How to make envelope of signal that connects its peaks?

I want to make exactly this picture above

I used this code

clc

vmax=1;
f=50;
w=2*pi*f;
R=0.0019462;
L=3*10^-3;
Z=sqrt((R)^2+(w*L)^2);
t=[0:0.01*pi:3*pi];

alpha=0; %The parameter controls the instant on the voltage wave when short circuit occurs.

vs=sqrt(2)*vmax*sind(w*t+alpha);
%oThe short circuit is assumed to take place at t = 0

theta=rad2deg(atan(w*L/R));

is=((sqrt(2)*vmax)/Z)*sind(w*t+alpha-theta); %symmetrical sc component
it=((sqrt(2)*vmax)/Z)*sind(theta-alpha)*exp((-R/L)*t);  %DC offset current2
time_constant=L/R

time_constant = 1.5415

vanish_time=5*time_constant

vanish_time = 7.7073

imm=2*max(is) %if the decay is to be neglected

imm = 3.0008

%{
This has the maximum possible value for = 0, i.e. short circuit occurring 
when the voltage wave is going through zero.
%}

i=is+it;


plot(t,is,t,it,t,i)
hold on 
grid on
yticks(-3:1:3)
xlim([0 vanish_time])
yline(imm)

hold off

Answer 1

[Image Analyst]

Did you try envelope (requires the Signal Processing Toolbox)?

[Salah Alfiky]

It worked! thanks. but how to do the same for the negative peaks?

[Askic V]

THis small code should show you the trick:

t = 0:0.1:10;
y = exp(-0.1*t).*sin(10*t);
[yup,ylo] = envelope(y);
plot(t,y)
hold on
plot(t,yup,t,ylo)

[Salah Alfiky]

thank you it worked bu I added 'peak' to the attributes of the envelope function to make it look smooth

clc

vmax=1;
f=50;
w=2*pi*f;
R=0.0019462;
L=3*10^-3;
Z=sqrt((R)^2+(w*L)^2);
t=[0:0.01*pi:3*pi];

alpha=0; %The parameter controls the instant on the voltage wave when short circuit occurs.

vs=sqrt(2)*vmax*sind(w*t+alpha);
%oThe short circuit is assumed to take place at t = 0

theta=rad2deg(atan(w*L/R));

is=((sqrt(2)*vmax)/Z)*sind(w*t+alpha-theta); %symmetrical sc component
it=((sqrt(2)*vmax)/Z)*sind(theta-alpha)*exp((-R/L)*t);  %DC offset current2
time_constant=L/R

time_constant = 1.5415

vanish_time=5*time_constant

vanish_time = 7.7073

imm=2*max(is) %if the decay is to be neglected

imm = 3.0008

%{
This has the maximum possible value for = 0, i.e. short circuit occurring 
when the voltage wave is going through zero.
%}

i=is+it;

[yup, ydown]=envelope(i,30,'peak');

plot(t,i)
hold on 
plot(t,is,"LineStyle","--")
plot(t,it,"LineStyle","--")
grid on
yticks(-3:1:3)
xlim([0 vanish_time])
yline(imm)
ylabel("Short Circuit Current (A) / Voltage (V)")
xlabel("time (s)")
plot(t,vs)
plot(t,yup,"LineStyle","--")
plot(t,ydown,"LineStyle","--")
legend("Total SC Current","is","it","Vs")

hold off