diff --git a/build/debug/gainCalc.m b/build/debug/gainCalc.m new file mode 100644 index 0000000..4301efe --- /dev/null +++ b/build/debug/gainCalc.m @@ -0,0 +1,66 @@ +clear all; clc; +%% User Defined Values +M0 = 1.2; % [kg] +vehicleHeight = 0.5318; % [m] +vehicleRadius = 0.05105; % [m] + +%% Calcs +I11 = (1/12) * vehicleHeight^2 + 0.25 * vehicleRadius^2; % (1/12) * h^2 + 0.25 * r^2 +I22 = (1/12) * vehicleHeight^2 + 0.25 * vehicleRadius^2; % (1/12) * h^2 + 0.25 * r^2 +I33 = 0.5 * vehicleRadius^2; % 0.5 * r^2 +I = M0 * [I11 0 0; 0 I22 0; 0 0 I33]; + +Q = eye(6) * I(3, 3); +Mu = 398600; +r0 = [6678; 0; 0]; + +k1 = (I(2,2) - I(3,3)) / I(1,1); +k2 = (I(1,1) - I(3,3)) / I(2,2); +k3 = (I(2,2) - I(1,1)) / I(3,3); + +n = sqrt(Mu/(norm(r0)^3)); + +F = -2 * n^2 * [4 * k1, 0, 0; 0, 3 * k2, 0; 0, 0, k3]; +G = n * [0, 0, (1 - k1); 0, 0, 0; (k3 - 1), 0, 0]; + +Iinv = [1 / I(1,1), 0, 0; 0, 1 / I(2,2), 0; 0, 0, 1 / I(3,3)]; + +A = [zeros(3,3), 0.5 * eye(3); F, G]; +B = [zeros(3,3); Iinv]; + +R = eye(3)*10^-6; +Rinv = R^-1; + +S = icare(A, B, Q, R); + +K = Rinv * B' * S; + +%% Outputs +% Copy results in command window to LQRcalc function in C++ +fprintf("double K11 = %3.5f;\n", K(1, 1)) +fprintf("double K12 = %3.5f;\n", K(1, 2)) +fprintf("double K13 = %3.5f;\n", K(1, 3)) +fprintf("double K14 = %3.5f;\n", K(1, 4)) +fprintf("double K15 = %3.5f;\n", K(1, 5)) +fprintf("double K16 = %3.5f;\n", K(1, 6)) +fprintf("double K21 = %3.5f;\n", K(2, 1)) +fprintf("double K22 = %3.5f;\n", K(2, 2)) +fprintf("double K23 = %3.5f;\n", K(2, 3)) +fprintf("double K24 = %3.5f;\n", K(2, 4)) +fprintf("double K25 = %3.5f;\n", K(2, 5)) +fprintf("double K26 = %3.5f;\n", K(2, 6)) +fprintf("double K31 = %3.5f;\n", K(3, 1)) +fprintf("double K32 = %3.5f;\n", K(3, 2)) +fprintf("double K33 = %3.5f;\n", K(3, 3)) +fprintf("double K34 = %3.5f;\n", K(3, 4)) +fprintf("double K35 = %3.5f;\n", K(3, 5)) +fprintf("double K36 = %3.5f;\n", K(3, 6)) + +syms yaw pitch roll yawdot pitchdot rolldot gain +w = [0.5*yaw 0.5*pitch 0.5*roll yawdot pitchdot rolldot]'; + +syms K11 K12 K13 K14 K15 K16 K21 K22 K23 K24 K25 K26 K31 K32 K33 K34 K35 K36 +K = gain * [K11 K12 K13 K14 K15 K16; K21 K22 K23 K24 K25 K26; K31 K32 K33 K34 K35 K36]; + +simplify(K*w) + diff --git a/build/debug/main.exe b/build/debug/main.exe index a1dcb99..4708f92 100644 Binary files a/build/debug/main.exe and b/build/debug/main.exe differ diff --git a/build/debug/outputs/Accel-Vel-Alt vs Time.png b/build/debug/outputs/Accel-Vel-Alt vs Time.png new file mode 100644 index 0000000..23c9c69 Binary files /dev/null and b/build/debug/outputs/Accel-Vel-Alt vs Time.png differ diff --git a/build/debug/outputs/Euler Angles vs Time.png b/build/debug/outputs/Euler Angles vs Time.png new file mode 100644 index 0000000..ab82920 Binary files /dev/null and b/build/debug/outputs/Euler Angles vs Time.png differ diff --git a/build/debug/outputs/Servo Position vs Time.png b/build/debug/outputs/Servo Position vs Time.png new file mode 100644 index 0000000..7803c59 Binary files /dev/null and b/build/debug/outputs/Servo Position vs Time.png differ diff --git a/build/debug/simOut.csv b/build/debug/simOut.csv index dd8ab6f..61a7d43 100644 --- a/build/debug/simOut.csv +++ b/build/debug/simOut.csv @@ -1,4318 +1,4318 @@ -t, x, y, z, vx, vy, vz, ax, ay, az, yaw, pitch, roll, yawdot, pitchdot, rolldot, Servo1, Servo2, m, thrust, burnElapsed, Fz, LQRx, LQRy -0, 0, 0, 25.9961, 0, 0, 0, 0, 0, -9.81, 0, 0, 0, 0, 0, 0, 8.33706e-315, 3.20512e-317, 1.2, 0, 2000, -11.772, 0, -0 -1, 0, 0, 25.9961, 0, 0, -0.00981, 0, 0, -9.81, 0, 0, 0, 0, 0, 0, 8.33706e-315, 3.20512e-317, 1.2, 0, 2000, -11.772, 0, -0 -2, 0, 0, 25.9961, 0, 0, -0.01962, 0, 0, -9.81, 0, 0, 0, 0, 0, 0, 8.33706e-315, 3.20512e-317, 1.2, 0, 2000, -11.772, 0, -0 -3, 0, 0, 25.996, 0, 0, -0.02943, 0, 0, -9.81, 0, 0, 0, 0, 0, 0, 8.33706e-315, 3.20512e-317, 1.2, 0, 2000, -11.772, 0, -0 -4, 0, 0, 25.996, 0, 0, -0.03924, 0, 0, -9.81, 0, 0, 0, 0, 0, 0, 8.33706e-315, 3.20512e-317, 1.2, 0, 2000, -11.772, 0, -0 -5, 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-2.36775e-05, 0.000655644, -0, 1.14004, 13.334, 3.3, 2.15024, 0.000152583, -0 +4316, -0.000940678, -2.0967, 2.03461, -0.000191888, -1.10881, -1.35716, 0.000133807, -0.0625752, 1.93735, 2.71474, 0, 0, -2.638, 0, 0, 1.66415, 0, 0, 0.000742751, 0.000742751, 0.0014855, -1.18387e-05, -1.18387e-05, -2.36775e-05, 0.000655467, -0, 1.14002, 13.334, 3.301, 2.15042, 0.000152542, -0 diff --git a/build/debug/simPlot.m b/build/debug/simPlot.m index f0f48c3..8054283 100644 --- a/build/debug/simPlot.m +++ b/build/debug/simPlot.m @@ -18,10 +18,19 @@ roll = T(:, 13); yawdot = T(:, 14); pitchdot = T(:, 15); rolldot = T(:, 16); -Servo1 = T(:, 17); -Servo2 = T(:, 18); -m = T(:, 19); -thrust = T(:, 20); +yawddot = T(:, 17); +pitchddot = T(:, 18); +rollddot = T(:, 19); +I11 = T(:, 20); +I22 = T(:, 21); +I33 = T(:, 22); +I11dot = T(:, 23); +I22dot = T(:, 24); +I33dot = T(:, 25); +Servo1 = T(:, 26); +Servo2 = T(:, 27); +m = T(:, 28); +thrust = T(:, 29); % Acceleration subplot(3, 1, 1) diff --git a/build/release/outputs/Accel-Vel-Alt vs Time.png b/build/release/outputs/Accel-Vel-Alt vs Time.png new file mode 100644 index 0000000..7d3df82 Binary files /dev/null and b/build/release/outputs/Accel-Vel-Alt vs Time.png differ diff --git a/build/release/outputs/Euler Angles vs Time.png b/build/release/outputs/Euler Angles vs Time.png new file mode 100644 index 0000000..21e7870 Binary files /dev/null and b/build/release/outputs/Euler Angles vs Time.png differ diff --git a/build/release/outputs/Servo Position vs Time.png b/build/release/outputs/Servo Position vs Time.png new file mode 100644 index 0000000..1c0791e Binary files /dev/null and b/build/release/outputs/Servo Position vs Time.png differ diff --git a/build/release/simOut.csv b/build/release/simOut.csv new file mode 100644 index 0000000..3cf4f58 --- /dev/null +++ b/build/release/simOut.csv @@ -0,0 +1,4318 @@ +t, x, y, z, vx, vy, vz, ax, ay, az, yaw, pitch, roll, yawdot, pitchdot, rolldot, Servo1, Servo2, m, thrust, burnElapsed, 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a/include/sVars.h b/include/sVars.h index 6df6f0f..44add2a 100644 --- a/include/sVars.h +++ b/include/sVars.h @@ -21,7 +21,7 @@ struct sVars double yawddotPrev, pitchddotPrev, rollddotPrev; double m, m0, mp, mb, mdot; - double vehicleHeight, vehicleRadius; + double vehicleHeight, vehicleRadius, momentArm; double tb; double vb; diff --git a/src/main.cpp b/src/main.cpp index 3ddc22a..91536a0 100644 --- a/src/main.cpp +++ b/src/main.cpp @@ -14,22 +14,23 @@ int main() Vars.vz = 0; // [m/s] // Initial YPR - Vars.yaw = 0; // [rad] - Vars.pitch = 0; // [rad] - Vars.roll = 0; // [rad] + Vars.yaw = 15 * 3.1416 / 180; // [rad] + Vars.pitch = 0 * 3.1416 / 180; // [rad] + Vars.roll = 0 * 3.1416 / 180; // [rad] // Initial YPRdot - Vars.yawdot = 0; // [rad/s] - Vars.pitchdot = 0; // [rad/s] - Vars.rolldot = 0; // [rad/s] + Vars.yawdot = 0 * 3.1416 / 180; // [rad/s] + Vars.pitchdot = 0 * 3.1416 / 180; // [rad/s] + Vars.rolldot = 0 * 3.1416 / 180; // [rad/s] // Servo Limitation - Vars.maxServo = 0; // [degs] + Vars.maxServo = 15; // [degs] // Vehicle Properties Vars.m0 = 1.2; // [kg] Vars.vehicleHeight = 0.5318; // [m] Vars.vehicleRadius = 0.05105; // [m] + Vars.momentArm = 0.145; // [m] // Sim Step Size Vars.stepSize = 1; // [ms] @@ -43,6 +44,7 @@ int main() sim(Vars); std::cout << "Finished"; + std::cin.get(); return 0; } \ No newline at end of file diff --git a/src/sim.cpp b/src/sim.cpp index cf5b224..eb93056 100644 --- a/src/sim.cpp +++ b/src/sim.cpp @@ -28,7 +28,7 @@ void sim(struct sVars &Vars) // Output file header. These are the variables that we output - useful for // debugging outfile << "t, x, y, z, vx, vy, vz, ax, ay, az, yaw, pitch, roll, yawdot, " - "pitchdot, rolldot, Servo1, Servo2, m, thrust, burnElapsed, Fz, " + "pitchdot, rolldot, yawddot, pitchddot, rollddot, I11, I22, I33, I11dot, I22dot, I33dot, Servo1, Servo2, m, thrust, burnElapsed, Fz, " "LQRx, LQRy" << std::endl; @@ -108,8 +108,7 @@ void thrustSelection(struct sVars &Vars, int t) } else - Vars.burnElapsed = - 2000; // 2000 just an arbitrary number to make sure we don't burn + Vars.burnElapsed = 2000; // arbitrary number to ensure we don't burn bool b_thrustSelect; @@ -135,12 +134,15 @@ void thrustSelection(struct sVars &Vars, int t) void lqrCalc(struct sVars &Vars) { + Vars.I11 = Vars.m * ((1 / 12) * pow(Vars.vehicleHeight, 2) + pow(Vars.vehicleRadius, 2) / 4); Vars.I22 = Vars.m * ((1 / 12) * pow(Vars.vehicleHeight, 2) + pow(Vars.vehicleRadius, 2) / 4); Vars.I33 = Vars.m * 0.5 * pow(Vars.vehicleRadius, 2); + /* + double n = sqrt(398600 / pow(6678, 3)); double k1 = (Vars.I22 - Vars.I33) / Vars.I11; double k2 = (Vars.I11 - Vars.I33) / Vars.I22; @@ -164,6 +166,7 @@ void lqrCalc(struct sVars &Vars) Algorithm taken from LQR wikipedia page: https://en.wikipedia.org/wiki/Algebraic_Riccati_equation#Solution */ + /* double gain = 0.25; double K11 = @@ -190,9 +193,47 @@ void lqrCalc(struct sVars &Vars) (pow(abs(F33), 2) * pow(abs(Vars.I33), 4) * pow(abs(R33), 2) + 1)); // Matrix Multiply K with [YPR/2; w123] column vector and divide by moment arm - double momentArm = 0.145; - Vars.LQRx = (K11 * Vars.yaw / 2 + K16 * Vars.rolldot) / momentArm; - Vars.LQRy = (K22 * Vars.pitch / 2) / momentArm; + Vars.LQRx = (K11 * Vars.yaw / 2 + K16 * Vars.rolldot) / Vars.momentArm; + Vars.LQRy = (K22 * Vars.pitch / 2) / Vars.momentArm; + + */ + + double K11 = 39.54316; + double K12 = 0.00000; + double K13 = -0.00000; + double K14 = 39.55769; + double K15 = 0.00000; + double K16 = 0.00000; + double K21 = 0.00000; + double K22 = 39.54316; + double K23 = 0.00000; + double K24 = 0.00000; + double K25 = 39.55769; + double K26 = 0.00000; + double K31 = 0.00000; + double K32 = 0.00000; + double K33 = 39.54316; + double K34 = 0.00000; + double K35 = 0.00000; + double K36 = 39.54394; + + double gain = 0.25 * pow(10, -4); + + // Matrix Multiply K with [YPR/2; w123] column vector and divide by moment arm + Vars.LQRx = gain * ((K12 * Vars.pitch) / 2 + K15 * Vars.pitchdot + (K13 * Vars.roll) / 2 + K16 * Vars.rolldot + (K11 * Vars.yaw) / 2 + K14 * Vars.yawdot) / -Vars.momentArm; + Vars.LQRy = gain * ((K22 * Vars.pitch) / 2 + K25 * Vars.pitchdot + (K23 * Vars.roll) / 2 + K26 * Vars.rolldot + (K21 * Vars.yaw) / 2 + K24 * Vars.yawdot) / -Vars.momentArm; + + // LQR Force limiter X + if (Vars.LQRx > Vars.thrust) + Vars.LQRx = Vars.thrust; + else if (Vars.LQRx < -1 * Vars.thrust) + Vars.LQRx = -1 * Vars.thrust; + + // LQR Force limiter Y + if (Vars.LQRy > Vars.thrust) + Vars.LQRy = Vars.thrust; + else if (Vars.LQRy < -1 * Vars.thrust) + Vars.LQRy = -1 * Vars.thrust; } void TVC(struct sVars &Vars, double g) @@ -236,9 +277,8 @@ void TVC(struct sVars &Vars, double g) (Vars.m * g); // Calculate moment created by Fx and Fy - double momentArm = 0.145; - Vars.momentX = Vars.Fx * momentArm; - Vars.momentY = Vars.Fy * momentArm; + Vars.momentX = Vars.Fx * Vars.momentArm; + Vars.momentY = Vars.Fy * Vars.momentArm; Vars.momentZ = 0; } } @@ -378,6 +418,18 @@ void write2CSV(struct sVars &Vars, std::fstream &outfile, int t) outfile << Vars.pitchdot * 180 / 3.1416 << ", "; outfile << Vars.rolldot * 180 / 3.1416 << ", "; + outfile << Vars.yawddot * 180 / 3.1416 << ", "; + outfile << Vars.pitchddot * 180 / 3.1416 << ", "; + outfile << Vars.rollddot * 180 / 3.1416 << ", "; + + outfile << Vars.I11 << ", "; + outfile << Vars.I22 << ", "; + outfile << Vars.I33 << ", "; + + outfile << Vars.I11dot << ", "; + outfile << Vars.I22dot << ", "; + outfile << Vars.I33dot << ", "; + outfile << Vars.xServoDegs << ", "; outfile << Vars.yServoDegs << ", ";