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% 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:
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