i can not get the convolution of two unit step signal correct

%conv command

step = 0.01;

t1 = 0:step:3;

t2 = 3:step:5;

t = [t1 t2];

x1 = ones(size(t1));

x2 = ones(size(t2));

x = [x1,x2];

subplot(3,1,1)

plot(t,x,'m'),grid on

legend('x(t)')

subplot(3,1,2)

th = 0:step:4;

h1 = ones(size(th));

h2 = exp(-3).*th;

h = h2.*h1;

plot(th,h,'b'),grid on

legend('h(t)')

xlim([0 5])

subplot(3,1,3)

y = conv(x,h).*step;

yt = 0:step:6;

subplot(3,1,3)

plot(yt,y,'r'),grid on

legend('y(t)=x(t)*h(t)')