I have experienced the same problem on my E90 320 N46 early this year.It shudder/jerk at 1500-2000 rpm between 20-40kmh speed.Car feels struggling to build up speed at this rpm range.Above that, car can be driven as normal and the gear shift is rather smooth.Firstly suspect cause by low ATF level since got my ATF heat exchanger leaked. After change the ATF heat exchanger, the problem still persist. Went for a GB diagnose at Mscope Bt Caves, found out solenoid failure. Service the valve body (Mechatronic) and changed all 7 pieces of solenoids.After few programming sessions, the problem hidden for a while. Now it came back and I don't know whether it is related to GB issues or engine.Now i am trying to recall whether the problem started when I changed the ignition coils and spark plug. Could it be a wrong spark plug or as what Jarance said I should check the fuel pump.