path: root/uav_sim_step.m

% 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_musyn(params, model, ctrl, nsamp, T, 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)';

% 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 = .5 * 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 = linspace(0, T, nsamp);

% Simulate step responses
out_step_x_norm = lsim(P_nom_clp, in_step_x, t);
out_step_y_norm = lsim(P_nom_clp, in_step_y, t);
out_step_z_norm = lsim(P_nom_clp, in_step_z, t);

% Scale outputs
S_actuators = blkdiag(...
  eye(4) * params.actuators.ServoAbsMaxAngle, ...
  eye(1) * params.actuators.PropellerMaxAngularVelocity);

S_state = blkdiag(...
  eye(2) * params.normalization.HPosition, ...
  eye(1) * params.normalization.VPosition, ...
  eye(2) * params.normalization.HSpeed, ...
  eye(1) * params.normalization.VSpeed, ...
  eye(2) * params.normalization.PitchRollAngle, ...
  eye(1) * params.normalization.YawAngle, ...
  eye(3) * params.normalization.AngularRate);

S = blkdiag(S_actuators, S_state(1:9, 1:9), S_state, S_actuators, S_actuators);

out_step_x = out_step_x_norm * S';
out_step_y = out_step_y_norm * S';
out_step_z = out_step_z_norm * S';

% Return simulation
simout = struct(...
  'Time', t, ...
  'StepX', out_step_x_norm, ...
  'StepY', out_step_y_norm, ...
  'StepZ', out_step_z_norm, ...
  '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     = .5;
  alpha_max_deg = params.actuators.ServoAbsMaxAngle * to_deg;
  euler_lim_deg = 1.5;
  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, out_step_x(:, Ialpha(1)) * to_deg);
  plot(t, out_step_x(:, Ialpha(2)) * to_deg);
  plot(t, out_step_x(:, Ialpha(3)) * to_deg);
  plot(t, out_step_x(:, Ialpha(4)) * to_deg);
  plot([0, T], [1, 1] * alpha_max_deg, 'r--');
  plot([0, T], [-1, -1] * alpha_max_deg, 'r--');
  grid on;
  xlim([0, T]);
  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, out_step_y(:, Ialpha(1)) * to_deg);
  plot(t, out_step_y(:, Ialpha(2)) * to_deg);
  plot(t, out_step_y(:, Ialpha(3)) * to_deg);
  plot(t, out_step_y(:, Ialpha(4)) * to_deg);
  plot([0, T], [1, 1] * alpha_max_deg, 'r--');
  plot([0, T], [-1, -1] * alpha_max_deg, 'r--');
  grid on;
  xlim([0, T]);
  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, out_step_z(:, Ialpha(1)) * to_deg);
  plot(t, out_step_z(:, Ialpha(2)) * to_deg);
  plot(t, out_step_z(:, Ialpha(3)) * to_deg);
  plot(t, out_step_z(:, Ialpha(4)) * to_deg);
  plot([0, T], [1, 1] * alpha_max_deg, 'r--');
  plot([0, T], [-1, -1] * alpha_max_deg, 'r--');
  grid on;
  xlim([0, T]);
  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, out_step_x(:, ITheta(1)) * to_deg);
  plot(t, out_step_x(:, ITheta(2)) * to_deg);
  plot(t, out_step_x(:, ITheta(3)) * to_deg);
  grid on;
  xlim([0, T]);
  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, out_step_y(:, ITheta(1)) * to_deg);
  plot(t, out_step_y(:, ITheta(2)) * to_deg);
  plot(t, out_step_y(:, ITheta(3)) * to_deg);
  grid on;
  xlim([0, T]);
  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, out_step_z(:, ITheta(1)) * to_deg);
  plot(t, out_step_z(:, ITheta(2)) * to_deg);
  plot(t, out_step_z(:, ITheta(3)) * to_deg);
  grid on;
  xlim([0, T]);
  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);
  plot([0, T], [1, 1] * omega_min_rpm, 'r--');
  plot([0, T], [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, out_step_x(:, IP(1)));
  plot(t, out_step_y(:, IP(2)));
  % plot([0, T], [1, 1] * ref_value, 'r:');
  % plot(t, 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, out_step_x(:, IPdot(1)));
  plot(t, 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, out_step_z(:, IP(3)));
  % plot([0, T], [1, 1] * ref_value, 'r:');
  % plot(t, 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, 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
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