Michy mick001

## copulas_revised_1_7.R
par(mfrow = c(1, 3))
# 3D plain scatterplot of the density, plot of the density and contour plot
scatterplot3d(u[,1], u[,2], pdf_, color="red", main="Density", xlab ="u1", ylab="u2", zlab="dCopula", pch=".")
persp(mycopula, dCopula, main ="Density")
contour(mycopula, dCopula, xlim = c(0, 1), ylim=c(0, 1), main = "Contour plot")

par(mfrow = c(1, 3))
# 3D plain scatterplot of the CDF, plot of the CDF and contour plot
scatterplot3d(u[,1], u[,2], cdf, color="red", main="CDF", xlab = "u1", ylab="u2", zlab="pCopula",pch=".")
persp(mycopula, pCopula, main = "CDF")

## copulas_revised_1_8.R
frank <- frankCopula(dim = 2, param = 3)
clayton <- claytonCopula(dim = 2, param = 1.2)
gumbel <- gumbelCopula(dim = 2, param = 1.5)

par(mfrow = c(1, 3))

# Density plot
persp(frank, dCopula, main ="Frank copula density")
persp(clayton, dCopula, main ="Clayton copula density")
persp(gumbel, dCopula, main ="Gumbel copula density")

## mass_spring5.m
% Closed loop transfer function with proportional regulator
k = 50;
R = k;
L = R*G;
F = L/(1+L);
step(F)

% Root locus (k > 0)
rlocus(G)

## mass_spring4.m
% Step response
step(G)

% Impulse response
impulse(G)

## mass_spring3.m
% System response when u=sin(wt) and w=wc
w = 0.441;
H = G;
t = [0:0.01:500];
u = sin(w*t);
[y t x] = lsim(H,u,t);
plot(t,y,'red')

## mass_spring2.m
% Initialize Laplace domain variable
s = tf('s');

% Transfer function
G = C*inv(s*eye(2)-A)*B+D;

% Bode diagram
bode(G)

## mass_spring1.m
%Mass attached to the spring (Kg)
m = 10;

% Friction coefficient
rho = 0.8;

% Spring constant (N/m)
k = 2;

% State space representation

## matlabrlc.m
% Inductance (H)
l = 0.010;
% Capacitance (F)
c = 1*10^(-8);
% Resistance (Ohm)
r = 250;

% Generalized gain
m = 1

## highpass.m
% Capacitance
C = 10*10^(-6);

% Time constant
tau = R*C;

% Define the transfer function
sys = tf([1/R 0],[1 1/(R*C)]);

% Plot the frequency response

## copulas_example.R
#Load library mass and set seed
library(MASS)
set.seed(100)

# We are going to use 3 random variables
m <- 3

# Number of samples to be drawn
n <- 2000
	par(mfrow = c(1, 3))
	# 3D plain scatterplot of the density, plot of the density and contour plot
	scatterplot3d(u[,1], u[,2], pdf_, color="red", main="Density", xlab ="u1", ylab="u2", zlab="dCopula", pch=".")
	persp(mycopula, dCopula, main ="Density")
	contour(mycopula, dCopula, xlim = c(0, 1), ylim=c(0, 1), main = "Contour plot")

	par(mfrow = c(1, 3))
	# 3D plain scatterplot of the CDF, plot of the CDF and contour plot
	scatterplot3d(u[,1], u[,2], cdf, color="red", main="CDF", xlab = "u1", ylab="u2", zlab="pCopula",pch=".")
	persp(mycopula, pCopula, main = "CDF")
	frank <- frankCopula(dim = 2, param = 3)
	clayton <- claytonCopula(dim = 2, param = 1.2)
	gumbel <- gumbelCopula(dim = 2, param = 1.5)

	par(mfrow = c(1, 3))

	# Density plot
	persp(frank, dCopula, main ="Frank copula density")
	persp(clayton, dCopula, main ="Clayton copula density")
	persp(gumbel, dCopula, main ="Gumbel copula density")
	% Closed loop transfer function with proportional regulator
	k = 50;
	R = k;
	L = R*G;
	F = L/(1+L);
	step(F)

	% Root locus (k > 0)
	rlocus(G)
	% System response when u=sin(wt) and w=wc
	w = 0.441;
	H = G;
	t = [0:0.01:500];
	u = sin(w*t);
	[y t x] = lsim(H,u,t);
	plot(t,y,'red')
	% Initialize Laplace domain variable
	s = tf('s');

	% Transfer function
	G = Cinv(seye(2)-A)*B+D;

	% Bode diagram
	bode(G)
	%Mass attached to the spring (Kg)
	m = 10;

	% Friction coefficient
	rho = 0.8;

	% Spring constant (N/m)
	k = 2;

	% State space representation
	% Inductance (H)
	l = 0.010;
	% Capacitance (F)
	c = 1*10^(-8);
	% Resistance (Ohm)
	r = 250;

	% Generalized gain
	m = 1
	% Capacitance
	C = 10*10^(-6);

	% Time constant
	tau = R*C;

	% Define the transfer function
	sys = tf([1/R 0],[1 1/(R*C)]);

	% Plot the frequency response
	#Load library mass and set seed
	library(MASS)
	set.seed(100)

	# We are going to use 3 random variables
	m <- 3

	# Number of samples to be drawn
	n <- 2000