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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_hinf(params, model, ctrl, nsamp, do_plots, do_noise)
% Load closed loop model and add controller
% more or less equivalent to doing usys = lft(Pnom, K)
h = load_system('uav_model_uncertain_clp');
hws = get_param('uav_model_uncertain_clp', 'modelworkspace');
hws.assignin('K', ctrl.K);
ulmod_clp = linmod('uav_model_uncertain_clp');
usys_clp = ss(ulmod_clp.a, ulmod_clp.b, ulmod_clp.c, ulmod_clp.d);
% Take dynamics without uncertainty
% Also nominal ouput to make plots
P_nom_clp = minreal(usys_clp(...
[model.uncertain.index.OutputError;
model.uncertain.index.OutputNominal;
model.uncertain.index.OutputPlots], ...
model.uncertain.index.InputExogenous), [], false);
% Indices for exogenous inputs
Iwwind = (1:3)';
Iwalpha = (4:7)';
Ir = (8:10)';
% Indices for outputs
Iealpha = (1:4)';
Ieomega = 5;
IeP = (6:8)';
IePdot = (9:11)';
IeTheta = (12:14)';
% size([Iealpha; Ieomega; IeP; IePdot; IeTheta])
% Indices for y outputs (for plots)
IP = (15:17)';
IPdot = (18:20)';
ITheta = (21:23)';
IOmega = (24:26)';
% Indices for p outputs (for plots)
Ialpha = (27:30)';
Iomega = 31;
Iualpha = (32:35)';
Iuomega = 36;
noise = zeros(7, nsamp); % no noise
if do_noise
% Noise in percentage
noise_alpha_amp = (.5 * (pi / 180)) / params.actuators.ServoAbsMaxAngle;
noise_wind_amp = .1;
noise = [noise_wind_amp * randn(3, nsamp);
noise_alpha_amp * randn(4, nsamp)];
end
% Create step inputs (normalized)
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);
% Return simulation
simout = struct(...
'TimeXY', t_xy, ...
'StepX', out_step_x, ...
'StepY', out_step_y, ...
'Simulink', ulmod_clp, ...
'StateSpace', P_nom_clp);
simout.index = struct(...
'ErrorFlapAngles', Iealpha, ...
'ErrorThrust', Ieomega , ...
'ErrorPos', IeP, ...
'ErrorVel', IePdot, ...
'ErrorAngles', IeTheta, ...
'Position', IP, ...
'Velocity', IPdot, ...
'Angles', ITheta, ...
'FlapAngles', Ialpha, ...
'Thruster', Iomega, ...
'InputFlapAngles', Iualpha, ...
'InputThruster', Iuomega);
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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