Move entire graphic or make graphic goes to 0.5 instead of 0?

[elliotcupper291980 (Elliot Cupper)]

I have this function

t1 = 1;
t2 = 2;
Umax = 2;
u[t_] = (Limit[0.5 + ArcTan[(-(t) - (t1))/x]/Pi, (x -> 0)] + 
    Limit[0.5 + ArcTan[((t) - (t2))/x]/Pi, (x -> 0)])*(Umax)
    T = 2;
Plot[(u[t]), {t, -15, 15}]

I want to shift graph so it does not touch 0, or make the graph goes from 2 to 0.5 to 2 again
any idea?
Thanks in advance

[vaungureanu (Valeriu Ungureanu)]

t1 = 1;
t2 = 2;
Umax = 1.95;
u[t_] := 0.05 + Umax + Umax Limit[ArcTan[(-t - t1)/x]/[Pi], x → 0] +
Umax Limit[ArcTan[(t - t2)/x]/[Pi], x → 0]
Plot[{u[t], 0}, {t, -15, 15}]