% dfan_pitch.m - ducted fan computations for pitch axis control
% RMM, 24 Oct 94
%
% Updated 17 Nov 02 for MATLAB R11+

% System parameters
J = 0.0475;			% inertia around pitch axis
m = 1.5;			% pitch of fan
r = 0.25;			% distance to flaps
g = 10;				% gravitational constant
d = 0.05;			% damping factor (estimated)
l = 0.05;			% offset of center of mass

% Transfer function for pitch
dfsys = tf([r], [J d m*g*l]);

% Design a simple lead controller for the system
k = 15;  a = 25;  b = 300;
dfctr = tf(k*[1 a], [1/b 1]);

% Construct the loop transfer function and plot it
L = dfsys*dfctr;			% could also use series(dfsys,ctr)
bode(dfsys, dfctr, L);
title('Loop transfer function for Ducted Fan Pitch Controller');
print -dmeta 'pitch-loopbode.wmf'	% print windows meta file

nyquist(L);				% Nyquist plot to check stability
print -dmeta 'pitch-nyquest.wmf'

% Compute the sensitivity function and plot it
S = 1/(1 + L);
bode(S);
title('Sensitivity function for Ducted Fan Pitch Controller');
print -dmeta 'pitch-sensitivity.wmf'

% Plot the step response just to see how it looks
T = [0:100]/200;
[y, x] = step(feedback(L,1), T);
xlabel('Time (sec)');
ylabel('Pitch angle (rad)');
title('Step Response for Ducted Fan Pitch Controller');
print -dmeta 'pitch-stepresp.wmf';