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% Copyright (c) 2024, Naoki Sean Pross, ETH Zürich
%
% Controller design for a ducted fan VTOL micro-UAV.
% ------------------------------------------------------------------------
% Clear environment and generate parameters
clear; clc; close all; s = tf('s');
params = uav_params();
do_plots = false;
% ------------------------------------------------------------------------
%% Define performance requirements
% Mechanically, flaps are constrained to a max of 20~25 degrees,
% and they have a maximal angular speed
alpha_max = params.actuators.ServoAbsMaxAngle;
alpha_dot_max = params.actuators.ServoNominalAngularVelocity;
W_Palpha = (s + 100 * alpha_dot_max) / (s + alpha_dot_max);
W_Palpha = alpha_max * W_Palpha / dcgain(W_Palpha); % adjust gain
% Mechanically we have a maximal angular velocity for the propeller in the
% thruster, also there are a lot of unmodelled dynamics in the thruster
omega_max = params.actuators.TurbineMaxSpeed;
W_Pomega = (s + 50 * omega_max) / (s + omega_max);
% We want a nice and smooth movements
v_xy_max = params.performance.MaxHorizontalSpeed;
v_z_max = params.performance.MaxVerticalSpeed;
W_Pxy = 1 / (s + 1 / v_xy_max);
W_Pz = 1 / (s + 1 / v_z_max);
if do_plots
% Bode plots of performance requirements
figure; hold on;
bodemag(1/W_Palpha);
bodemag(1/W_Pomega);
bodemag(1/W_Pxy);
bodemag(1/W_Pz);
grid on;
legend('$W_{P,\alpha}$', '$W_{P,\omega}$', ...
'$W_{P,xy}$', '$W_{P,z}$', ...
'interpreter', 'latex', 'fontSize', 8);
title('Performance requirements');
% Step response of position requirements
figure; hold on;
step(W_Pxy); step(W_Pz);
grid on;
legend('$W_{P,xy}$', '$W_{P,z}$', 'interpreter', 'latex', 'fontSize', 8);
title('Step responses of position performance requirements');
end
% Construct performance for position vector by combining xy and z
W_PP = blkdiag(W_Pxy * eye(2), W_Pz);
W_PPdot = tf(1,1) * eye(3);
W_PTheta = tf(1,1) * eye(3);
W_POmega = tf(1,1) * eye(3);
perf = struct(...
'FlapAngle', W_Palpha * eye(4), ...
'Thrust', W_Pomega, ...
'Position', W_PP, ...
'Velocity', W_PPdot, ...
'Angle', W_PTheta, ...
'AngularVelocity', W_POmega);
% ------------------------------------------------------------------------
%% Define stability requirements
W_malpha = tf(1,1);
W_momega = tf(1,1);
W_mState = tf(1,1);
if do_plots
figure; hold on;
bodemag(W_malpha);
bodemag(W_momega);
bodemag(W_mState);
grid on;
legend('$W_{m,\alpha}$', '$W_{m,\omega}$', ...
'$W_{m,\Theta}$', '$W_{m,\Omega}$', ...
'interpreter', 'latex', 'fontSize', 8);
title('Uncertainties')
end
uncert = struct(...
'FlapAngle', W_malpha * eye(4), ...
'Thrust', W_momega, ...
'StateLinApprox', W_mState * eye(12));
% ------------------------------------------------------------------------
% Create UAV model
model = uav_model(params, perf, uncert);
% ------------------------------------------------------------------------
%% Perform H-infinity design
idx = model.uncertain.index;
idx_ey = [idx.OutputError; idx.OutputNominal];
idx_wu = [idx.InputDisturbance; idx.InputReference; idx.InputNominal];
nmeas = max(size(idx.OutputNominal)); % size of y
nctrl = max(size(idx.InputNominal)); % size of u
% Get nominal system without uncertainty (lower LFT)
G = minreal(model.uncertain.StateSpace(idx_ey, idx_wu));
hinfopt = hinfsynOptions('Display', 'on', 'Method', 'RIC', 'RelTol', 0.01);
[K_inf, N_inf, gamma, info] = hinfsyn(G, nmeas, nctrl, hinfopt);
% ------------------------------------------------------------------------
% Verify performance satisfaction
% ------------------------------------------------------------------------
% Perform mu-Analysis & DK iteration
% vim: ts=2 sw=2 et:
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