clear all;
close all;
clc;

%% help <topics>
help eig

%% Commands concerning matrix manipulation
% Building matrix
A=[1 2; 3 4];
B=eye(2);
C=ones(2,2);
D=zeros(2);
F=diag(ones(3,1));
G=tril(ones(4,4),-1);

% Matrix operations
Add=A+B;
Multi=A*B;
Power=A^2;
Element_power=A.^2;
Tran=A';

% Matrix functions
determinant=det(A);
Rank=rank(A);
Inverse=inv(A);
Eigenvalue=eig(A);

%% Define transfer funcions in different form
num=[3 12];
den=[1 11 10];
% Find TF of system
sys=tf(num,den);

% Find TF of system in state space form
sys1=ss(sys);

% Find TF of system in Zero/pole/gain form
sys2=zpk(sys);
% Plot the poles and zeros in a complex plane
pzmap(sys);

%% Useful command to deal with polynomials

%Convert between partial fraction expansion and polynomial coefficients
[r p k]=residue(num,den);

% Inverse Laplace transform
syms s;
sys3=(3*s+12)/(s^2+11*s+10);
y_t=ilaplace(sys2);

zeros=roots(num);
poles=roots(den);

%% Simulate LTI system
% Impulse input
impulse(sys);
% Step input
step(sys);
% Other inputs
t=0:1:1000;
lsim(sys,t,t);  % ramp input

lsim(sys,sin(0.05*t),t); % sinusoidal input

lsim(sys,t.^2,t)     % input is t^2

%% Bode plot

bode(sys);
margin(sys);

% plot the root locus of system
rlocus(sys);

%% Create and plot signals
y=sin(0.05*t);
plot(t,y,'rd'); % plot the signal with red color and diamond marker

y1=t.^2;
plot(t,y1,'b.'); % plot the signal with blue color and dot marker

% plot the figure in 3 dimensional coordinate
t1 = 0:pi/50:10*pi;
plot3(sin(t1),cos(t1),t1)
grid on
axis square

% Use surface command to plot 3-d figure
x=-3:.2:3;
y=-3:.2:3;
[X,Y]=meshgrid(x,y);
Z=X.^2+Y.^2;
mesh(X,Y,Z);
% contour figure
contour(X,Y,Z);
colorbar;