = 0.00000;
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double K22 = 39.54316;
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double K23 = 0.00000;
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double K24 = 0.00000;
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double K25 = 39.55769;
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double K26 = 0.00000;
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double K31 = 0.00000;
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double K32 = 0.00000;
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double K33 = 39.54316;
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double K34 = 0.00000;
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double K35 = 0.00000;
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double K36 = 39.54394;
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double gain =
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0.25 *
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pow(10, -4); // changing exponenet drastically changes results of LQR
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// Matrix Multiply K with [YPR/2; w123] column vector and divide by moment arm
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Vars.LQRx =
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gain *
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((K12 * Vars.pitch) / 2 + K15 * Vars.pitchdot + (K13 * Vars.roll) / 2 +
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K16 * Vars.rolldot + (K11 * Vars.yaw) / 2 + K14 * Vars.yawdot) /
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-Vars.momentArm;
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Vars.LQRy =
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gain *
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((K22 * Vars.pitch) / 2 + K25 * Vars.pitchdot + (K23 * Vars.roll) / 2 +
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K26 * Vars.rolldot + (K21 * Vars.yaw) / 2 + K24 * Vars.yawdot) /
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-Vars.momentArm;
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// LQR Force limiter X
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if (Vars.LQRx > Vars.thrust)
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Vars.LQRx = Vars.thrust;
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else if (Vars.LQRx < -1 * Vars.thrust)
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Vars.LQRx = -1 * Vars.thrust;
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// LQR Force limiter Y
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if (Vars.LQRy > Vars.thrust)
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Vars.LQRy = Vars.thrust;
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else if (Vars.LQRy < -1 * Vars.thrust)
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Vars.LQRy = -1 * Vars.thrust;
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}
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void TVC(struct sVars &Vars, double g) {
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if (Vars.thrust < 1) {
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// Define forces and moments for t = 0
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Vars.Fx = 0;
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Vars.Fy = 0;
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Vars.Fz = g * Vars.m0;
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Vars.momentX = 0;
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Vars.momentY = 0;
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Vars.momentZ = 0;
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}
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else {
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// Convert servo position to degrees for comparison to max allowable
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Vars.xServoDegs = (180 / 3.1416) * asin(Vars.LQRx / Vars.thrust);
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// Servo position limiter
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if (Vars.xServoDegs > Vars.maxServo)
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Vars.xServoDegs = Vars.maxServo;
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else if (Vars.xServoDegs < -1 * Vars.maxServo)
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Vars.xServoDegs = -1 * Vars.maxServo;
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// Convert servo position to degrees for comparison to max allowable
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Vars.yServoDegs = (180 / 3.1416) * asin(Vars.LQRy / Vars.thrust);
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// Servo position limiter
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if (Vars.yServoDegs > Vars.maxServo)
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Vars.yServoDegs = Vars.maxServo;
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else if (Vars.yServoDegs < -1 * Vars.maxServo)
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Vars.yServoDegs = -1 * Vars.maxServo;
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// Vector math to aqcuire thrust vector components
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Vars.Fx = Vars.thrust * sin(Vars.xServoDegs * (3.1416 / 180));
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Vars.Fy = Vars.thrust * sin(Vars.yServoDegs * (3.1416 / 180));
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Vars.Fz = sqrt(pow(Vars.thrust, 2) - (pow(Vars.Fx, 2) + pow(Vars.Fy, 2))) +
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(Vars.m * g);
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// Calculate moment created by Fx and Fy
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Vars.momentX = Vars.Fx * Vars.momentArm;
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Vars.momentY = Vars.Fy * Vars.momentArm;
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Vars.momentZ = 0;
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}
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}
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void vehicleDynamics(struct sVars &Vars, int t) {
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// Idot
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if (t < 1) {
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Vars.I11dot = 0;
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Vars.I22dot = 0;
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Vars.I33dot = 0;
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} else {
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Vars.I11dot = derivative(Vars.I11, Vars.I11prev, Vars.stepSize);
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Vars.I22dot = derivative(Vars.I22, Vars.I22prev, Vars.stepSize);
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Vars.I33dot = derivative(Vars.I33, Vars.I33prev, Vars.stepSize);
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}
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// pdot, qdot, rdot
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Vars.yawddot = (Vars.momentX - Vars.I11dot * Vars.yawdot +
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Vars.I22 * Vars.pitchdot * Vars.rolldot -
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Vars.I33 * Vars.pitchdot * Vars.rolldot) /
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Vars.I11;
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Vars.pitchddot = (Vars.momentY - Vars.I22dot * Vars.pitchdot -
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Vars.I11 * Vars.rolldot * Vars.yawdot +
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Vars.I33 * Vars.rolldot * Vars.yawdot) /
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Vars.I22;
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Vars.rollddot = (Vars.momentZ - Vars.I33dot * Vars.rolldot +
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Vars.I11 * Vars.pitchdot * Vars.yawdot -
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Vars.I22 * Vars.pitchdot * Vars.yawdot) /
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Vars.I33;
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if (t < 1) {
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Vars.x = 0;
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Vars.y = 0;
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Vars.ax = 0;
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Vars.ay = 0;
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Vars.az = Vars.Fz / Vars.m0;
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}
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else {
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// p, q, r
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Vars.yawdot = integral(Vars.yawddot, Vars.yawdotPrev, Vars.stepSize);
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Vars.pitchdot = integral(Vars.pitchddot, Vars.pitchdotPrev, Vars.stepSize);
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Vars.rolldot = integral(Vars.rollddot, Vars.rolldotPrev, Vars.stepSize);
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// ax ay az
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Vars.ax =
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(Vars.Fx / Vars.m) + (Vars.pitchdot * Vars.vz - Vars.rolldot * Vars.vy);
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Vars.ay =
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(Vars.Fy / Vars.m) + (Vars.rolldot * Vars.vx - Vars.vz * Vars.yawdot);
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Vars.az =
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(Vars.Fz / Vars.m) + (Vars.vy * Vars.yawdot - Vars.pitchdot * Vars.vx);
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// vx vy vz in Body frame
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Vars.vx = integral(Vars.ax, Vars.vxPrev, Vars.stepSize);
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Vars.vy = integral(Vars.ay, Vars.vyPrev, Vars.stepSize);
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Vars.vz = integral(Vars.az, Vars.vzPrev, Vars.stepSize);
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// Xe
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Vars.x = integral(Vars.vx, Vars.xPrev, Vars.stepSize);
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Vars.y = integral(Vars.vy, Vars.yPrev, Vars.stepSize);
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Vars.z = integral(Vars.vz, Vars.zPrev, Vars.stepSize);
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// Euler Angles
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Vars.phidot = Vars.yawdot + (Vars.pitchdot * sin(Vars.yaw) +
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Vars.rolldot * cos(Vars.yaw)) *
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(sin(Vars.pitch) / cos(Vars.pitch));
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Vars.thetadot =
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Vars.pitchdot * cos(Vars.yaw) - Vars.rolldot * sin(Vars.pitch);
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Vars.psidot =
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(Vars.pitchdot * sin(Vars.yaw) + Vars.rolldot * cos(Vars.yaw)) /
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cos(Vars.pitch);
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Vars.yaw = integral(Vars.phidot, Vars.yawPrev, Vars.stepSize);
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Vars.pitch = integral(Vars.thetadot, Vars.pitchPrev, Vars.stepSize);
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Vars.roll = integral(Vars.psidot, Vars.rollPrev, Vars.stepSize);
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}
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// Set "prev" values for next timestep
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Vars.I11prev = Vars.I11;
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Vars.I22prev = Vars.I22;
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Vars.I33prev = Vars.I33;
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Vars.yawPrev = Vars.yaw;
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Vars.pitchPrev = Vars.pitch;
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Vars.rollPrev = Vars.roll;
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Vars.yawdotPrev = Vars.yawdot;
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Vars.pitchdotPrev = Vars.pitchdot;
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Vars.rolldotPrev = Vars.rolldot;
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Vars.yawddotPrev = Vars.yawddot;
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Vars.pitchddotPrev = Vars.pitchddot;
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Vars.rollddotPrev = Vars.rollddot;
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Vars.axPrev = Vars.ax;
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Vars.ayPrev = Vars.ay;
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Vars.azPrev = Vars.az;
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Vars.vxPrev = Vars.vx;
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Vars.vyPrev = Vars.vy;
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Vars.vzPrev = Vars.vz;
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Vars.xPrev = Vars.x;
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Vars.yPrev = Vars.y;
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Vars.zPrev = Vars.z;
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}
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void write2CSV(struct sVars &Vars, std::fstream &outfile, int t) {
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// writing to output file
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outfile << t << ", ";
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outfile << Vars.x << ", ";
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outfile << Vars.y << ", ";
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outfile << Vars.z << ", ";
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outfile << Vars.vx << ", ";
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outfile << Vars.vy << ", ";
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outfile << Vars.vz << ", ";
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outfile << Vars.ax << ", ";
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outfile << Vars.ay << ", ";
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outfile << Vars.az << ", ";
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outfile << Vars.yaw * 180 / 3.1416 << ", ";
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outfile << Vars.pitch * 180 / 3.1416 << ", ";
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outfile << Vars.roll * 180 / 3.1416 << ", ";
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outfile << Vars.yawdot * 180 / 3.1416 << ", ";
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outfile << Vars.pitchdot * 180 / 3.1416 << ", ";
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outfile << Vars.rolldot * 180 / 3.1416 << ", ";
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outfile << Vars.yawddot * 180 / 3.1416 << ", ";
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outfile << Vars.pitchddot * 180 / 3.1416 << ", ";
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outfile << Vars.rollddot * 180 / 3.1416 << ", ";
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outfile << Vars.I11 << ", ";
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outfile << Vars.I22 << ", ";
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outfile << Vars.I33 << ", ";
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outfile << Vars.I11dot << ", ";
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outfile << Vars.I22dot << ", ";
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outfile << Vars.I33dot << ", ";
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outfile << Vars.xServoDegs << ", ";
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outfile << Vars.yServoDegs << ", ";
|
|
|
|
outfile << Vars.m << ", ";
|
|
outfile << Vars.thrust << ", ";
|
|
outfile << Vars.burnElapsed << ", ";
|
|
outfile << Vars.Fz << ", ";
|
|
|
|
outfile << Vars.LQRx << ", ";
|
|
outfile << Vars.LQRy << std::endl;
|
|
}
|
|
|
|
double derivative(double x2, double x1, double dt) {
|
|
double dxdt = (x2 - x1) / (dt / 1000);
|
|
return dxdt;
|
|
}
|
|
|
|
double integral(double x, double y, double dt) {
|
|
double integ = (x * dt / 1000) + y;
|
|
return integ;
|
|
} |