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LQR implementation and general improvements
This commit is contained in:
Brendan McGeeney
@@ -3,77 +3,130 @@ close all; clear all; clc;
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%% User Defined Values
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% Initial Conditions
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v_0 = 0; % Initial Velocity [m/s]
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v0 = 0; % Initial Velocity (z) [m/s]
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M0 = 1.2; % Initial Mass [kg]
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yaw0 = 0; % Initial Yaw [deg]
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pitch0 = 5; % Initial Pitch [deg]
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roll0 = 0; % Initial Roll [deg]
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p0 = 0; % Initial Angular Velocity (x) [deg/s]
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q0 = 0; % Initial Angular Velocity (y) [deg/s]
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r0 = 0; % Initial Angular Velocity (z) [deg/s]
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% Thrust Curve Data from Text File [t, N]
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Tcurve = readmatrix('F15_thrustCurve.txt');
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Tcurve = readmatrix('F15_thrustCurve.txt'); % Thrust Curve from .txt [t, N]
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% Constants
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g = -9.81; % Gravitational Acceleration [m/s2]
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M0 = 0.8; % Initial Mass [kg]
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Mp = 0.06; % Propellant Mass [kg]
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Mb = M0 - Mp; % Burnout Mass [kg]
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tb = Tcurve(end, 1); % Burn Time [s]
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mdot = Mp / tb; % Mass Flow Rate [kg/s]
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D = 0; % Drag [N]
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stepSize = 0.001; % Simulation Step Size [s]
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g = -9.81; % Gravitational Acceleration [m/s2]
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Mp = 0.06; % Propellant Mass [kg]
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Mb = M0 - Mp; % Burnout Mass [kg]
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tb = Tcurve(end, 1) - Tcurve(1, 1); % Burn Time [s]
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mdot = Mp / tb; % Mass Flow Rate [kg/s]
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D = 0; % Drag [N]
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stepSize = 0.001; % Simulation Step Size [s]
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maxServo = 15; % Max Servo Rotation [deg]
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[h_0, vb, burnStartTime] = burnStartTimeCalc(Tcurve, tb, M0, mdot, Mb)
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% Moment of Inertia / Mass
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I11 = (1/12) * 0.5318^2 + 0.25 * 0.05105^2; % (1/12) * h^2 + 0.25 * r^2
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I22 = (1/12) * 0.5318^2 + 0.25 * 0.05105^2; % (1/12) * h^2 + 0.25 * r^2
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I33 = 0.5 * 0.05105^2; % 0.5 * r^2
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I = [I11 0 0; 0 I22 0; 0 0 I33]; % I divided by Mass... this is taken care of in Simulink since our mass isn't constant
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%% Pre-Sim Calcs
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K = calcLQR(I*M0); % LQR Gain Calcs
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[h0, vb, burnStartTime] = burnStartTimeCalc(Tcurve, tb, M0, mdot, Mb, v0); % Burn Start Time Calc
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simTime = burnStartTime + tb; % Simulation Time [s]
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yaw0 = yaw0 * pi / 180; % Initial Yaw [rad]
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pitch0 = pitch0 * pi / 180; % Initial Pitch [rad]
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roll0 = roll0 * pi / 180; % Initial Roll [rad]
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p0 = p0 * pi / 180; % Initial Angular Velocity (x) [rad/s]
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q0 = q0 * pi / 180; % Initial Angular Velocity (y) [rad/s]
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r0 = r0 * pi / 180; % Initial Angular Velocity (z) [rad/s]
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%% Simulink
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tic
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simTime = burnStartTime + tb; % Simulation Time [s]
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model = 'simProtoype';
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load_system(model);
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simOut = sim(model);
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toc
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%% Output
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% Acceleration
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%% Outputs
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figure(1)
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plot(simOut.a)
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% Acceleration
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subplot(3, 1, 1)
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plot(simOut.a.Data(:, 3))
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title('Acceleration vs Time')
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xlabel('Time (s)')
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ylabel('Acceleration (g''s)')
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legend('X','Y')
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saveas(gcf,'outputs/Acceleration vs Time.png')
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% Velocity
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figure(2)
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plot(simOut.v)
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subplot(3, 1, 2)
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plot(simOut.v.Data(:, 3))
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title('Velocity vs Time')
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xlabel('Time (s)')
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ylabel('Velocity (m/s)')
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legend('X','Y')
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saveas(gcf,'outputs/Velocity vs Time.png')
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% Altitude
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figure(3)%k)
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plot(sqrt(simOut.h.Data(:,2).^2 + simOut.h.Data(:,1).^2), simOut.h.Time)
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subplot(3, 1, 3)
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plot(simOut.h.Time, simOut.h.Data(:,3))
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title('Altitude vs Time')
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% title(['burnStart = ',num2str(burnStart),' s'])
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xlabel('Time (s)')
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ylabel('Altitude (m)')
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saveas(gcf,'outputs/Altitude vs Time.png')
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ylim([0 h0+5])
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saveas(gcf,'outputs/Accel-Vel-Alt vs Time.png')
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figure(2)
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% Euler Angles
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subplot(2, 1, 1)
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plot(simOut.YPR.Data)
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title('Euler Angles vs Time')
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xlabel('Time (ms)')
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ylabel('Euler Angles (deg)')
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legend('Yaw', 'Pitch', 'Roll')
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% Angular Velocity
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subplot(2, 1, 2)
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plot(simOut.YPRdot.Data)
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title('Angular Velocity vs Time')
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xlabel('Time (ms)')
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ylabel('Angular Velocity (deg/s)')
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legend('X', 'Y', 'Z')
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saveas(gcf,'outputs/Euler Angles vs Time.png')
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figure(3)
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% Servo 1 Position
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subplot(2, 1, 1)
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plot(simOut.servo1.Data)
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title('Servo 1 Position vs Time')
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xlabel('Time (ms)')
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ylabel('Servo 1 Position (rad)')
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% Servo 2 Position
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subplot(2, 1, 2)
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plot(simOut.servo2.Data)
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title('Servo 2 Position vs Time')
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xlabel('Time (ms)')
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ylabel('Servo 2 Position (rad)')
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saveas(gcf,'outputs/Servo Position vs Time.png')
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% Animation
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h = figure(4);
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K = animatedline('Marker', 'o');
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axis([0, 2, 0, h_0])
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axis([-10, 10, 0, h0])
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xlabel('X-Position (m)')
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ylabel('Altitude (m)')
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title('Altitude')
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grid on
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for i = 1 : length(simOut.h.Data)
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clearpoints(K);
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addpoints(K, 1, simOut.h.Data(i, 2));
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addpoints(K, simOut.h.Data(i, 1), simOut.h.Data(i, 3));
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title(sprintf('Altitude at T = %f', simOut.h.Time(i)))
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drawnow limitrate
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% Write Animation to gif, set to zero when testing since its slow to render.
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outframes = 50; % 50 is a nice default
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if outframes
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@@ -98,5 +151,4 @@ for i = 1 : length(simOut.h.Data)
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imwrite(imind,cm,'outputs/Altitude.gif','gif','WriteMode','append', 'DelayTime', .2);
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end
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end
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end
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end
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