Untitled

%Q1
load('SysIdenData_StudentVersion.mat');
t = LogData.time;
y_act = LogData.signals(1).values(:,2);
y_actm = LogData.signals(1).values(:,1);
u_act = LogData.signals(2).values;
Ts = 0.75;

figure;
subplot(2,1,1);

plot(t,y_act,'b','DisplayName','Noise-Reduced Output');
hold on;
plot(t,y_actm,'r','DisplayName', 'Measured Output');
hold off;

xlim([0 700]);
ylim([1 4]);
title('Actual Output Signal');
xlabel('Time (sec)');
ylabel('Water Level (V)');
legend;
grid on;

subplot(2,1,2);
plot(t,u_act,'b','DisplayName','Actual Input');
xlim([0 700]);
ylim([1 3]);
title('Actual Input Signal');
xlabel('Time (sec)');
ylabel('Pump Voltage (V)');
legend;
grid on;
%% 

%offset (Q1)
i = 1;
while u_act(i) == u_act(1)
    i = i+1;
end
y_offset = mean(y_act(1:i-1));
y = y_act - y_offset;
u_offset = mean(u_act(1:i-1));
u = u_act - u_offset;

figure
subplot(2,1,1);
plot(t,y,'r','DisplayName','Actual Output');
title('Actual Offset-Free Output Signal');
xlim([0 700]);
ylim([-2 1]);
xlabel('Time (sec)');
ylabel('Water Level (V)');
legend;
grid on;

subplot(2,1,2);
plot(t,u,'b','DisplayName','Actual Input');
title('Actual Offset-Free Input Signal');
xlim([0 700]);
ylim([-0.5 0.5]);
xlabel('Time (sec)');
ylabel('Pump Voltage (V)');
legend;
grid on;
%% 
%Q2 a)
k = 3;
Halfsize = floor(length(t)/2);
phi(1,:) = [0 0 0 0]; %initial value
phi(2,:) = [y(1) 0 u(1) 0];
while k <= Halfsize
    phi(k,:) = [y(k-1) y(k-2) u(k-1) u(k-2)];
        k = k+1;
end

%Q2 b)
Y = y(1:Halfsize);
theta_hat = (transpose(phi)*phi)^-1*transpose(phi)*Y;
a1 = -theta_hat(1);
a2 = -theta_hat(2);
b1 = theta_hat(3);
b2 = theta_hat(4);

%Q2 c)
z = tf('z',Ts);
GZ = (b1*z+b2)/(z^2+a1*z+a2);
G = [0 1; -a2 -a1];
H = [0;1];
C = [b2 b1];
D = 0;
equ2 = ss(G,H,C,D,Ts);