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Full-state State Observer
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| % SIMULATION | |
| m = 1; | |
| I = 0.1677; | |
| R = 0.02; | |
| h = 0.02; | |
| g = 9.81; | |
| A = [0, 0, 0, -m*g/I; 1, 0, 0, 0; 0, -2/3*g, 0, 0; 0, 0, 1, 0]; | |
| B = [1, 0, 0, 0]'; | |
| C = [0, 1, 0, 0]; | |
| D = 0; | |
| RealSystem = ss(A, B, C, D); | |
| X0 = [0, 0.1, 0, 0.035]'; | |
| tmax = 1; | |
| [y_real,t_real,x_real] = initial(RealSystem, X0, tmax); | |
| fig = figure(); | |
| subplot(2,1,1); | |
| plot(t_real, y_real) | |
| ylabel('theta (rad)') | |
| xlabel('t (s)') | |
| subplot(2,1,2); | |
| plot(t_real, x_real(:,4)) | |
| ylabel('r (m)') | |
| xlabel('t (s)') | |
| saveas(fig, 'initial.png') | |
| % OBSERVER | |
| Q = 3e4; R = 0.01; | |
| [kest,L,P] = kalman(RealSystem,Q,R,[]); | |
| disp(L) | |
| eig(A-L*C) | |
| xdot = @(t, x) A*x + L * (interp1(t_real,y_real,t) - C*x); | |
| [t_observed, x_observed] = ode45(xdot, [0,tmax], [0,0,0,0]); | |
| fig = figure(); | |
| plot(t_real, x_real); | |
| hold on; | |
| set(gca,'ColorOrderIndex',1) | |
| plot(t_observed, x_observed, '--'); | |
| ylabel('X') | |
| xlabel('t') | |
| ylim([-.5, 1]) | |
| legend('theta-dot', 'theta', 'r-dot', 'r', 'theta-dot (observed)', 'theta (observed)', 'r-dot (observed)', 'r (observed)') | |
| saveas(fig, 'observed.png') | |
| % ANIMATION 1 | |
| for t=0:0.01:tmax | |
| f = figure('visible','off'); | |
| X = interp1(t_real,x_real,t); | |
| theta = X(2); | |
| r = X(4); | |
| plot([-0.1*cos(theta), 0.1*cos(theta)], [-0.1*sin(theta), 0.1*sin(theta)], 'LineWidth', 2); | |
| hold on | |
| viscircles([r*cos(theta)+R*sin(theta) r*sin(theta)+R*cos(theta)], R); | |
| xlim([-0.1,0.1]); | |
| ylim([-0.1,0.1]); | |
| axis('equal'); | |
| saveas(f, sprintf('sim-%.2f.png', t)); | |
| end | |
| % ANIMATION 2 | |
| for t=0:0.01:tmax | |
| f = figure('visible','off'); | |
| X = interp1(t_real,x_real,t); | |
| X_observed = interp1(t_observed,x_observed,t); | |
| theta = X(2); | |
| r = X(4); | |
| theta_obs = X_observed(2); | |
| r_obs = X_observed(4); | |
| plot([-0.1*cos(theta), 0.1*cos(theta)], [-0.1*sin(theta), 0.1*sin(theta)], 'LineWidth', 2) | |
| hold on | |
| plot([-0.1*cos(theta_obs), 0.1*cos(theta_obs)], [-0.1*sin(theta_obs), 0.1*sin(theta_obs)], '--', 'LineWidth', 2) | |
| hold on | |
| viscircles([r*cos(theta)+R*sin(theta) r*sin(theta)+R*cos(theta)], [R]) | |
| hold on | |
| viscircles([r_obs*cos(theta_obs)+R*sin(theta_obs) r_obs*sin(theta_obs)+R*cos(theta_obs)], [R], 'LineStyle', '--') | |
| xlim([-0.1,0.1]) | |
| ylim([-0.1,0.1]) | |
| axis('equal') | |
| saveas(f, sprintf('obs-%.2f.png', t)); | |
| end |
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