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% Generate transfer functions for loop shaping stability (uncertainty)
% requirements from parameters specified in uav_params.m
%
% Copyright (C) 2024, Naoki Sean Pross, ETH Zürich
% This work is distributed under a permissive license, see LICENSE.txt
%
% Arguments:
% PARAMS Struct of design parameters and constants generated by uav_params
% PLOT When set to 'true' it plots the inverse magnitude of the
% performance transfer function
%
% Return value:
% UNCERT Struct of uncertainty transfer functions
function [uncert] = uav_performance(params, do_plots)
s = tf('s');
% relative errors
eps_T = params.aerodynamics.ThrustOmegaPropUncertainty;
eps_r = params.mechanical.GyroscopicInertiaZUncertainty;
eps_S = params.aerodynamics.FlapAreaUncertainty;
eps_l = params.aerodynamics.LiftCoefficientUncertainty;
eps_d = params.aerodynamics.DragCoefficientsUncertainties(1);
% eps_0 = params.aerodynamics.DragCoefficients(2);
eps_omega = max(.5 * eps_T, eps_r);
eps_alpha = max(eps_l + eps_S + 2 * eps_omega, eps_S + eps_d + eps_omega);
% TODO: set proper constraints
% band pass parameters for W_malpha
% wh = 20; % high freq
% wl = .1; % low freq
% W_malpha = eps_alpha * (s / wl) / ((s / wh + 1) * (s / wl + 1));
% W_momega = eps_omega * 10 / (s + 10);
% W_mState = .01 * 10 / (s + 10);
b = 1e3;
W_malpha = make_weight(b, 1 / eps_alpha, 1e-2);
W_momega = tf(0);
W_mState = 1 - 1 / (s / 50 + 1);
uncert = struct(...
'FlapAngle', W_malpha * eye(4), ...
'Thrust', W_momega, ...
'StateLinApprox', W_mState * eye(12));
if do_plots
% Bode plots of performance requirements
figure; hold on;
bodemag(W_malpha);
bodemag(W_momega);
bodemag(W_mState);
grid on;
legend('$W_{m,\alpha}$', '$W_{m,\omega}$', '$W_{m,\mathbf{P}}$', ...
'interpreter', 'latex')
title('\bfseries Stability Requirement (only for $\mu$-Synthesis)', ...
'interpreter', 'latex')
end
end
% Make a n-order performance weight function
%
% Arguments:
% OMEGA Cutting frequency (-3dB)
% A Magnitude at DC, i.e. |Wp(0)|
% M Magnitude at infinity, i.e. |Wp(inf)|
% ORD Order
function [Wp] = make_weight(omega, A, M, ord)
if nargin > 3
n = ord;
else
n = 1;
end
s = tf('s');
Wp = (s / (M^(1/n)) + omega)^n / (s + omega * A^(1/n))^n;
end
% vim: ts=2 sw=2 et:
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