Help for a first order transfert function

If you know the parameters of your first order ( td,tm,km) then you can write

1. Delta U=1 and Delta PV=km : km gain of the process
2. ti=t1=td : td is the pure delay
3. t3=3*tm+td and t2=tm+td: with tm the process time constant.
4. vi=km/tm : the speed of your process.

In the case where td=0 or small, we normally set tg=tm or whatever you want (tg>6*tre). It depends on what control value you want at t=0