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| -rw-r--r-- | uav_requirements.m | 123 |
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diff --git a/uav_requirements.m b/uav_requirements.m new file mode 100644 index 0000000..9ccaeea --- /dev/null +++ b/uav_requirements.m @@ -0,0 +1,123 @@ +% Generate transfer functions for loop shaping performance 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: +% MODEL Struct performance transfer functions + + +function [perf] = uav_requirements(params, plot) + +% Laplace variable +s = tf('s'); + +alpha_max = params.actuators.ServoAbsMaxAngle; +alpha_max_omega = params.actuators.ServoNominalAngularVelocity; + +T_xy = params.performance.HorizontalSettleTime; +T_z = params.performance.VerticalSettleTime; + +omega_nxy = 5 / T_xy; +omega_nz = 10 / T_z; + +% W_Palpha = 1 / (s^2 + 2 * alpha_max_omega * s + alpha_max_omega^2); +% W_Palpha = (1 - W_Palpha / dcgain(W_Palpha)) * .8; +% W_Pomega = (1 - 1 / (T_z / 5 * s + 1)) * .1; + +W_Palpha = make_weight(alpha_max_omega, 15, 1.1, 3); +W_Pomega = make_weight(omega_nz, 50, 10); + +% zeta = 1; % Almost critically damped +% W_Pxy = 1 / (s^2 + 2 * zeta * omega_nxy * s + omega_nxy^2); +% W_Pxy = 1 * W_Pxy / dcgain(W_Pxy); +% W_Pz = 1 / (s^2 + 2 * zeta * omega_nz * s + omega_nz^2); +% W_Pz = 1 * W_Pz / dcgain(W_Pz); + +W_Pxy = make_weight(omega_nxy, 2, 5); +W_Pz = make_weight(omega_nz, 1, 10); + +% Set a speed limit +W_Pxydot = .2 * tf(1, 1); +W_Pzdot = .2 * tf(1, 1); + +W_Pphitheta = .01 * tf(1, [.1, 1]); +W_Ppsi = .01 * tf(1, 1); % don't care + +W_PTheta = tf(1, [.1, 1]) * eye(3); + +% Construct performance vector by combining xy and z +W_PP = blkdiag(W_Pxy * eye(2), W_Pz); +W_PPdot = blkdiag(W_Pxydot * eye(2), W_Pzdot); +W_PTheta = blkdiag(W_Pphitheta * eye(2), W_Ppsi); + +perf = struct(... + 'FlapAngle', W_Palpha * eye(4), ... + 'Thrust', W_Pomega, ... + 'Position', W_PP, ... + 'Velocity', W_PPdot, ... + 'Angles', W_PTheta); + +if plot + % Bode plots of performance requirements + figure; hold on; + + bodemag(W_Palpha); + bodemag(W_Pomega); + bodemag(W_Pxy); + bodemag(W_Pz); + bodemag(W_Pxydot); + bodemag(W_Pzdot); + bodemag(W_Pphitheta); + bodemag(W_Ppsi); + + grid on; + legend('$W_{P,\alpha}$', '$W_{P,\omega}$', ... + '$W_{P,xy}$', '$W_{P,z}$', ... + '$W_{P,\dot{x}\dot{y}}$', '$W_{P,\dot{z}}$', ... + '$W_{P,\phi\theta}$', '$W_{P,\psi}$', ... + 'interpreter', 'latex', 'fontSize', 8); + title('Performance Requirements'); + + % Step response of position requirements + figure; hold on; + step(W_Pxy); step(W_Pz); + step(W_Pxydot); step(W_Pzdot); + step(W_Palpha); + step(W_Pomega); + grid on; + legend('$W_{P,xy}$', '$W_{P,z}$', ... + '$W_{P,\dot{x}\dot{y}}$', '$W_{P,\dot{z}}$', ... + '$W_{P,\alpha}$', '$W_{P,\omega}$', ... + 'interpreter', 'latex', 'fontSize', 8); + title('Step responses of performance requirements'); +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: |