Improve H-infinity, system parameters, add simulations and plots

1 files changed, 211 insertions, 0 deletions

diff --git a/uav_sim_step_lqr.m b/uav_sim_step_lqr.m
new file mode 100644
index 0000000..e672d35
--- /dev/null
+++ b/uav_sim_step_lqr.m
@@ -0,0 +1,211 @@
+% Simulate a step responses of ducted-fan VTOL micro-UAV.
+%
+% Copyright (C) 2024, Naoki Sean Pross, ETH Zürich
+% This work is distributed under a permissive license, see LICENSE.txt
+
+function [simout] = uav_sim_step_lqr(params, model, ctrl, nsamp, do_plots)
+
+% TODO: Close loop
+
+% Create step inputs (normalized)
+noise = zeros(7, nsamp); % no noise
+ref_step = ones(1, nsamp); % 1d step function
+
+in_step_x = [ noise; ref_step; zeros(2, nsamp) ];
+in_step_y = [ noise; zeros(1, nsamp); ref_step; zeros(1, nsamp) ];
+in_step_z = [ noise; zeros(2, nsamp); ref_step ];
+
+% Simulation time
+n_settle_times = 10;
+T_final_horiz = n_settle_times * params.performance.HorizontalSettleTime;
+T_final_vert = n_settle_times * params.performance.VerticalSettleTime;
+
+t_xy = linspace(0, T_final_horiz, nsamp);
+t_z = linspace(0, T_final_vert, nsamp);
+
+% Simulate step responses
+out_step_x = lsim(P_nom_clp, in_step_x, t_xy);
+out_step_y = lsim(P_nom_clp, in_step_y, t_xy);
+out_step_z = lsim(P_nom_clp, in_step_z, t_z);
+
+if do_plots
+  % Conversion factors
+  to_deg = 180 / pi; % radians to degrees
+  to_rpm = pi / 30; % rad / s to RPM
+
+  % Figure for flaps and Euler angles
+  figure;
+  sgtitle(sprintf(...
+    '\\bfseries Step Response of Flap and Euler Angles (%s)', ...
+    ctrl.Name), 'Interpreter', 'latex');
+
+  % Plot limits
+  ref_value     = params.performance.ReferencePosMaxDistance;
+  alpha_max_deg = params.actuators.ServoAbsMaxAngle * to_deg;
+  euler_lim_deg = 1.5; % params.performance.AngleMaxPitchRoll * to_deg;
+  omega_max_rpm = (params.actuators.PropellerMaxAngularVelocity ...
+    - params.linearization.Inputs(5)) * to_rpm;
+  omega_min_rpm = -params.linearization.Inputs(5) * to_rpm;
+
+  % Plot step response from x to alpha
+  subplot(2, 3, 1);
+  hold on;
+  plot(t_xy, out_step_x(:, Ialpha(1)) * to_deg);
+  plot(t_xy, out_step_x(:, Ialpha(2)) * to_deg);
+  plot(t_xy, out_step_x(:, Ialpha(3)) * to_deg);
+  plot(t_xy, out_step_x(:, Ialpha(4)) * to_deg);
+  plot([0, T_final_horiz], [1, 1] * alpha_max_deg, 'r--');
+  plot([0, T_final_horiz], [-1, -1] * alpha_max_deg, 'r--');
+  grid on;
+  xlim([0, T_final_horiz]);
+  ylim([-alpha_max_deg * 1.1, alpha_max_deg * 1.1]);
+  title('Horizontal $x$ to Flaps', 'Interpreter', 'latex');
+  ylabel('Flap Angle (degrees)', 'Interpreter', 'latex');
+  xlabel('Time (seconds)', 'Interpreter', 'latex');
+  legend('$\alpha_1(t)$', '$\alpha_2(t)$', '$\alpha_3(t)$', '$\alpha_4(t)$', ...
+    'Interpreter', 'latex');
+
+  % Plot step response from y to alpha
+  subplot(2, 3, 2); hold on;
+  plot(t_xy, out_step_y(:, Ialpha(1)) * to_deg);
+  plot(t_xy, out_step_y(:, Ialpha(2)) * to_deg);
+  plot(t_xy, out_step_y(:, Ialpha(3)) * to_deg);
+  plot(t_xy, out_step_y(:, Ialpha(4)) * to_deg);
+  plot([0, T_final_horiz], [1, 1] * alpha_max_deg, 'r--');
+  plot([0, T_final_horiz], [-1, -1] * alpha_max_deg, 'r--');
+  grid on;
+  xlim([0, T_final_horiz]);
+  ylim([-alpha_max_deg * 1.1, alpha_max_deg * 1.1]);
+  title('Horizontal $y$ to Flaps', 'Interpreter', 'latex');
+  ylabel('Flap Angle (degrees)', 'Interpreter', 'latex');
+  xlabel('Time (seconds)', 'Interpreter', 'latex');
+  legend('$\alpha_1(t)$', '$\alpha_2(t)$', '$\alpha_3(t)$', '$\alpha_4(t)$', ...
+    'Interpreter', 'latex');
+
+  % Plot step response from z to alpha
+  subplot(2, 3, 3); hold on;
+  plot(t_z, out_step_z(:, Ialpha(1)) * to_deg);
+  plot(t_z, out_step_z(:, Ialpha(2)) * to_deg);
+  plot(t_z, out_step_z(:, Ialpha(3)) * to_deg);
+  plot(t_z, out_step_z(:, Ialpha(4)) * to_deg);
+  plot([0, T_final_vert], [1, 1] * alpha_max_deg, 'r--');
+  plot([0, T_final_vert], [-1, -1] * alpha_max_deg, 'r--');
+  grid on;
+  xlim([0, T_final_vert]);
+  ylim([-alpha_max_deg * 1.1, alpha_max_deg * 1.1]);
+  title('Vertical $z$ to Flaps', 'Interpreter', 'latex');
+  ylabel('Flap Angle (degrees)', 'Interpreter', 'latex');
+  xlabel('Time (seconds)', 'Interpreter', 'latex');
+  legend('$\alpha_1(t)$', '$\alpha_2(t)$', '$\alpha_3(t)$', '$\alpha_4(t)$', ...
+    'Interpreter', 'latex');
+
+  % Plot step response from x to Theta
+  subplot(2, 3, 4); hold on;
+  plot(t_xy, out_step_x(:, ITheta(1)) * to_deg);
+  plot(t_xy, out_step_x(:, ITheta(2)) * to_deg);
+  plot(t_xy, out_step_x(:, ITheta(3)) * to_deg);
+  grid on;
+  xlim([0, T_final_horiz]);
+  ylim([-euler_lim_deg, euler_lim_deg]);
+  title('Horizontal $x$ to Euler Angles', 'Interpreter', 'latex');
+  ylabel('Euler Angle (degrees)', 'Interpreter', 'latex');
+  xlabel('Time (seconds)', 'Interpreter', 'latex');
+  legend('$\phi(t)$ Roll ', '$\theta(t)$ Pitch ', '$\psi(t)$ Yaw ', ...
+    'Interpreter', 'latex');
+
+  % Plot step response from y to Theta
+  subplot(2, 3, 5); hold on;
+  plot(t_xy, out_step_y(:, ITheta(1)) * to_deg);
+  plot(t_xy, out_step_y(:, ITheta(2)) * to_deg);
+  plot(t_xy, out_step_y(:, ITheta(3)) * to_deg);
+  grid on;
+  xlim([0, T_final_horiz]);
+  ylim([-euler_lim_deg, euler_lim_deg]);
+  title('Horizontal $y$ to Euler Angles', 'Interpreter', 'latex');
+  ylabel('Euler Angle (degrees)', 'Interpreter', 'latex');
+  xlabel('Time (seconds)', 'Interpreter', 'latex');
+  legend('$\phi(t)$ Roll ', '$\theta(t)$ Pitch ', '$\psi(t)$ Yaw ', ...
+    'Interpreter', 'latex');
+
+  % Plot step response from z to Theta
+  subplot(2, 3, 6); hold on;
+  plot(t_z, out_step_z(:, ITheta(1)) * to_deg);
+  plot(t_z, out_step_z(:, ITheta(2)) * to_deg);
+  plot(t_z, out_step_z(:, ITheta(3)) * to_deg);
+  grid on;
+  xlim([0, T_final_vert]);
+  ylim([-euler_lim_deg, euler_lim_deg]);
+  title('Vertical $z$ to Euler Angles', 'Interpreter', 'latex');
+  ylabel('Euler Angle (degrees)', 'Interpreter', 'latex');
+  xlabel('Time (seconds)', 'Interpreter', 'latex');
+  legend('$\phi(t)$ Roll ', '$\theta(t)$ Pitch ', '$\psi(t)$ Yaw ', ...
+    'Interpreter', 'latex');
+
+  % Plot step response from z to omega
+  figure;
+  sgtitle(sprintf(...
+    '\\bfseries Step Response to Propeller (%s)', ...
+    ctrl.Name), 'Interpreter', 'latex');
+
+  hold on;
+  step(P_nom_clp(Iomega, Ir(3)) * to_rpm, T_final_vert);
+  plot([0, T_final_vert], [1, 1] * omega_min_rpm, 'r--');
+  plot([0, T_final_vert], [1, 1] * omega_max_rpm, 'r--');
+  grid on;
+  ylim([omega_min_rpm - 1, omega_max_rpm + 1]);
+  title('Vertical $z$ to Thruster $\omega$', 'Interpreter', 'latex');
+  ylabel('Angular Velocity (RPM)', 'Interpreter', 'latex');
+  xlabel('Time (seconds)', 'Interpreter', 'latex');
+  legend('$\omega(t)$', 'Interpreter', 'latex');
+
+  % Figure for position and velocity
+  figure;
+  sgtitle(sprintf(...
+    '\\bfseries Step Response of Position and Speed (%s)', ...
+    ctrl.Name), 'Interpreter', 'latex');
+
+  % Plot step response from horizontal reference to horizontal position
+  subplot(2, 2, 1); hold on;
+  plot(t_xy, out_step_x(:, IP(1)));
+  plot(t_xy, out_step_y(:, IP(2)));
+  % plot([0, T_final_horiz], [1, 1] * ref_value, 'r:');
+  % plot(t_xy, out_step_xydes, 'r--');
+  grid on;
+  title('Horizontal Position Error', 'Interpreter', 'latex');
+  ylabel('Error (meters)', 'Interpreter', 'latex');
+  xlabel('Time (seconds)', 'Interpreter', 'latex');
+  legend('$x(t)$', '$y(t)$', 'Interpreter', 'latex');
+
+  % Plot step response horizontal reference to horizontal speed
+  subplot(2, 2, 2); hold on;
+  plot(t_xy, out_step_x(:, IPdot(1)));
+  plot(t_xy, out_step_y(:, IPdot(2)));
+  grid on;
+  title('Horizontal Velocity', 'Interpreter', 'latex');
+  ylabel('Velocity (m / s)', 'Interpreter', 'latex');
+  xlabel('Time (seconds)', 'Interpreter', 'latex');
+  legend('$\dot{x}(t)$', '$\dot{y}(t)$', 'Interpreter', 'latex');
+
+  % Plot step response from vertical reference to vertical position
+  subplot(2, 2, 3); hold on;
+  plot(t_z, out_step_z(:, IP(3)));
+  % plot([0, T_final_vert], [1, 1] * ref_value, 'r:');
+  % plot(t_z, out_step_zdes, 'r--');
+  grid on;
+  title('Vertical Position Error', 'Interpreter', 'latex');
+  ylabel('Error (meters)', 'Interpreter', 'latex');
+  xlabel('Time (seconds)', 'Interpreter', 'latex');
+  legend('$z(t)$', 'Interpreter', 'latex');
+
+  % Plot step response vertical reference to vertical speed
+  subplot(2, 2, 4); hold on;
+  plot(t_z, out_step_z(:, IPdot(3)));
+  grid on;
+  title('Vertical Velocity', 'Interpreter', 'latex');
+  ylabel('Velocity (m / s)', 'Interpreter', 'latex');
+  xlabel('Time (seconds)', 'Interpreter', 'latex');
+  legend('$\dot{z}(t)$', 'Interpreter', 'latex');
+end
+
+end
+% vim:ts=2 sw=2 et: