This problem will address the importance of FRF phase in the

This problem will address the importance of FRF phase in the context of time delay. A communication satellite that links a control center to a micro-drone is shown at The right. The transmission delay time is denoted as Delta. This delay is present in sending a signal to the drone and also in receiving a signal from it. A lead compensator, designed to add PM to the system, resulted in the following forward loop transfer function: G(s) = G_c (s) G_p (s) = (0.1174s + 1/0.0155s + 1)(100 e^-s Delta/s(0.5s + 1)). The feedback is H(s) = e^-s Delta. The open loop Bode plot for Delta = 0 sec is shown at right. Determine then maximum value of Delta for which the closed loop will remain stable. Solution:

Solution

%clearing window, variables and figures
clear all;
close all;
clf;
clc;
j=0;
s=tf(\'s\'); dt=1.465*10^-2:.0000001:1; %reduce samplimg time starting from .01 and start dt from corresponding result next time

l=length(dt);
i=1;
while i<=l && j<=0
Gc=(0.1174*s+1)/(0.0155*s+1);
Gp=(100*exp(-s*dt(:,i)))/(s*(0.5*s+1));
sys=feedback(Gp*Gc,exp(-s*dt(:,i)));
[Pm,Gm,Wg,Wp]=margin(sys);
if Pm<=0 || Gm<=0
fprintf(\'\ The maximum value is:%d\ \',dt(:,i));
j=j+1;
end
i=i+1;
end

Result;

The maximum value is:1.465080e-02