function PSET12
% Coded by NFR on 12.4.2018
% This code solves some of the problems for the week
%
close all
clc
% Problem 2 - Practice with a smith predictor
%
Kp = 1.2;
Tau1 = 10;
Tau2 = 7;
Kc = 1.7;
TauI = 13.7;
%
s = tf('s');
Gc = Kc*(1+1/(TauI*s));
%
% Part (a)
figure
theta = 0;
Gp = Kp*exp(-theta*s)/(Tau1*s+1)/(Tau2*s+1);
Gcl = (Gp*Gc/(1+Gp*Gc));
step(Gcl);
xlabel('Time (min)')
ylabel('Response');
hold on
theta = 5;
Gp = Kp*exp(-theta*s)/(Tau1*s+1)/(Tau2*s+1);
Gcl = (Gp*Gc/(1+Gp*Gc));
step(Gcl);
legend('No time delay','5 min time delay')
title('Problem 2 - Part (a)')
hold off
% Part (b) - Multiple ways to solve this one, I will just increase theta
% until it starts oscillating out of control.
figure
theta = 8; %<--- Looks like at 8min it will start going out of control
Gp = Kp*exp(-theta*s)/(Tau1*s+1)/(Tau2*s+1);
Gcl = (Gp*Gc/(1+Gp*Gc));
step(Gcl);
xlabel('Time (min)')
ylabel('Response');
title('Problem 2 - Part (b)')
%
% Smith predictor - let's do it with the case of the system being out of
% control at theta = 8 min.  Gc stays the same, but we break up Go
Gstar = Kp/(Tau1*s+1)/(Tau2*s+1);
Gcl = Gc*Gstar*exp(-theta*s)/(1+Gc*Gstar);
figure
step(Gcl);
xlabel('Time (min)')
ylabel('Response');
title('Problem 2 - Part (c)')
% Whoa cool!  it fixes the problem....
% 
% Problem 3
Gv = 5;
Gp1 = 2/(10*s+1);
Gm2 = 0.5/(0.5*s+1);
Gm1 = 1/(5*s+1);
Kc1 = 0.5;
TI1 = 15;
Kc2 = 1.0;
Gp2 = 1;
Gd1 = Gp1;
Gd2 = Gp2;
Gc1 = Kc1*(1+1/(TI1*s));
Gc2 = Kc2;
%
% Transfer function for disturbance D2
Gcl = Gp1*Gd2/(1+Gp2*Gv*Gc2*Gm2+Gp1*Gp2*Gv*Gc2*Gc1*Gm1);
figure
impulse(Gcl)
hold on
% Plot the second system, that has these changes
Gm2 = 2/(5*s+1);
Gm1 = 0.2/(5*s+1);
Kc1 = 2.5;
Kc2 = 0.25;
Gc1 = Kc1*(1+1/(TI1*s));
Gc2 = Kc2;
%
% Transfer function for disturbance D2
Gcl = Gp1*Gd2/(1+Gp2*Gv*Gc2*Gm2+Gp1*Gp2*Gv*Gc2*Gc1*Gm1);
impulse(Gcl)
xlabel('Time (min)')
ylabel('Response');
title('Problem 3')
legend('System A', 'System B')
% System A responds faster.  This is to be expected, as inspection of the
% transfer functions shows a faster inner loop (Gm2) for this system.
%




end